diff --git a/phpseclib/Common/Functions/Strings.php b/phpseclib/Common/Functions/Strings.php
index 76ff62ff..4edf3b97 100644
--- a/phpseclib/Common/Functions/Strings.php
+++ b/phpseclib/Common/Functions/Strings.php
@@ -16,6 +16,7 @@
 namespace phpseclib\Common\Functions;
 
 use phpseclib\Math\BigInteger;
+use phpseclib\Math\Common\FiniteField;
 
 /**
  * Common String Functions
@@ -106,9 +107,8 @@ abstract class Strings
      * @param string $format
      * @param $data
      * @return mixed
-     * @access public
      */
-    public static function unpackSSH2($format, $data)
+    public static function unpackSSH2($format, &$data)
     {
         $result = [];
         for ($i = 0; $i < strlen($format); $i++) {
@@ -205,8 +205,8 @@ abstract class Strings
                     $result.= pack('Na*', strlen($element), $element);
                     break;
                 case 'i':
-                    if (!$element instanceof BigInteger) {
-                        throw new \InvalidArgumentException('A phpseclib\Math\BigInteger object was expected.');
+                    if (!$element instanceof BigInteger && !$element instanceof FiniteField\Integer) {
+                        throw new \InvalidArgumentException('A phpseclib\Math\BigInteger or phpseclib\Math\Common\FiniteField\Integer object was expected.');
                     }
                     $element = $element->toBytes(true);
                     $result.= pack('Na*', strlen($element), $element);
@@ -224,4 +224,95 @@ abstract class Strings
         }
         return $result;
     }
+
+    /**
+     * Convert binary data into bits
+     *
+     * bin2hex / hex2bin refer to base-256 encoded data as binary, whilst
+     * decbin / bindec refer to base-2 encoded data as binary. For the purposes
+     * of this function, bin refers to base-256 encoded data whilst bits refers
+     * to base-2 encoded data
+     *
+     * @access public
+     * @param string $x
+     * @return string
+     */
+    public static function bits2bin($x)
+    {
+        /*
+        // the pure-PHP approach is faster than the GMP approach
+        if (function_exists('gmp_export')) {
+             return strlen($x) ? gmp_export(gmp_init($x, 2)) : gmp_init(0);
+        }
+        */
+
+        if (preg_match('#[^01]#', $x)) {
+            throw new \RuntimeException('The only valid characters are 0 and 1');
+        }
+
+        if (!defined('PHP_INT_MIN')) {
+            define('PHP_INT_MIN', ~PHP_INT_MAX);
+        }
+
+        $length = strlen($x);
+        if (!$length) {
+            return '';
+        }
+        $block_size = PHP_INT_SIZE << 3;
+        $pad = $block_size - ($length % $block_size);
+        if ($pad != $block_size) {
+            $x = str_repeat('0', $pad) . $x;
+        }
+
+        $parts = str_split($x, $block_size);
+        $str = '';
+        foreach ($parts as $part) {
+            $xor = $part[0] == '1' ? PHP_INT_MIN : 0;
+            $part[0] = '0';
+            $str.= pack(
+                PHP_INT_SIZE == 4 ? 'N' : 'J',
+                $xor ^ eval('return 0b' . $part . ';')
+            );
+        }
+        return ltrim($str, "\0");
+    }
+
+    /**
+     * Convert bits to binary data
+     *
+     * @access public
+     * @param string $x
+     * @return string
+     */
+    public static function bin2bits($x)
+    {
+        /*
+        // the pure-PHP approach is slower than the GMP approach BUT
+        // i want to the pure-PHP version to be easily unit tested as well
+        if (function_exists('gmp_import')) {
+            return gmp_strval(gmp_import($x), 2);
+        }
+        */
+
+        $len = strlen($x);
+        $mod = $len % PHP_INT_SIZE;
+        if ($mod) {
+            $x = str_pad($x, $len + PHP_INT_SIZE - $mod, "\0", STR_PAD_LEFT);
+        }
+
+        $bits = '';
+        if (PHP_INT_SIZE == 4) {
+            $digits = unpack('N*', $x);
+            foreach ($digits as $digit) {
+                $bits.= sprintf('%032b', $digit);
+            }
+        } else {
+            $digits = unpack('J*', $x);
+            foreach ($digits as $digit) {
+                $bits.= sprintf('%064b', $digit);
+            }
+        }
+
+        return ltrim($bits, '0');
+    }
 }
diff --git a/phpseclib/Crypt/Blowfish.php b/phpseclib/Crypt/Blowfish.php
index c3c9cb10..08c942ac 100644
--- a/phpseclib/Crypt/Blowfish.php
+++ b/phpseclib/Crypt/Blowfish.php
@@ -84,7 +84,7 @@ class Blowfish extends BlockCipher
      * @access private
      * @var    array
      */
-    private $sbox0 = [
+    private static $sbox0 = [
         0xd1310ba6, 0x98dfb5ac, 0x2ffd72db, 0xd01adfb7, 0xb8e1afed, 0x6a267e96, 0xba7c9045, 0xf12c7f99,
         0x24a19947, 0xb3916cf7, 0x0801f2e2, 0x858efc16, 0x636920d8, 0x71574e69, 0xa458fea3, 0xf4933d7e,
         0x0d95748f, 0x728eb658, 0x718bcd58, 0x82154aee, 0x7b54a41d, 0xc25a59b5, 0x9c30d539, 0x2af26013,
@@ -125,7 +125,7 @@ class Blowfish extends BlockCipher
      * @access private
      * @var    array
      */
-    private $sbox1 = [
+    private static $sbox1 = [
         0x4b7a70e9, 0xb5b32944, 0xdb75092e, 0xc4192623, 0xad6ea6b0, 0x49a7df7d, 0x9cee60b8, 0x8fedb266,
         0xecaa8c71, 0x699a17ff, 0x5664526c, 0xc2b19ee1, 0x193602a5, 0x75094c29, 0xa0591340, 0xe4183a3e,
         0x3f54989a, 0x5b429d65, 0x6b8fe4d6, 0x99f73fd6, 0xa1d29c07, 0xefe830f5, 0x4d2d38e6, 0xf0255dc1,
@@ -166,7 +166,7 @@ class Blowfish extends BlockCipher
      * @access private
      * @var    array
      */
-    private $sbox2 = [
+    private static $sbox2 = [
         0xe93d5a68, 0x948140f7, 0xf64c261c, 0x94692934, 0x411520f7, 0x7602d4f7, 0xbcf46b2e, 0xd4a20068,
         0xd4082471, 0x3320f46a, 0x43b7d4b7, 0x500061af, 0x1e39f62e, 0x97244546, 0x14214f74, 0xbf8b8840,
         0x4d95fc1d, 0x96b591af, 0x70f4ddd3, 0x66a02f45, 0xbfbc09ec, 0x03bd9785, 0x7fac6dd0, 0x31cb8504,
@@ -207,7 +207,7 @@ class Blowfish extends BlockCipher
      * @access private
      * @var    array
      */
-    private $sbox3 = [
+    private static $sbox3 = [
         0x3a39ce37, 0xd3faf5cf, 0xabc27737, 0x5ac52d1b, 0x5cb0679e, 0x4fa33742, 0xd3822740, 0x99bc9bbe,
         0xd5118e9d, 0xbf0f7315, 0xd62d1c7e, 0xc700c47b, 0xb78c1b6b, 0x21a19045, 0xb26eb1be, 0x6a366eb4,
         0x5748ab2f, 0xbc946e79, 0xc6a376d2, 0x6549c2c8, 0x530ff8ee, 0x468dde7d, 0xd5730a1d, 0x4cd04dc6,
@@ -248,7 +248,7 @@ class Blowfish extends BlockCipher
      * @var array
      * @access private
      */
-    private $parray = [
+    private static $parray = [
         0x243f6a88, 0x85a308d3, 0x13198a2e, 0x03707344, 0xa4093822, 0x299f31d0,
         0x082efa98, 0xec4e6c89, 0x452821e6, 0x38d01377, 0xbe5466cf, 0x34e90c6c,
         0xc0ac29b7, 0xc97c50dd, 0x3f84d5b5, 0xb5470917, 0x9216d5d9, 0x8979fb1b
@@ -364,10 +364,10 @@ class Blowfish extends BlockCipher
         $this->bctx = [
             'p'  => [],
             'sb' => [
-                $this->sbox0,
-                $this->sbox1,
-                $this->sbox2,
-                $this->sbox3
+                self::$sbox0,
+                self::$sbox1,
+                self::$sbox2,
+                self::$sbox3
             ]
         ];
 
@@ -382,7 +382,7 @@ class Blowfish extends BlockCipher
                     $j = 0;
                 }
             }
-            $this->bctx['p'][] = $this->parray[$i] ^ $data;
+            $this->bctx['p'][] = self::$parray[$i] ^ $data;
         }
 
         // encrypt the zero-string, replace P1 and P2 with the encrypted data,
@@ -411,14 +411,14 @@ class Blowfish extends BlockCipher
      */
     protected function encryptBlock($in)
     {
-        $p = $this->bctx["p"];
-        // extract($this->bctx["sb"], EXTR_PREFIX_ALL, "sb"); // slower
-        $sb_0 = $this->bctx["sb"][0];
-        $sb_1 = $this->bctx["sb"][1];
-        $sb_2 = $this->bctx["sb"][2];
-        $sb_3 = $this->bctx["sb"][3];
+        $p = $this->bctx['p'];
+        // extract($this->bctx['sb'], EXTR_PREFIX_ALL, 'sb'); // slower
+        $sb_0 = $this->bctx['sb'][0];
+        $sb_1 = $this->bctx['sb'][1];
+        $sb_2 = $this->bctx['sb'][2];
+        $sb_3 = $this->bctx['sb'][3];
 
-        $in = unpack("N*", $in);
+        $in = unpack('N*', $in);
         $l = $in[1];
         $r = $in[2];
 
@@ -433,7 +433,7 @@ class Blowfish extends BlockCipher
                   $sb_2[$r >>  8 & 0xff]) +
                   $sb_3[$r       & 0xff]);
         }
-        return pack("N*", $r ^ $p[17], $l ^ $p[16]);
+        return pack('N*', $r ^ $p[17], $l ^ $p[16]);
     }
 
     /**
@@ -445,13 +445,13 @@ class Blowfish extends BlockCipher
      */
     protected function decryptBlock($in)
     {
-        $p = $this->bctx["p"];
-        $sb_0 = $this->bctx["sb"][0];
-        $sb_1 = $this->bctx["sb"][1];
-        $sb_2 = $this->bctx["sb"][2];
-        $sb_3 = $this->bctx["sb"][3];
+        $p = $this->bctx['p'];
+        $sb_0 = $this->bctx['sb'][0];
+        $sb_1 = $this->bctx['sb'][1];
+        $sb_2 = $this->bctx['sb'][2];
+        $sb_3 = $this->bctx['sb'][3];
 
-        $in = unpack("N*", $in);
+        $in = unpack('N*', $in);
         $l = $in[1];
         $r = $in[2];
 
@@ -466,7 +466,7 @@ class Blowfish extends BlockCipher
                   $sb_2[$r >>  8 & 0xff]) +
                   $sb_3[$r       & 0xff]);
         }
-        return pack("N*", $r ^ $p[0], $l ^ $p[1]);
+        return pack('N*', $r ^ $p[0], $l ^ $p[1]);
     }
 
     /**
diff --git a/phpseclib/Crypt/Common/AsymmetricKey.php b/phpseclib/Crypt/Common/AsymmetricKey.php
index 2fd479d6..a95f7e80 100644
--- a/phpseclib/Crypt/Common/AsymmetricKey.php
+++ b/phpseclib/Crypt/Common/AsymmetricKey.php
@@ -18,6 +18,8 @@ namespace phpseclib\Crypt\Common;
 use phpseclib\Math\BigInteger;
 use phpseclib\Crypt\Hash;
 use ParagonIE\ConstantTime\Base64;
+use phpseclib\Exception\UnsupportedOperationException;
+use phpseclib\Exception\FileNotFoundException;
 
 /**
  * Base Class for all stream cipher classes
@@ -43,16 +45,6 @@ abstract class AsymmetricKey
      */
     protected static $one;
 
-    /**
-     * Engine
-     *
-     * This is only used for key generation. Valid values are RSA::ENGINE_INTERNAL and RSA::ENGINE_OPENSSL
-     *
-     * @var int
-     * @access private
-     */
-    protected static $engine = NULL;
-
     /**
      * OpenSSL configuration file name.
      *
@@ -132,6 +124,17 @@ abstract class AsymmetricKey
      */
     protected $publicKeyFormat = 'PKCS8';
 
+    /**
+     * Parameters Format
+     *
+     * No setParametersFormat method exists because PKCS1 is the only format that supports
+     * parameters in both DSA and ECDSA (RSA doesn't have an analog)
+     *
+     * @var string
+     * @access private
+     */
+    protected $parametersFormat = 'PKCS1';
+
     /**
      * Hash function
      *
@@ -148,21 +151,21 @@ abstract class AsymmetricKey
      */
     private $hmac;
 
-    /**#@+
-     * @access private
-     * @see self::__construct()
-     */
     /**
-     * To use the pure-PHP implementation
-     */
-    const ENGINE_INTERNAL = 1;
-    /**
-     * To use the OpenSSL library
+     * Hash manually set?
      *
-     * (if enabled; otherwise, the internal implementation will be used)
+     * @var bool
+     * @access private
      */
-    const ENGINE_OPENSSL = 2;
-    /**#@-*/
+    protected $hashManuallySet = false;
+
+    /**
+     * Available Engines
+     *
+     * @var boolean[]
+     * @access private
+     */
+    protected static $engines = [];
 
     /**
      * The constructor
@@ -180,57 +183,35 @@ abstract class AsymmetricKey
     /**
      * Tests engine validity
      *
-     * @return boolean
      * @access public
      * @param int $val
      */
-    public static function isValidEngine($val)
+    public static function useBestEngine()
     {
-        switch ($val) {
-            case self::ENGINE_OPENSSL:
-                return extension_loaded('openssl') && file_exists(self::$configFile);
-            case self::ENGINE_INTERNAL:
-                return true;
-        }
-
-        return false;
-    }
-
-    /**
-     * Sets the engine
-     *
-     * Only used in RSA::createKey. Valid values are RSA::ENGINE_OPENSSL and RSA::ENGINE_INTERNAL
-     *
-     * @access public
-     * @param int $val
-     */
-    public static function setPreferredEngine($val)
-    {
-        static::$engine = null;
-        $candidateEngines = [
-            $val,
-            self::ENGINE_OPENSSL
+        static::$engines = [
+            'PHP' => true,
+            'OpenSSL' => extension_loaded('openssl') && file_exists(self::$configFile),
+            // this test can be satisfied by either of the following:
+            // http://php.net/manual/en/book.sodium.php
+            // https://github.com/paragonie/sodium_compat
+            'libsodium' => function_exists('sodium_crypto_sign_keypair')
         ];
-        foreach ($candidateEngines as $engine) {
-            if (static::isValidEngine($engine)) {
-                static::$engine = $engine;
-                break;
-            }
-        }
-        if (!isset(static::$engine)) {
-            static::$engine = self::ENGINE_INTERNAL;
-        }
+
+        return static::$engines;
     }
 
     /**
-     * Returns the engine
+     * Flag to use internal engine only (useful for unit testing)
      *
      * @access public
-     * @return int
      */
-    public static function getEngine()
+    public static function useInternalEngine()
     {
-        return self::$engine;
+        static::$engines = [
+            'PHP' => true,
+            'OpenSSL' => false,
+            'libsodium' => false
+        ];
     }
 
     /**
@@ -243,7 +224,7 @@ abstract class AsymmetricKey
         if (!isset(self::$zero)) {
             self::$zero= new BigInteger(0);
             self::$one = new BigInteger(1);
-            self::$configFile = __DIR__ . '/../openssl.cnf';
+            self::$configFile = __DIR__ . '/../../openssl.cnf';
         }
 
         self::loadPlugins('Keys');
@@ -268,6 +249,10 @@ abstract class AsymmetricKey
                 }
                 $name = $file->getBasename('.php');
                 $type = 'phpseclib\Crypt\\' . static::ALGORITHM . '\\' . $format . '\\' . $name;
+                $reflect = new \ReflectionClass($type);
+                if ($reflect->isTrait()) {
+                    continue;
+                }
                 self::$plugins[static::ALGORITHM][$format][strtolower($name)] = $type;
                 self::$origPlugins[static::ALGORITHM][$format][] = $name;
             }
@@ -305,8 +290,14 @@ abstract class AsymmetricKey
      * @param string $type
      * @return array|bool
      */
-    public function load($key, $type)
+    protected function load($key, $type)
     {
+        if ($key instanceof self) {
+            $this->hmac = $key->hmac;
+
+            return;
+        }
+
         $components = false;
         if ($type === false) {
             foreach (self::$plugins[static::ALGORITHM]['Keys'] as $format) {
@@ -343,9 +334,9 @@ abstract class AsymmetricKey
      * @access private
      * @param string $key
      * @param string $type
-     * @return array|bool
+     * @return array
      */
-    public function setPublicKey($key, $type)
+    protected function setPublicKey($key, $type)
     {
         $components = false;
         if ($type === false) {
@@ -409,7 +400,7 @@ abstract class AsymmetricKey
         self::initialize_static_variables();
 
         if (class_exists($fullname)) {
-            $meta = new \ReflectionClass($path);
+            $meta = new \ReflectionClass($fullname);
             $shortname = $meta->getShortName();
             self::$plugins[static::ALGORITHM]['Keys'][strtolower($shortname)] = $fullname;
             self::$origPlugins[static::ALGORITHM]['Keys'][] = $shortname;
@@ -471,6 +462,15 @@ abstract class AsymmetricKey
                 return $key;
             }
             $key = $this->getPublicKey($this->publicKeyFormat);
+            if (is_string($key)) {
+                return $key;
+            }
+
+            if (!method_exists($this, 'getParameters')) {
+                return '';
+            }
+
+            $key = $this->getParameters($this->parametersFormat);
             return is_string($key) ? $key : '';
         } catch (\Exception $e) {
             return '';
@@ -499,6 +499,16 @@ abstract class AsymmetricKey
      */
     public function setPrivateKeyFormat($format)
     {
+        $type = self::validatePlugin('Keys', $format);
+        if ($type === false) {
+            throw new FileNotFoundException('Plugin not found');
+        }
+
+        $type = self::validatePlugin('Keys', $format, 'savePrivateKey');
+        if ($type === false) {
+            throw new UnsupportedOperationException('Plugin does not support private keys');
+        }
+
         $this->privateKeyFormat = $format;
     }
 
@@ -511,9 +521,47 @@ abstract class AsymmetricKey
      */
     public function setPublicKeyFormat($format)
     {
+        $type = self::validatePlugin('Keys', $format);
+        if ($type === false) {
+            throw new FileNotFoundException('Plugin not found');
+        }
+
+        $type = self::validatePlugin('Keys', $format, 'savePublicKey');
+        if ($type === false) {
+            throw new UnsupportedOperationException('Plugin does not support public keys');
+        }
+
         $this->publicKeyFormat = $format;
     }
 
+    /**
+     * Determines the key format
+     *
+     * Sets both the public key and private key formats to the specified format if those formats support
+     * the key type
+     *
+     * @see self::__toString()
+     * @access public
+     * @param string $format
+     */
+    public function setKeyFormat($format)
+    {
+        $type = self::validatePlugin('Keys', $format);
+        if ($type === false) {
+            throw new FileNotFoundException('Plugin not found');
+        }
+
+        try {
+            $this->setPrivateKeyFormat($format);
+        } catch (\Exception $e) {
+        }
+
+        try {
+            $this->setPublicKeyFormat($format);
+        } catch (\Exception $e) {
+        }
+    }
+
     /**
      * Returns the format of the loaded key.
      *
@@ -560,6 +608,8 @@ abstract class AsymmetricKey
     {
         $this->hash = new Hash($hash);
         $this->hmac = new Hash($hash);
+
+        $this->hashManuallySet = true;
     }
 
     /**
diff --git a/phpseclib/Crypt/Common/Keys/OpenSSH.php b/phpseclib/Crypt/Common/Keys/OpenSSH.php
index e0e18679..b66beab8 100644
--- a/phpseclib/Crypt/Common/Keys/OpenSSH.php
+++ b/phpseclib/Crypt/Common/Keys/OpenSSH.php
@@ -64,12 +64,12 @@ abstract class OpenSSH
      * @access public
      * @param string $key
      * @param string $type
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $type)
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $parts = explode(' ', $key, 3);
@@ -79,21 +79,20 @@ abstract class OpenSSH
             $comment = isset($parts[1]) ? $parts[1] : false;
         } else {
             if ($parts[0] != $type) {
-                return false;
+                throw new \UnexpectedValueException('Expected a ' . $type . ' key - got a ' . $parts[0] . ' key');
             }
             $key = Base64::decode($parts[1]);
             $comment = isset($parts[2]) ? $parts[2] : false;
         }
         if ($key === false) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
-        if (substr($key, 0, 11) != "\0\0\0\7$type") {
-            return false;
+        if (Strings::shift($key, strlen($type) + 4) != "\0\0\0" . chr(strlen($type)) . $type) {
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
-        Strings::shift($key, 11);
         if (strlen($key) <= 4) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         return $key;
diff --git a/phpseclib/Crypt/Common/Keys/PKCS1.php b/phpseclib/Crypt/Common/Keys/PKCS1.php
index 6ae8588d..297f1c85 100644
--- a/phpseclib/Crypt/Common/Keys/PKCS1.php
+++ b/phpseclib/Crypt/Common/Keys/PKCS1.php
@@ -22,6 +22,7 @@ use phpseclib\Crypt\AES;
 use phpseclib\Crypt\DES;
 use phpseclib\Crypt\TripleDES;
 use phpseclib\File\ASN1;
+use phpseclib\Exception\UnsupportedAlgorithmException;
 
 /**
  * PKCS1 Formatted Key Handler
@@ -93,7 +94,7 @@ abstract class PKCS1 extends PKCS
             case preg_match("#^DES-$modes$#", $algo, $matches):
                 return new DES(self::getEncryptionMode($matches[1]));
             default:
-                throw new \UnexpectedValueException('Unsupported encryption algorithmn');
+                throw new UnsupportedAlgorithmException($algo . ' is not a supported algorithm');
         }
     }
 
@@ -122,12 +123,12 @@ abstract class PKCS1 extends PKCS
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     protected static function load($key, $password)
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         /* Although PKCS#1 proposes a format that public and private keys can use, encrypting them is
@@ -163,7 +164,7 @@ abstract class PKCS1 extends PKCS
                 if ($decoded !== false) {
                     $key = $decoded;
                 } elseif (self::$format == self::MODE_PEM) {
-                    return false;
+                    throw new \UnexpectedValueException('Expected base64-encoded PEM format but was unable to decode base64 text');
                 }
             }
         }
diff --git a/phpseclib/Crypt/Common/Keys/PKCS8.php b/phpseclib/Crypt/Common/Keys/PKCS8.php
index 579b7633..c6b3eae4 100644
--- a/phpseclib/Crypt/Common/Keys/PKCS8.php
+++ b/phpseclib/Crypt/Common/Keys/PKCS8.php
@@ -138,6 +138,7 @@ abstract class PKCS8 extends PKCS
 
     /**
      * Returns a SymmetricKey object based on a PBES1 $algo
+     *
      * @return \phpseclib\Crypt\Common\SymmetricKey
      * @access public
      * @param string $algo
@@ -267,51 +268,54 @@ abstract class PKCS8 extends PKCS
     private static function initialize_static_variables()
     {
         if (!static::$childOIDsLoaded) {
-            ASN1::loadOIDs([static::OID_VALUE => static::OID_NAME]);
+            ASN1::loadOIDs(is_array(static::OID_NAME) ?
+                array_combine(static::OID_NAME, static::OID_VALUE) :
+                [static::OID_NAME => static::OID_VALUE]
+            );
             static::$childOIDsLoaded = true;
         }
         if (!self::$oidsLoaded) {
             // from https://tools.ietf.org/html/rfc2898
             ASN1::loadOIDs([
-                // PBES1 encryption schemes
-                '1.2.840.113549.1.5.1' => 'pbeWithMD2AndDES-CBC',
-                '1.2.840.113549.1.5.4' => 'pbeWithMD2AndRC2-CBC',
-                '1.2.840.113549.1.5.3' => 'pbeWithMD5AndDES-CBC',
-                '1.2.840.113549.1.5.6' => 'pbeWithMD5AndRC2-CBC',
-                '1.2.840.113549.1.5.10'=> 'pbeWithSHA1AndDES-CBC',
-                '1.2.840.113549.1.5.11'=> 'pbeWithSHA1AndRC2-CBC',
+               // PBES1 encryption schemes
+               'pbeWithMD2AndDES-CBC' => '1.2.840.113549.1.5.1',
+               'pbeWithMD2AndRC2-CBC' => '1.2.840.113549.1.5.4',
+               'pbeWithMD5AndDES-CBC' => '1.2.840.113549.1.5.3',
+               'pbeWithMD5AndRC2-CBC' => '1.2.840.113549.1.5.6',
+               'pbeWithSHA1AndDES-CBC'=> '1.2.840.113549.1.5.10',
+               'pbeWithSHA1AndRC2-CBC'=> '1.2.840.113549.1.5.11',
 
-                // from PKCS#12:
-                // https://tools.ietf.org/html/rfc7292
-                '1.2.840.113549.1.12.1.1' => 'pbeWithSHAAnd128BitRC4',
-                '1.2.840.113549.1.12.1.2' => 'pbeWithSHAAnd40BitRC4',
-                '1.2.840.113549.1.12.1.3' => 'pbeWithSHAAnd3-KeyTripleDES-CBC',
-                '1.2.840.113549.1.12.1.4' => 'pbeWithSHAAnd2-KeyTripleDES-CBC',
-                '1.2.840.113549.1.12.1.5' => 'pbeWithSHAAnd128BitRC2-CBC',
-                '1.2.840.113549.1.12.1.6' => 'pbeWithSHAAnd40BitRC2-CBC',
+               // from PKCS#12:
+               // https://tools.ietf.org/html/rfc7292
+               'pbeWithSHAAnd128BitRC4' => '1.2.840.113549.1.12.1.1',
+               'pbeWithSHAAnd40BitRC4' => '1.2.840.113549.1.12.1.2',
+               'pbeWithSHAAnd3-KeyTripleDES-CBC' => '1.2.840.113549.1.12.1.3',
+               'pbeWithSHAAnd2-KeyTripleDES-CBC' => '1.2.840.113549.1.12.1.4',
+               'pbeWithSHAAnd128BitRC2-CBC' => '1.2.840.113549.1.12.1.5',
+               'pbeWithSHAAnd40BitRC2-CBC' => '1.2.840.113549.1.12.1.6',
 
-                '1.2.840.113549.1.5.12' => 'id-PBKDF2',
-                '1.2.840.113549.1.5.13' => 'id-PBES2',
-                '1.2.840.113549.1.5.14' => 'id-PBMAC1',
+               'id-PBKDF2' => '1.2.840.113549.1.5.12',
+               'id-PBES2' => '1.2.840.113549.1.5.13',
+               'id-PBMAC1' => '1.2.840.113549.1.5.14',
 
-                // from PKCS#5 v2.1:
-                // http://www.rsa.com/rsalabs/pkcs/files/h11302-wp-pkcs5v2-1-password-based-cryptography-standard.pdf
-                '1.2.840.113549.2.7' => 'id-hmacWithSHA1',
-                '1.2.840.113549.2.8' => 'id-hmacWithSHA224',
-                '1.2.840.113549.2.9' => 'id-hmacWithSHA256',
-                '1.2.840.113549.2.10'=> 'id-hmacWithSHA384',
-                '1.2.840.113549.2.11'=> 'id-hmacWithSHA512',
-                '1.2.840.113549.2.12'=> 'id-hmacWithSHA512-224',
-                '1.2.840.113549.2.13'=> 'id-hmacWithSHA512-256',
+               // from PKCS#5 v2.1:
+               // http://www.rsa.com/rsalabs/pkcs/files/h11302-wp-pkcs5v2-1-password-based-cryptography-standard.pdf
+               'id-hmacWithSHA1' => '1.2.840.113549.2.7',
+               'id-hmacWithSHA224' => '1.2.840.113549.2.8',
+               'id-hmacWithSHA256' => '1.2.840.113549.2.9',
+               'id-hmacWithSHA384'=> '1.2.840.113549.2.10',
+               'id-hmacWithSHA512'=> '1.2.840.113549.2.11',
+               'id-hmacWithSHA512-224'=> '1.2.840.113549.2.12',
+               'id-hmacWithSHA512-256'=> '1.2.840.113549.2.13',
 
-                '1.3.14.3.2.7'       => 'desCBC',
-                '1.2.840.113549.3.7' => 'des-EDE3-CBC',
-                '1.2.840.113549.3.2' => 'rc2CBC',
-                '1.2.840.113549.3.9' => 'rc5-CBC-PAD',
+               'desCBC'       => '1.3.14.3.2.7',
+               'des-EDE3-CBC' => '1.2.840.113549.3.7',
+               'rc2CBC' => '1.2.840.113549.3.2',
+               'rc5-CBC-PAD' => '1.2.840.113549.3.9',
 
-                '2.16.840.1.101.3.4.1.2' => 'aes128-CBC-PAD',
-                '2.16.840.1.101.3.4.1.22'=> 'aes192-CBC-PAD',
-                '2.16.840.1.101.3.4.1.42'=> 'aes256-CBC-PAD'
+               'aes128-CBC-PAD' => '2.16.840.1.101.3.4.1.2',
+               'aes192-CBC-PAD'=> '2.16.840.1.101.3.4.1.22',
+               'aes256-CBC-PAD'=> '2.16.840.1.101.3.4.1.42'
             ]);
             self::$oidsLoaded = true;
         }
@@ -323,14 +327,14 @@ abstract class PKCS8 extends PKCS
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     protected static function load($key, $password = '')
     {
         self::initialize_static_variables();
 
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         if (self::$format != self::MODE_DER) {
@@ -338,13 +342,13 @@ abstract class PKCS8 extends PKCS
             if ($decoded !== false) {
                 $key = $decoded;
             } elseif (self::$format == self::MODE_PEM) {
-                return false;
+                throw new \UnexpectedValueException('Expected base64-encoded PEM format but was unable to decode base64 text');
             }
         }
 
         $decoded = ASN1::decodeBER($key);
         if (empty($decoded)) {
-            return false;
+            throw new \RuntimeException('Unable to decode BER');
         }
 
         $meta = [];
@@ -379,7 +383,7 @@ abstract class PKCS8 extends PKCS
                     $key = $cipher->decrypt($decrypted['encryptedData']);
                     $decoded = ASN1::decodeBER($key);
                     if (empty($decoded)) {
-                        return false;
+                        throw new \RuntimeException('Unable to decode BER 2');
                     }
 
                     break;
@@ -442,7 +446,7 @@ abstract class PKCS8 extends PKCS
                             $key = $cipher->decrypt($decrypted['encryptedData']);
                             $decoded = ASN1::decodeBER($key);
                             if (empty($decoded)) {
-                                return false;
+                                throw new \RuntimeException('Unable to decode BER 3');
                             }
                             break;
                         default:
@@ -458,11 +462,22 @@ abstract class PKCS8 extends PKCS
             }
         }
 
-        $private = ASN1::asn1map($decoded[0], Maps\PrivateKeyInfo::MAP);
+        $private = ASN1::asn1map($decoded[0], Maps\OneAsymmetricKey::MAP);
         if (is_array($private)) {
-            return $private['privateKeyAlgorithm']['algorithm'] == static::OID_NAME ?
-                $private + $meta :
-                false;
+            if (isset($private['privateKeyAlgorithm']['parameters']) && !$private['privateKeyAlgorithm']['parameters'] instanceof ASN1\Element && isset($decoded[0]['content'][1]['content'][1])) {
+                $temp = $decoded[0]['content'][1]['content'][1];
+                $private['privateKeyAlgorithm']['parameters'] = new ASN1\Element(substr($key, $temp['start'], $temp['length']));
+            }
+            if (is_array(static::OID_NAME)) {
+                if (!in_array($private['privateKeyAlgorithm']['algorithm'], static::OID_NAME)) {
+                    throw new UnsupportedAlgorithmException($private['privateKeyAlgorithm']['algorithm'] . ' is not a supported key type');
+                }
+            } else {
+                if ($private['privateKeyAlgorithm']['algorithm'] != static::OID_NAME) {
+                    throw new UnsupportedAlgorithmException('Only ' . static::OID_NAME . ' keys are supported; this is a ' . $private['privateKeyAlgorithm']['algorithm'] . ' key');
+                }
+            }
+            return $private + $meta;
         }
 
         // EncryptedPrivateKeyInfo and PublicKeyInfo have largely identical "signatures". the only difference
@@ -470,9 +485,23 @@ abstract class PKCS8 extends PKCS
         // string represents the number of bits in the last byte that are to be ignored but, currently,
         // bit strings wanting a non-zero amount of bits trimmed are not supported
         $public = ASN1::asn1map($decoded[0], Maps\PublicKeyInfo::MAP);
+
         if (is_array($public)) {
-            if ($public['publicKey'][0] != "\0" || $public['publicKeyAlgorithm']['algorithm'] != static::OID_NAME) {
-                return false;
+            if ($public['publicKey'][0] != "\0") {
+                throw new \UnexpectedValueException('The first byte of the public key should be null - not ' . Hex::encode($val));
+            }
+            if (is_array(static::OID_NAME)) {
+                if (!in_array($public['publicKeyAlgorithm']['algorithm'], static::OID_NAME)) {
+                    throw new UnsupportedAlgorithmException($private['publicKeyAlgorithm']['algorithm'] . ' is not a supported key type');
+                }
+            } else {
+                if ($public['publicKeyAlgorithm']['algorithm'] != static::OID_NAME) {
+                    throw new UnsupportedAlgorithmException('Only ' . static::OID_NAME . ' keys are supported; this is a ' . $private['publicKeyAlgorithm']['algorithm'] . ' key');
+                }
+            }
+            if (isset($public['publicKeyAlgorithm']['parameters']) && !$public['publicKeyAlgorithm']['parameters'] instanceof ASN1\Element && isset($decoded[0]['content'][0]['content'][1])) {
+                $temp = $decoded[0]['content'][0]['content'][1];
+                $public['publicKeyAlgorithm']['parameters'] = new ASN1\Element(substr($key, $temp['start'], $temp['length']));
             }
             $public['publicKey'] = substr($public['publicKey'], 1);
             return $public;
@@ -489,16 +518,18 @@ abstract class PKCS8 extends PKCS
      * @param string $attr
      * @param mixed $params
      * @param string $password
+     * @param string $oid optional
+     * @param string $publicKey optional
      * @return string
      */
-    protected static function wrapPrivateKey($key, $attr, $params, $password)
+    protected static function wrapPrivateKey($key, $attr, $params, $password, $oid = null, $publicKey = '')
     {
         self::initialize_static_variables();
 
         $key = [
             'version' => 'v1',
             'privateKeyAlgorithm' => [
-                'algorithm' => static::OID_NAME,
+                'algorithm' => is_string(static::OID_NAME) ? static::OID_NAME : $oid,
                 'parameters' => $params
              ],
             'privateKey' => $key
@@ -506,7 +537,11 @@ abstract class PKCS8 extends PKCS
         if (!empty($attr)) {
             $key['attributes'] = $attr;
         }
-        $key = ASN1::encodeDER($key, Maps\PrivateKeyInfo::MAP);
+        if (!empty($publicKey)) {
+            $key['version'] = 'v2';
+            $key['publicKey'] = $publicKey;
+        }
+        $key = ASN1::encodeDER($key, Maps\OneAsymmetricKey::MAP);
         if (!empty($password) && is_string($password)) {
             $salt = Random::string(8);
             $iterationCount = self::$defaultIterationCount;
@@ -590,13 +625,13 @@ abstract class PKCS8 extends PKCS
      * @param mixed $params
      * @return string
      */
-    protected static function wrapPublicKey($key, $params)
+    protected static function wrapPublicKey($key, $params, $oid = null)
     {
         self::initialize_static_variables();
 
         $key = [
             'publicKeyAlgorithm' => [
-                'algorithm' => static::OID_NAME,
+                'algorithm' => is_string(static::OID_NAME) ? static::OID_NAME : $oid,
                 'parameters' => $params
             ],
             'publicKey' => "\0" . $key
diff --git a/phpseclib/Crypt/Common/Keys/PuTTY.php b/phpseclib/Crypt/Common/Keys/PuTTY.php
index d2357c3b..ba223697 100644
--- a/phpseclib/Crypt/Common/Keys/PuTTY.php
+++ b/phpseclib/Crypt/Common/Keys/PuTTY.php
@@ -21,6 +21,7 @@ use phpseclib\Crypt\AES;
 use phpseclib\Crypt\Hash;
 use phpseclib\Crypt\Random;
 use phpseclib\Common\Functions\Strings;
+use phpseclib\Exception\UnsupportedAlgorithmException;
 
 /**
  * PuTTY Formatted Key Handler
@@ -75,26 +76,26 @@ abstract class PuTTY
      * @access public
      * @param string $key
      * @param string $password
-     * @return array|bool
+     * @return array
      */
     protected static function load($key, $password)
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
-        if (strpos($key, 'BEGIN SSH2 PUBLIC KEY')) {
+        if (strpos($key, 'BEGIN SSH2 PUBLIC KEY') !== false) {
             $data = preg_split('#[\r\n]+#', $key);
             $data = array_splice($data, 2, -1);
             $data = implode('', $data);
 
             $components = call_user_func([static::PUBLIC_HANDLER, 'load'], $data);
             if ($components === false) {
-                return false;
+                throw new \UnexpectedValueException('Unable to decode public key');
             }
 
             if (!preg_match('#Comment: "(.+)"#', $key, $matches)) {
-                return false;
+                throw new \UnexpectedValueException('Key is missing a comment');
             }
             $components['comment'] = str_replace(['\\\\', '\"'], ['\\', '"'], $matches[1]);
 
@@ -105,8 +106,12 @@ abstract class PuTTY
 
         $key = preg_split('#\r\n|\r|\n#', trim($key));
         $type = trim(preg_replace('#PuTTY-User-Key-File-2: (.+)#', '$1', $key[0]));
-        if ($type != static::TYPE) {
-            return false;
+        $components['type'] = $type;
+        if (!in_array($type, static::$types)) {
+            $error = count(static::$types) == 1 ?
+                'Only ' . static::$types[0] . ' keys are supported. ' :
+                '';
+            throw new UnsupportedAlgorithmException($error . 'This is an unsupported ' . $type . ' key');
         }
         $encryption = trim(preg_replace('#Encryption: (.+)#', '$1', $key[1]));
         $components['comment'] = trim(preg_replace('#Comment: (.+)#', '$1', $key[2]));
@@ -114,12 +119,12 @@ abstract class PuTTY
         $publicLength = trim(preg_replace('#Public-Lines: (\d+)#', '$1', $key[3]));
         $public = Base64::decode(implode('', array_map('trim', array_slice($key, 4, $publicLength))));
 
-        $source = Strings::packSSH2('ssss', static::TYPE, $encryption, $components['comment'], $public);
+        $source = Strings::packSSH2('ssss', $type, $encryption, $components['comment'], $public);
 
         extract(unpack('Nlength', Strings::shift($public, 4)));
-        /** @var integer $length */
-        if (Strings::shift($public, $length) != static::TYPE) {
-            return false;
+        $newtype = Strings::shift($public, $length);
+        if ($newtype != $type) {
+            throw new \RuntimeException('The binary type does not match the human readable type field');
         }
 
         $components['public'] = $public;
@@ -165,19 +170,20 @@ abstract class PuTTY
      * @access private
      * @param string $public
      * @param string $private
+     * @param string $type
      * @param string $password
      * @return string
      */
-    protected static function wrapPrivateKey($public, $private, $password)
+    protected static function wrapPrivateKey($public, $private, $type, $password)
     {
-        $key = "PuTTY-User-Key-File-2: " . static::TYPE . "\r\nEncryption: ";
+        $key = "PuTTY-User-Key-File-2: " . $type . "\r\nEncryption: ";
         $encryption = (!empty($password) || is_string($password)) ? 'aes256-cbc' : 'none';
         $key.= $encryption;
         $key.= "\r\nComment: " . self::$comment . "\r\n";
 
-        $public = Strings::packSSH2('s', static::TYPE) . $public;
+        $public = Strings::packSSH2('s', $type) . $public;
 
-        $source = Strings::packSSH2('ssss', static::TYPE, $encryption, self::$comment, $public);
+        $source = Strings::packSSH2('ssss', $type, $encryption, self::$comment, $public);
 
         $public = Base64::encode($public);
         $key.= "Public-Lines: " . ((strlen($public) + 63) >> 6) . "\r\n";
@@ -215,11 +221,12 @@ abstract class PuTTY
      *
      * @access private
      * @param string $key
+     * @param string $type
      * @return string
      */
-    protected static function wrapPublicKey($key)
+    protected static function wrapPublicKey($key, $type)
     {
-        $key = pack('Na*a*', strlen(static::TYPE), static::TYPE, $key);
+        $key = pack('Na*a*', strlen($type), $type, $key);
         $key = "---- BEGIN SSH2 PUBLIC KEY ----\r\n" .
                'Comment: "' . str_replace(['\\', '"'], ['\\\\', '\"'], self::$comment) . "\"\r\n" .
                chunk_split(Base64::encode($key), 64) .
diff --git a/phpseclib/Crypt/Common/SymmetricKey.php b/phpseclib/Crypt/Common/SymmetricKey.php
index 8f14d06b..6e630de3 100644
--- a/phpseclib/Crypt/Common/SymmetricKey.php
+++ b/phpseclib/Crypt/Common/SymmetricKey.php
@@ -2133,6 +2133,10 @@ abstract class SymmetricKey
             throw new \UnexpectedValueException('No IV has been defined');
         }
 
+        if ($this->key === false) {
+            throw new \UnexpectedValueException('No key has been defined');
+        }
+
         $this->encryptIV = $this->decryptIV = $this->iv;
     }
 
diff --git a/phpseclib/Crypt/DES.php b/phpseclib/Crypt/DES.php
index b7c45ee4..665dc2e0 100644
--- a/phpseclib/Crypt/DES.php
+++ b/phpseclib/Crypt/DES.php
@@ -161,7 +161,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $shuffle = [
+    protected static $shuffle = [
         "\x00\x00\x00\x00\x00\x00\x00\x00", "\x00\x00\x00\x00\x00\x00\x00\xFF",
         "\x00\x00\x00\x00\x00\x00\xFF\x00", "\x00\x00\x00\x00\x00\x00\xFF\xFF",
         "\x00\x00\x00\x00\x00\xFF\x00\x00", "\x00\x00\x00\x00\x00\xFF\x00\xFF",
@@ -300,7 +300,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $ipmap = [
+    protected static $ipmap = [
         0x00, 0x10, 0x01, 0x11, 0x20, 0x30, 0x21, 0x31,
         0x02, 0x12, 0x03, 0x13, 0x22, 0x32, 0x23, 0x33,
         0x40, 0x50, 0x41, 0x51, 0x60, 0x70, 0x61, 0x71,
@@ -342,7 +342,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $invipmap = [
+    protected static $invipmap = [
         0x00, 0x80, 0x40, 0xC0, 0x20, 0xA0, 0x60, 0xE0,
         0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,
         0x08, 0x88, 0x48, 0xC8, 0x28, 0xA8, 0x68, 0xE8,
@@ -386,7 +386,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox1 = [
+    protected static $sbox1 = [
         0x00808200, 0x00000000, 0x00008000, 0x00808202,
         0x00808002, 0x00008202, 0x00000002, 0x00008000,
         0x00000200, 0x00808200, 0x00808202, 0x00000200,
@@ -411,7 +411,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox2 = [
+    protected static $sbox2 = [
         0x40084010, 0x40004000, 0x00004000, 0x00084010,
         0x00080000, 0x00000010, 0x40080010, 0x40004010,
         0x40000010, 0x40084010, 0x40084000, 0x40000000,
@@ -436,7 +436,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox3 = [
+    protected static $sbox3 = [
         0x00000104, 0x04010100, 0x00000000, 0x04010004,
         0x04000100, 0x00000000, 0x00010104, 0x04000100,
         0x00010004, 0x04000004, 0x04000004, 0x00010000,
@@ -461,7 +461,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox4 = [
+    protected static $sbox4 = [
         0x80401000, 0x80001040, 0x80001040, 0x00000040,
         0x00401040, 0x80400040, 0x80400000, 0x80001000,
         0x00000000, 0x00401000, 0x00401000, 0x80401040,
@@ -486,7 +486,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox5 = [
+    protected static $sbox5 = [
         0x00000080, 0x01040080, 0x01040000, 0x21000080,
         0x00040000, 0x00000080, 0x20000000, 0x01040000,
         0x20040080, 0x00040000, 0x01000080, 0x20040080,
@@ -511,7 +511,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox6 = [
+    protected static $sbox6 = [
         0x10000008, 0x10200000, 0x00002000, 0x10202008,
         0x10200000, 0x00000008, 0x10202008, 0x00200000,
         0x10002000, 0x00202008, 0x00200000, 0x10000008,
@@ -536,7 +536,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox7 = [
+    protected static $sbox7 = [
         0x00100000, 0x02100001, 0x02000401, 0x00000000,
         0x00000400, 0x02000401, 0x00100401, 0x02100400,
         0x02100401, 0x00100000, 0x00000000, 0x02000001,
@@ -561,7 +561,7 @@ class DES extends BlockCipher
      * @var array
      * @access private
      */
-    protected $sbox8 = [
+    protected static $sbox8 = [
         0x08000820, 0x00000800, 0x00020000, 0x08020820,
         0x08000000, 0x08000820, 0x00000020, 0x08000000,
         0x00020020, 0x08020000, 0x08020820, 0x00020800,
@@ -687,18 +687,18 @@ class DES extends BlockCipher
     {
         static $sbox1, $sbox2, $sbox3, $sbox4, $sbox5, $sbox6, $sbox7, $sbox8, $shuffleip, $shuffleinvip;
         if (!$sbox1) {
-            $sbox1 = array_map("intval", $this->sbox1);
-            $sbox2 = array_map("intval", $this->sbox2);
-            $sbox3 = array_map("intval", $this->sbox3);
-            $sbox4 = array_map("intval", $this->sbox4);
-            $sbox5 = array_map("intval", $this->sbox5);
-            $sbox6 = array_map("intval", $this->sbox6);
-            $sbox7 = array_map("intval", $this->sbox7);
-            $sbox8 = array_map("intval", $this->sbox8);
+            $sbox1 = array_map('intval', self::$sbox1);
+            $sbox2 = array_map('intval', self::$sbox2);
+            $sbox3 = array_map('intval', self::$sbox3);
+            $sbox4 = array_map('intval', self::$sbox4);
+            $sbox5 = array_map('intval', self::$sbox5);
+            $sbox6 = array_map('intval', self::$sbox6);
+            $sbox7 = array_map('intval', self::$sbox7);
+            $sbox8 = array_map('intval', self::$sbox8);
             /* Merge $shuffle with $[inv]ipmap */
             for ($i = 0; $i < 256; ++$i) {
-                $shuffleip[]    =  $this->shuffle[$this->ipmap[$i]];
-                $shuffleinvip[] =  $this->shuffle[$this->invipmap[$i]];
+                $shuffleip[]    =  self::$shuffle[self::$ipmap[$i]];
+                $shuffleinvip[] =  self::$shuffle[self::$invipmap[$i]];
             }
         }
 
@@ -1229,14 +1229,14 @@ class DES extends BlockCipher
             // Perform the PC/1 transformation and compute C and D.
             $t = unpack('Nl/Nr', $key);
             list($l, $r) = [$t['l'], $t['r']];
-            $key = ($this->shuffle[$pc1map[ $r        & 0xFF]] & "\x80\x80\x80\x80\x80\x80\x80\x00") |
-                   ($this->shuffle[$pc1map[($r >>  8) & 0xFF]] & "\x40\x40\x40\x40\x40\x40\x40\x00") |
-                   ($this->shuffle[$pc1map[($r >> 16) & 0xFF]] & "\x20\x20\x20\x20\x20\x20\x20\x00") |
-                   ($this->shuffle[$pc1map[($r >> 24) & 0xFF]] & "\x10\x10\x10\x10\x10\x10\x10\x00") |
-                   ($this->shuffle[$pc1map[ $l        & 0xFF]] & "\x08\x08\x08\x08\x08\x08\x08\x00") |
-                   ($this->shuffle[$pc1map[($l >>  8) & 0xFF]] & "\x04\x04\x04\x04\x04\x04\x04\x00") |
-                   ($this->shuffle[$pc1map[($l >> 16) & 0xFF]] & "\x02\x02\x02\x02\x02\x02\x02\x00") |
-                   ($this->shuffle[$pc1map[($l >> 24) & 0xFF]] & "\x01\x01\x01\x01\x01\x01\x01\x00");
+            $key = (self::$shuffle[$pc1map[ $r        & 0xFF]] & "\x80\x80\x80\x80\x80\x80\x80\x00") |
+                   (self::$shuffle[$pc1map[($r >>  8) & 0xFF]] & "\x40\x40\x40\x40\x40\x40\x40\x00") |
+                   (self::$shuffle[$pc1map[($r >> 16) & 0xFF]] & "\x20\x20\x20\x20\x20\x20\x20\x00") |
+                   (self::$shuffle[$pc1map[($r >> 24) & 0xFF]] & "\x10\x10\x10\x10\x10\x10\x10\x00") |
+                   (self::$shuffle[$pc1map[ $l        & 0xFF]] & "\x08\x08\x08\x08\x08\x08\x08\x00") |
+                   (self::$shuffle[$pc1map[($l >>  8) & 0xFF]] & "\x04\x04\x04\x04\x04\x04\x04\x00") |
+                   (self::$shuffle[$pc1map[($l >> 16) & 0xFF]] & "\x02\x02\x02\x02\x02\x02\x02\x00") |
+                   (self::$shuffle[$pc1map[($l >> 24) & 0xFF]] & "\x01\x01\x01\x01\x01\x01\x01\x00");
             $key = unpack('Nc/Nd', $key);
             $c = ( $key['c'] >> 4) & 0x0FFFFFFF;
             $d = (($key['d'] >> 4) & 0x0FFFFFF0) | ($key['c'] & 0x0F);
@@ -1308,18 +1308,18 @@ class DES extends BlockCipher
 
         $init_crypt = 'static $sbox1, $sbox2, $sbox3, $sbox4, $sbox5, $sbox6, $sbox7, $sbox8, $shuffleip, $shuffleinvip;
             if (!$sbox1) {
-                $sbox1 = array_map("intval", $this->sbox1);
-                $sbox2 = array_map("intval", $this->sbox2);
-                $sbox3 = array_map("intval", $this->sbox3);
-                $sbox4 = array_map("intval", $this->sbox4);
-                $sbox5 = array_map("intval", $this->sbox5);
-                $sbox6 = array_map("intval", $this->sbox6);
-                $sbox7 = array_map("intval", $this->sbox7);
-                $sbox8 = array_map("intval", $this->sbox8);'
+                $sbox1 = array_map("intval", self::$sbox1);
+                $sbox2 = array_map("intval", self::$sbox2);
+                $sbox3 = array_map("intval", self::$sbox3);
+                $sbox4 = array_map("intval", self::$sbox4);
+                $sbox5 = array_map("intval", self::$sbox5);
+                $sbox6 = array_map("intval", self::$sbox6);
+                $sbox7 = array_map("intval", self::$sbox7);
+                $sbox8 = array_map("intval", self::$sbox8);'
                 /* Merge $shuffle with $[inv]ipmap */ . '
                 for ($i = 0; $i < 256; ++$i) {
-                    $shuffleip[]    =  $this->shuffle[$this->ipmap[$i]];
-                    $shuffleinvip[] =  $this->shuffle[$this->invipmap[$i]];
+                    $shuffleip[]    =  self::$shuffle[self::$ipmap[$i]];
+                    $shuffleinvip[] =  self::$shuffle[self::$invipmap[$i]];
                 }
             }
         ';
diff --git a/phpseclib/Crypt/DSA.php b/phpseclib/Crypt/DSA.php
index 7b8c0762..b8a85903 100644
--- a/phpseclib/Crypt/DSA.php
+++ b/phpseclib/Crypt/DSA.php
@@ -34,7 +34,10 @@ use ParagonIE\ConstantTime\Base64;
 use phpseclib\File\ASN1;
 use phpseclib\Math\BigInteger;
 use phpseclib\Crypt\Common\AsymmetricKey;
-use phpseclib\Common\Functions\Strings;
+use phpseclib\Math\PrimeField;
+use phpseclib\Crypt\ECDSA\Signature\ASN1 as ASN1Signature;
+use phpseclib\Exception\UnsupportedOperationException;
+use phpseclib\Exception\NoKeyLoadedException;
 
 /**
  * Pure-PHP FIPS 186-4 compliant implementation of DSA.
@@ -95,14 +98,6 @@ class DSA extends AsymmetricKey
      */
     private $y;
 
-    /**
-     * Parameters Format
-     *
-     * @var string
-     * @access private
-     */
-    private $parametersFormat = 'PKCS1';
-
     /**
      * Create DSA parameters
      *
@@ -111,10 +106,14 @@ class DSA extends AsymmetricKey
      * @param int $N
      * @return \phpseclib\Crypt\DSA|bool
      */
-    static function createParameters($L = 2048, $N = 224)
+    public static function createParameters($L = 2048, $N = 224)
     {
         self::initialize_static_variables();
 
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
         switch (true) {
             case $N == 160:
             /*
@@ -186,10 +185,14 @@ class DSA extends AsymmetricKey
      * @access public
      * @return array|DSA
      */
-    static function createKey(...$args)
+    public static function createKey(...$args)
     {
         self::initialize_static_variables();
 
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
         if (count($args) == 2 && is_int($args[0]) && is_int($args[1])) {
             $private = self::createParameters($args[0], $args[1]);
         } else if (count($args) == 1 && $args[0] instanceof DSA) {
@@ -220,6 +223,12 @@ class DSA extends AsymmetricKey
      */
     public function load($key, $type = false)
     {
+        self::initialize_static_variables();
+
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
         if ($key instanceof DSA) {
             $this->privateKeyFormat = $key->privateKeyFormat;
             $this->publicKeyFormat = $key->publicKeyFormat;
@@ -236,6 +245,13 @@ class DSA extends AsymmetricKey
 
         $components = parent::load($key, $type);
         if ($components === false) {
+            $this->format = null;
+            $this->p = null;
+            $this->q = null;
+            $this->g = null;
+            $this->x = null;
+            $this->y = null;
+
             return false;
         }
 
@@ -252,9 +268,7 @@ class DSA extends AsymmetricKey
             $this->g = $components['g'];
         }
 
-        if (isset($components['x'])) {
-            $this->x = $components['x'];
-        }
+        $this->x = isset($components['x']) ? $components['x'] : null;
 
         if (isset($components['y'])) {
             $this->y = $components['y'];
@@ -281,27 +295,6 @@ class DSA extends AsymmetricKey
             ['L' => 0, 'N' => 0];
     }
 
-    /**
-     * __toString() magic method
-     *
-     * @access public
-     * @return string
-     */
-    public function __toString()
-    {
-        $key = parent::__toString();
-        if (!empty($key)) {
-            return $key;
-        }
-
-        try {
-            $key = $this->getParameters($this->parametersFormat);
-            return is_string($key) ? $key : '';
-        } catch (\Exception $e) {
-            return '';
-        }
-    }
-
     /**
      * Returns the private key
      *
@@ -331,6 +324,28 @@ class DSA extends AsymmetricKey
         return $type::savePrivateKey($this->p, $this->q, $this->g, $this->y, $this->x, $this->password);
     }
 
+    /**
+     * Is the key a private key?
+     *
+     * @access public
+     * @return bool
+     */
+    public function isPrivateKey()
+    {
+        return isset($this->x);
+    }
+
+    /**
+     * Is the key a public key?
+     *
+     * @access public
+     * @return bool
+     */
+    public function isPublicKey()
+    {
+        return isset($this->p);
+    }
+
     /**
      * Returns the public key
      *
@@ -354,8 +369,14 @@ class DSA extends AsymmetricKey
      * @param string $type optional
      * @return mixed
      */
-    public function getPublicKey($type = 'PKCS8')
+    public function getPublicKey($type = null)
     {
+        $returnObj = false;
+        if ($type === null) {
+            $returnObj = true;
+            $type = 'PKCS8';
+        }
+
         $type = self::validatePlugin('Keys', $type, 'savePublicKey');
         if ($type === false) {
             return false;
@@ -368,7 +389,15 @@ class DSA extends AsymmetricKey
             $this->y = $this->g->powMod($this->x, $this->p);
         }
 
-        return $type::savePublicKey($this->p, $this->q, $this->g, $this->y);
+        $key = $type::savePublicKey($this->p, $this->q, $this->g, $this->y);
+        if (!$returnObj) {
+            return $key;
+        }
+
+        $public = clone $this;
+        $public->load($key, 'PKCS8');
+
+        return $public;
     }
 
     /**
@@ -397,6 +426,20 @@ class DSA extends AsymmetricKey
         return $type::saveParameters($this->p, $this->q, $this->g);
     }
 
+    /**
+     * Returns the current engine being used
+     *
+     * @see self::useInternalEngine()
+     * @see self::useBestEngine()
+     * @access public
+     * @return string
+     */
+    public function getEngine()
+    {
+        return self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods()) ?
+            'OpenSSL' : 'PHP';
+    }
+
     /**
      * Create a signature
      *
@@ -406,17 +449,43 @@ class DSA extends AsymmetricKey
      * @param string $format optional
      * @return mixed
      */
-    function sign($message, $format = 'Raw')
+    public function sign($message, $format = 'ASN1')
     {
+        $shortFormat = $format;
         $format = self::validatePlugin('Signature', $format);
         if ($format === false) {
             return false;
         }
 
-        if (empty($this->x) || empty($this->p)) {
-            return false;
+        if (empty($this->x)) {
+            if (empty($this->y)) {
+                throw new NoKeyLoadedException('No key has been loaded');
+            }
+            throw new UnsupportedOperationException('A public key cannot be used to sign data');
         }
 
+        if (empty($this->p)) {
+            throw new \RuntimeException('DSA Prime P is not set');
+        }
+
+        if (self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods())) {
+            $signature = '';
+            $result = openssl_sign($message, $signature, $this->getPrivateKey(), $this->hash->getHash());
+
+            if ($result) {
+                if ($shortFormat == 'ASN1') {
+                    return $signature;
+                }
+
+                extract(ASN1Signature::load($signature));
+
+                return $format::save($r, $s);
+            }
+        }
+
+        $h = $this->hash->hash($message);
+        $h = $this->bits2int($h);
+
         while (true) {
             $k = BigInteger::randomRange(self::$one, $this->q->subtract(self::$one));
             $r = $this->g->powMod($k, $this->p);
@@ -425,8 +494,6 @@ class DSA extends AsymmetricKey
                 continue;
             }
             $kinv = $k->modInverse($this->q);
-            $h = $this->hash->hash($message);
-            $h = $this->bits2int($h);
             $temp = $h->add($this->x->multiply($r));
             $temp = $kinv->multiply($temp);
             list(, $s) = $temp->divide($this->q);
@@ -464,7 +531,7 @@ class DSA extends AsymmetricKey
      * @param string $format optional
      * @return mixed
      */
-    function verify($message, $signature, $format = 'Raw')
+    public function verify($message, $signature, $format = 'ASN1')
     {
         $format = self::validatePlugin('Signature', $format);
         if ($format === false) {
@@ -477,8 +544,25 @@ class DSA extends AsymmetricKey
         }
         extract($params);
 
-        if (empty($this->y) || empty($this->p)) {
-            return false;
+        if (empty($this->y)) {
+            if (empty($this->x)) {
+                throw new NoKeyLoadedException('No key has been loaded');
+            }
+            throw new UnsupportedOperationException('A private key cannot be used to sign data');
+        }
+
+        if (empty($this->p)) {
+            throw new \RuntimeException('DSA Prime P is not set');
+        }
+
+        if (self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods())) {
+            $sig = $format != 'ASN1' ? ASN1Signature::save($r, $s) : $signature;
+
+            $result = openssl_verify($message, $sig, $this->getPublicKey(), $this->hash->getHash());
+
+            if ($result != -1) {
+                return (bool) $result;
+            }
         }
 
         $q_1 = $this->q->subtract(self::$one);
@@ -496,6 +580,6 @@ class DSA extends AsymmetricKey
         list(, $v) = $v1->multiply($v2)->divide($this->p);
         list(, $v) = $v->divide($this->q);
 
-        return Strings::equals($v->toBytes(), $r->toBytes());
+        return $v->equals($r);
     }
 }
\ No newline at end of file
diff --git a/phpseclib/Crypt/DSA/Keys/OpenSSH.php b/phpseclib/Crypt/DSA/Keys/OpenSSH.php
index 0b5d47b4..4b4163c8 100644
--- a/phpseclib/Crypt/DSA/Keys/OpenSSH.php
+++ b/phpseclib/Crypt/DSA/Keys/OpenSSH.php
@@ -37,18 +37,15 @@ abstract class OpenSSH extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         $key = parent::load($key, 'ssh-dss');
-        if ($key === false) {
-            return false;
-        }
 
         $result = Strings::unpackSSH2('iiii', $key);
         if ($result === false) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
         list($p, $q, $g, $y) = $result;
 
diff --git a/phpseclib/Crypt/DSA/Keys/PKCS1.php b/phpseclib/Crypt/DSA/Keys/PKCS1.php
index fefe3117..7d569409 100644
--- a/phpseclib/Crypt/DSA/Keys/PKCS1.php
+++ b/phpseclib/Crypt/DSA/Keys/PKCS1.php
@@ -15,6 +15,10 @@
  *
  * Analogous to ssh-keygen's pem format (as specified by -m)
  *
+ * Also, technically, PKCS1 decribes RSA but I am not aware of a formal specification for DSA.
+ * The DSA private key format seems to have been adapted from the RSA private key format so
+ * we're just re-using that as the name.
+ *
  * @category  Crypt
  * @package   DSA
  * @author    Jim Wigginton <terrafrost@php.net>
@@ -32,7 +36,7 @@ use phpseclib\File\ASN1\Maps;
 use ParagonIE\ConstantTime\Base64;
 
 /**
- * PKCS#1 Formatted RSA Key Handler
+ * PKCS#1 Formatted DSA Key Handler
  *
  * @package RSA
  * @author  Jim Wigginton <terrafrost@php.net>
@@ -46,22 +50,15 @@ abstract class PKCS1 extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
-        if (!is_string($key)) {
-            return false;
-        }
-
         $key = parent::load($key, $password);
-        if ($key === false) {
-            return false;
-        }
 
         $decoded = ASN1::decodeBER($key);
         if (empty($decoded)) {
-            return false;
+            throw new \RuntimeException('Unable to decode BER');
         }
 
         $key = ASN1::asn1map($decoded[0], Maps\DSAParams::MAP);
@@ -75,7 +72,11 @@ abstract class PKCS1 extends Progenitor
         }
 
         $key = ASN1::asn1map($decoded[0], Maps\DSAPublicKey::MAP);
-        return is_array($key) ? $key : false;
+        if (is_array($key)) {
+            return $key;
+        }
+
+        throw new \RuntimeException('Unable to perform ASN1 mapping');
     }
 
     /**
diff --git a/phpseclib/Crypt/DSA/Keys/PKCS8.php b/phpseclib/Crypt/DSA/Keys/PKCS8.php
index 4a94a861..f5447b46 100644
--- a/phpseclib/Crypt/DSA/Keys/PKCS8.php
+++ b/phpseclib/Crypt/DSA/Keys/PKCS8.php
@@ -69,47 +69,45 @@ abstract class PKCS8 extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $isPublic = strpos($key, 'PUBLIC') !== false;
 
         $key = parent::load($key, $password);
-        if ($key === false) {
-            return false;
-        }
 
         $type = isset($key['privateKey']) ? 'privateKey' : 'publicKey';
 
         switch (true) {
             case !$isPublic && $type == 'publicKey':
+                throw new \UnexpectedValueException('Human readable string claims non-public key but DER encoded string claims public key');
             case $isPublic && $type == 'privateKey':
-                return false;
+                throw new \UnexpectedValueException('Human readable string claims public key but DER encoded string claims private key');
         }
 
         $decoded = ASN1::decodeBER($key[$type . 'Algorithm']['parameters']->element);
         if (empty($decoded)) {
-            return false;
+            throw new \RuntimeException('Unable to decode BER of parameters');
         }
         $components = ASN1::asn1map($decoded[0], Maps\DSAParams::MAP);
         if (!is_array($components)) {
-            return false;
+            throw new \RuntimeException('Unable to perform ASN1 mapping on parameters');
         }
 
         $decoded = ASN1::decodeBER($key[$type]);
         if (empty($decoded)) {
-            return false;
+            throw new \RuntimeException('Unable to decode BER');
         }
 
         $var = $type == 'privateKey' ? 'x' : 'y';
         $components[$var] = ASN1::asn1map($decoded[0], Maps\DSAPublicKey::MAP);
         if (!$components[$var] instanceof BigInteger) {
-            return false;
+            throw new \RuntimeException('Unable to perform ASN1 mapping');
         }
 
         if (isset($key['meta'])) {
diff --git a/phpseclib/Crypt/DSA/Keys/PuTTY.php b/phpseclib/Crypt/DSA/Keys/PuTTY.php
index 3429a54f..2f85fcfe 100644
--- a/phpseclib/Crypt/DSA/Keys/PuTTY.php
+++ b/phpseclib/Crypt/DSA/Keys/PuTTY.php
@@ -44,10 +44,10 @@ abstract class PuTTY extends Progenitor
     /**
      * Algorithm Identifier
      *
-     * @var string
+     * @var array
      * @access private
      */
-    const TYPE = 'ssh-dss';
+    protected static $types = ['ssh-dss'];
 
     /**
      * Break a public or private key down into its constituent components
@@ -55,31 +55,29 @@ abstract class PuTTY extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         $components = parent::load($key, $password);
-        if ($components === false || !isset($components['private'])) {
+        if (!isset($components['private'])) {
             return $components;
         }
+        extract($components);
+        unset($components['public'], $components['private']);
 
-        $result = Strings::unpackSSH2('iiii', $components['public']);
+        $result = Strings::unpackSSH2('iiii', $public);
         if ($result === false) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
         list($p, $q, $g, $y) = $result;
 
-        $result = Strings::unpackSSH2('i', $components['private']);
+        $result = Strings::unpackSSH2('i', $private);
         if ($result === false) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
         list($x) = $result;
 
-        if (isset($components['comment'])) {
-            $comment = $components['comment'];
-        }
-
         return compact('p', 'q', 'g', 'y', 'x', 'comment');
     }
 
@@ -95,7 +93,7 @@ abstract class PuTTY extends Progenitor
      * @param string $password optional
      * @return string
      */
-    public static function savePrivateKey(BigInteger $p, BigInteger $q, BigInteger $g, BigInteger $y, BigInteger $x, $password = '')
+    public static function savePrivateKey(BigInteger $p, BigInteger $q, BigInteger $g, BigInteger $y, BigInteger $x, $password = false)
     {
         if ($q->getLength() != 160) {
             throw new \InvalidArgumentException('SSH only supports keys with an N (length of Group Order q) of 160');
@@ -104,7 +102,7 @@ abstract class PuTTY extends Progenitor
         $public = Strings::packSSH2('iiii', $p, $q, $g, $y);
         $private = Strings::packSSH2('i', $x);
 
-        return self::wrapPrivateKey($public, $private, $password);
+        return self::wrapPrivateKey($public, $private, 'ssh-dsa', $password);
     }
 
     /**
@@ -123,6 +121,6 @@ abstract class PuTTY extends Progenitor
             throw new \InvalidArgumentException('SSH only supports keys with an N (length of Group Order q) of 160');
         }
 
-        return self::wrapPublicKey(Strings::packSSH2('iiii', $p, $q, $g, $y));
+        return self::wrapPublicKey(Strings::packSSH2('iiii', $p, $q, $g, $y), 'ssh-dsa');
     }
 }
diff --git a/phpseclib/Crypt/DSA/Keys/Raw.php b/phpseclib/Crypt/DSA/Keys/Raw.php
index 7adbb363..568c1821 100644
--- a/phpseclib/Crypt/DSA/Keys/Raw.php
+++ b/phpseclib/Crypt/DSA/Keys/Raw.php
@@ -34,12 +34,12 @@ abstract class Raw
      * @access public
      * @param array $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_array($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a array - not a ' . gettype($key));
         }
 
         switch (true) {
@@ -50,7 +50,7 @@ abstract class Raw
             case !isset($key['x']) && !isset($key['y']):
             case isset($key['x']) && !$key['x'] instanceof BigInteger:
             case isset($key['y']) && !$key['y'] instanceof BigInteger:
-                return false;
+                throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         $options = ['p' => 1, 'q' => 1, 'g' => 1, 'x' => 1, 'y' => 1];
diff --git a/phpseclib/Crypt/DSA/Keys/XML.php b/phpseclib/Crypt/DSA/Keys/XML.php
index 0741ae5f..d6a8725b 100644
--- a/phpseclib/Crypt/DSA/Keys/XML.php
+++ b/phpseclib/Crypt/DSA/Keys/XML.php
@@ -39,12 +39,12 @@ abstract class XML
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $use_errors = libxml_use_internal_errors(true);
@@ -54,7 +54,7 @@ abstract class XML
             $key = '<xml>' . $key . '</xml>';
         }
         if (!$dom->loadXML($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key does not appear to contain XML');
         }
         $xpath = new \DOMXPath($dom);
         $keys = ['p', 'q', 'g', 'y', 'j', 'seed', 'pgencounter'];
@@ -95,7 +95,7 @@ abstract class XML
         libxml_use_internal_errors($use_errors);
 
         if (!isset($components['y'])) {
-            return false;
+            throw new \UnexpectedValueException('Key is missing y component');
         }
 
         switch (true) {
diff --git a/phpseclib/Crypt/DSA/Signature/PKCS.php b/phpseclib/Crypt/DSA/Signature/ASN1.php
similarity index 84%
rename from phpseclib/Crypt/DSA/Signature/PKCS.php
rename to phpseclib/Crypt/DSA/Signature/ASN1.php
index 6a3f4c31..009e5c18 100644
--- a/phpseclib/Crypt/DSA/Signature/PKCS.php
+++ b/phpseclib/Crypt/DSA/Signature/ASN1.php
@@ -1,7 +1,7 @@
 <?php
 
 /**
- * PKCS Signature Handler
+ * ASN1 Signature Handler
  *
  * PHP version 5
  *
@@ -19,17 +19,17 @@
 namespace phpseclib\Crypt\DSA\Signature;
 
 use phpseclib\Math\BigInteger;
-use phpseclib\File\ASN1;
+use phpseclib\File\ASN1 as Encoder;
 use phpseclib\File\ASN1\Maps;
 
 /**
- * PKCS Signature Handler
+ * ASN1 Signature Handler
  *
  * @package Common
  * @author  Jim Wigginton <terrafrost@php.net>
  * @access  public
  */
-abstract class PKCS
+abstract class ASN1
 {
     /**
      * Loads a signature
@@ -44,11 +44,11 @@ abstract class PKCS
             return false;
         }
 
-        $decoded = ASN1::decodeBER($sig);
+        $decoded = Encoder::decodeBER($sig);
         if (empty($decoded)) {
             return false;
         }
-        $components = ASN1::asn1map($decoded[0], Maps\DssSigValue::MAP);
+        $components = Encoder::asn1map($decoded[0], Maps\DssSigValue::MAP);
 
         return $components;
     }
diff --git a/phpseclib/Crypt/ECDSA.php b/phpseclib/Crypt/ECDSA.php
new file mode 100644
index 00000000..0224cc70
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA.php
@@ -0,0 +1,756 @@
+<?php
+
+/**
+ * Pure-PHP implementation of ECDSA.
+ *
+ * PHP version 5
+ *
+ * Here's an example of how to create signatures and verify signatures with this library:
+ * <code>
+ * <?php
+ * include 'vendor/autoload.php';
+ *
+ * extract(\phpseclib\Crypt\ECDSA::createKey());
+ *
+ * $plaintext = 'terrafrost';
+ *
+ * $signature = $privatekey->sign($plaintext, 'ASN1');
+ *
+ * echo $publickey->verify($plaintext, $signature) ? 'verified' : 'unverified';
+ * ?>
+ * </code>
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt;
+
+use phpseclib\Math\BigInteger;
+use phpseclib\Crypt\Common\AsymmetricKey;
+use phpseclib\Exception\UnsupportedCurveException;
+use phpseclib\Exception\UnsupportedOperationException;
+use phpseclib\Exception\NoKeyLoadedException;
+use phpseclib\File\ASN1;
+use phpseclib\File\ASN1\Maps\ECParameters;
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+use phpseclib\Crypt\ECDSA\Curves\Ed25519;
+use phpseclib\Crypt\ECDSA\Curves\Ed448;
+use phpseclib\Crypt\ECDSA\Keys\PKCS1;
+use phpseclib\Crypt\ECDSA\Keys\PKCS8;
+use phpseclib\Crypt\ECDSA\Signature\ASN1 as ASN1Signature;
+
+/**
+ * Pure-PHP implementation of ECDSA.
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class ECDSA extends AsymmetricKey
+{
+    /**
+     * Algorithm Name
+     *
+     * @var string
+     * @access private
+     */
+    const ALGORITHM = 'ECDSA';
+
+    /**
+     * Private Key dA
+     *
+     * sign() converts this to a BigInteger so one might wonder why this is a FiniteFieldInteger instead of
+     * a BigInteger. That's because a FiniteFieldInteger, when converted to a byte string, is null padded by
+     * a certain amount whereas a BigInteger isn't.
+     *
+     * @var object
+     */
+    private $dA;
+
+    /**
+     * Public Key QA
+     *
+     * @var object[]
+     */
+    private $QA;
+
+    /**
+     * Curve
+     *
+     * @var \phpseclib\Crypt\ECDSA\BaseCurves\Base
+     */
+    private $curve;
+
+    /**
+     * Curve Name
+     *
+     * @var string
+     */
+    private $curveName;
+
+    /**
+     * Curve Order
+     *
+     * Used for deterministic ECDSA
+     *
+     * @var \phpseclib\Math\BigInteger
+     */
+    protected $q;
+
+    /**
+     * Alias for the private key
+     *
+     * Used for deterministic ECDSA. AsymmetricKey expects $x. I don't like x because
+     * with x you have x * the base point yielding an (x, y)-coordinate that is the
+     * public key. But the x is different depending on which side of the equal sign
+     * you're on. It's less ambiguous if you do dA * base point = (x, y)-coordinate.
+     *
+     * @var \phpseclib\Math\BigInteger
+     */
+    protected $x;
+
+    /**
+     * Alias for the private key
+     *
+     * Used for deterministic ECDSA. AsymmetricKey expects $x. I don't like x because
+     * with x you have x * the base point yielding an (x, y)-coordinate that is the
+     * public key. But the x is different depending on which side of the equal sign
+     * you're on. It's less ambiguous if you do dA * base point = (x, y)-coordinate.
+     *
+     * @var \phpseclib\Math\BigInteger
+     */
+    private $context;
+
+    /**
+     * Create public / private key pair.
+     *
+     * @access public
+     * @param string $curve
+     * @return \phpseclib\Crypt\ECDSA[]
+     */
+    public static function createKey($curve)
+    {
+        self::initialize_static_variables();
+
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
+        if (self::$engines['libsodium'] && $curve == 'Ed25519' && function_exists('sodium_crypto_sign_keypair')) {
+            $kp = sodium_crypto_sign_keypair();
+
+            $privatekey = new static();
+            $privatekey->load(sodium_crypto_sign_secretkey($kp));
+
+            $publickey = new static();
+            $publickey->load(sodium_crypto_sign_publickey($kp));
+
+            $publickey->curveName = $privatekey->curveName = $curve;
+
+            return compact('privatekey', 'publickey');
+        }
+
+        $privatekey = new static();
+
+        $curveName = $curve;
+        $curve = '\phpseclib\Crypt\ECDSA\Curves\\' . $curve;
+        if (!class_exists($curve)) {
+            throw new UnsupportedCurveException('Named Curve of ' . $curve . ' is not supported');
+        }
+        $curve = new $curve();
+        $privatekey->dA = $dA = $curve->createRandomMultiplier();
+        $privatekey->QA = $curve->multiplyPoint($curve->getBasePoint(), $dA);
+        $privatekey->curve = $curve;
+
+        $publickey = clone $privatekey;
+        unset($publickey->dA);
+        unset($publickey->x);
+
+        $publickey->curveName = $privatekey->curveName = $curveName;
+
+        return compact('privatekey', 'publickey');
+    }
+
+    /**
+     * Loads a public or private key
+     *
+     * Returns true on success and false on failure (ie. an incorrect password was provided or the key was malformed)
+     *
+     * @access public
+     * @param string $key
+     * @param int $type optional
+     */
+    public function load($key, $type = false)
+    {
+        self::initialize_static_variables();
+
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
+        if ($key instanceof ECDSA) {
+            $this->privateKeyFormat = $key->privateKeyFormat;
+            $this->publicKeyFormat = $key->publicKeyFormat;
+            $this->format = $key->format;
+            $this->dA = isset($key->dA) ? $key->dA : null;
+            $this->QA = $key->QA;
+            $this->curve = $key->curve;
+            $this->parametersFormat = $key->parametersFormat;
+            $this->hash = $key->hash;
+
+            parent::load($key, false);
+
+            return true;
+        }
+
+        $components = parent::load($key, $type);
+        if ($components === false) {
+            $this->clearKey();
+            return false;
+        }
+
+        if ($components['curve'] instanceof Ed25519 && $this->hashManuallySet && $this->hash->getHash() != 'sha512') {
+            $this->clearKey();
+            throw new \RuntimeException('Ed25519 only supports sha512 as a hash');
+        }
+        if ($components['curve'] instanceof Ed448 && $this->hashManuallySet && $this->hash->getHash() != 'shake256-912') {
+            $this->clearKey();
+            throw new \RuntimeException('Ed448 only supports shake256 with a length of 114 bytes');
+        }
+
+        $this->curve = $components['curve'];
+        $this->QA = $components['QA'];
+        $this->dA = isset($components['dA']) ? $components['dA'] : null;
+
+        return true;
+    }
+
+    /**
+     * Removes a key
+     *
+     * @access private
+     */
+    private function clearKey()
+    {
+        $this->format = null;
+        $this->dA = null;
+        $this->QA = null;
+        $this->curve = null;
+    }
+
+    /**
+     * Returns the curve
+     *
+     * Returns a string if it's a named curve, an array if not
+     *
+     * @access public
+     * @return string|array
+     */
+    public function getCurve()
+    {
+        if ($this->curveName) {
+            return $this->curveName;
+        }
+
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            $this->curveName = $this->curve instanceof Ed25519 ? 'Ed25519' : 'Ed448';
+            return $this->curveName;
+        }
+
+        $namedCurves = PKCS1::isUsingNamedCurves();
+        PKCS1::useNamedCurve();
+
+        $params = $this->getParameters();
+        $decoded = ASN1::extractBER($params);
+        $decoded = ASN1::decodeBER($decoded);
+        $decoded = ASN1::asn1map($decoded[0], ECParameters::MAP);
+        if (isset($decoded['namedCurve'])) {
+            $this->curveName = $decoded['namedCurve'];
+
+            if (!$namedCurves) {
+                PKCS1::useSpecifiedCurve();
+            }
+
+            return $decoded['namedCurve'];
+        }
+
+        if (!$namedCurves) {
+            PKCS1::useSpecifiedCurve();
+        }
+
+        return $decoded;
+    }
+
+    /**
+     * Returns the key size
+     *
+     * Quoting https://tools.ietf.org/html/rfc5656#section-2,
+     *
+     * "The size of a set of elliptic curve domain parameters on a prime
+     *  curve is defined as the number of bits in the binary representation
+     *  of the field order, commonly denoted by p.  Size on a
+     *  characteristic-2 curve is defined as the number of bits in the binary
+     *  representation of the field, commonly denoted by m.  A set of
+     *  elliptic curve domain parameters defines a group of order n generated
+     *  by a base point P"
+     *
+     * @access public
+     * @return int
+     */
+    public function getLength()
+    {
+        if (!isset($this->QA)) {
+            return 0;
+        }
+
+        return $this->curve->getLength();
+    }
+
+    /**
+     * Is the key a private key?
+     *
+     * @access public
+     * @return bool
+     */
+    public function isPrivateKey()
+    {
+        return isset($this->dA);
+    }
+
+    /**
+     * Is the key a public key?
+     *
+     * @access public
+     * @return bool
+     */
+    public function isPublicKey()
+    {
+        return isset($this->QA);
+    }
+
+    /**
+     * Returns the private key
+     *
+     * @see self::getPublicKey()
+     * @access public
+     * @param string $type optional
+     * @return mixed
+     */
+    public function getPrivateKey($type = 'PKCS8')
+    {
+        $type = self::validatePlugin('Keys', $type, 'savePrivateKey');
+        if ($type === false) {
+            return false;
+        }
+
+        if (!isset($this->dA)) {
+            return false;
+        }
+
+        return $type::savePrivateKey($this->dA, $this->curve, $this->QA, $this->password);
+    }
+
+    /**
+     * Returns the public key
+     *
+     * @see self::getPrivateKey()
+     * @access public
+     * @param string $type optional
+     * @return mixed
+     */
+    public function getPublicKey($type = null)
+    {
+        $returnObj = false;
+        if ($type === null) {
+            $returnObj = true;
+            $type = 'PKCS8';
+        }
+        $type = self::validatePlugin('Keys', $type, 'savePublicKey');
+        if ($type === false) {
+            return false;
+        }
+
+        if (!isset($this->QA)) {
+            return false;
+        }
+
+        $key = $type::savePublicKey($this->curve, $this->QA);
+        if ($returnObj) {
+            $public = clone $this;
+            $public->load($key, 'PKCS8');
+
+            return $public;
+        }
+        return $key;
+    }
+
+    /**
+     * Returns the parameters
+     *
+     * A public / private key is only returned if the currently loaded "key" contains an x or y
+     * value.
+     *
+     * @see self::getPublicKey()
+     * @see self::getPrivateKey()
+     * @access public
+     * @param string $type optional
+     * @return mixed
+     */
+    public function getParameters($type = 'PKCS1')
+    {
+        $type = self::validatePlugin('Keys', $type, 'saveParameters');
+        if ($type === false) {
+            return false;
+        }
+
+        if (!isset($this->curve) || $this->curve instanceof TwistedEdwardsCurve) {
+            return false;
+        }
+
+        return $type::saveParameters($this->curve);
+    }
+
+    /**
+     * Returns the current engine being used
+     *
+     * @see self::useInternalEngine()
+     * @see self::useBestEngine()
+     * @access public
+     * @return string
+     */
+    public function getEngine()
+    {
+        if (!isset($this->curve)) {
+            throw new \RuntimeException('getEngine should not be called until after a key has been loaded');
+        }
+
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            return $this->curve instanceof Ed25519 && self::$engines['libsodium'] && !isset($this->context) ?
+                'libsodium' : 'PHP';
+        }
+
+        return self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods()) ?
+            'OpenSSL' : 'PHP';
+    }
+
+    /**
+     * Sets the context
+     *
+     * Used by Ed25519 / Ed448.
+     *
+     * @see self::sign()
+     * @see self::verify()
+     * @access public
+     * @param string $context optional
+     */
+    public function setContext($context = null)
+    {
+        if (!isset($context)) {
+            $this->context = null;
+            return;
+        }
+        if (!is_string($context)) {
+            throw new \RuntimeException('setContext expects a string');
+        }
+        if (strlen($context) > 255) {
+            throw new \RuntimeException('The context is supposed to be, at most, 255 bytes long');
+        }
+        $this->context = $context;
+    }
+
+    /**
+     * Determines which hashing function should be used
+     *
+     * @access public
+     * @param string $hash
+     */
+    public function setHash($hash)
+    {
+        if ($this->curve instanceof Ed25519 && $this->hash != 'sha512') {
+            throw new \RuntimeException('Ed25519 only supports sha512 as a hash');
+        }
+        if ($this->curve instanceof Ed448 && $this->hash != 'shake256-912') {
+            throw new \RuntimeException('Ed448 only supports shake256 with a length of 114 bytes');
+        }
+
+        parent::setHash($hash);
+    }
+
+    /**
+     * Create a signature
+     *
+     * @see self::verify()
+     * @access public
+     * @param string $message
+     * @param string $format optional
+     * @return mixed
+     */
+    public function sign($message, $format = 'ASN1')
+    {
+        if (!isset($this->dA)) {
+            if (!isset($this->QA)) {
+                throw new NoKeyLoadedException('No key has been loaded');
+            }
+            throw new UnsupportedOperationException('A public key cannot be used to sign data');
+        }
+
+        $dA = $this->dA->toBigInteger();
+
+        $order = $this->curve->getOrder();
+
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            if ($this->curve instanceof Ed25519 && self::$engines['libsodium'] && !isset($this->context)) {
+                return sodium_crypto_sign_detached($message, $this->getPrivateKey('libsodium'));
+            }
+
+            // contexts (Ed25519ctx) are supported but prehashing (Ed25519ph) is not.
+            // quoting https://tools.ietf.org/html/rfc8032#section-8.5 ,
+            // "The Ed25519ph and Ed448ph variants ... SHOULD NOT be used"
+            $A = $this->curve->encodePoint($this->QA);
+            $curve = $this->curve;
+            $hash = new Hash($curve::HASH);
+
+            $secret = substr($hash->hash($this->dA->secret), $curve::SIZE);
+
+            if ($curve instanceof Ed25519) {
+                $dom = !isset($this->context) ? '' :
+                    'SigEd25519 no Ed25519 collisions' . "\0" . chr(strlen($this->context)) . $this->context;
+            } else {
+                $context = isset($this->context) ? $this->context : '';
+                $dom = 'SigEd448' . "\0" . chr(strlen($context)) . $context;
+            }
+            // SHA-512(dom2(F, C) || prefix || PH(M))
+            $r = $hash->hash($dom . $secret . $message);
+            $r = strrev($r);
+            $r = new BigInteger($r, 256);
+            list(, $r) = $r->divide($order);
+            $R = $curve->multiplyPoint($curve->getBasePoint(), $curve->convertInteger($r));
+            $R = $curve->encodePoint($R);
+            $k = $hash->hash($dom . $R . $A . $message);
+            $k = strrev($k);
+            $k = new BigInteger($k, 256);
+            list(, $k) = $k->divide($order);
+            $S = $k->multiply($dA)->add($r);
+            list(, $S) = $S->divide($order);
+            $S = str_pad(strrev($S->toBytes()), $curve::SIZE, "\0");
+            return $R . $S;
+        }
+
+        $shortFormat = $format;
+        $format = self::validatePlugin('Signature', $format);
+        if ($format === false) {
+            return false;
+        }
+
+        if (self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods())) {
+            $namedCurves = PKCS8::isUsingNamedCurves();
+
+            // use specified curves to avoid issues with OpenSSL possibly not supporting a given named curve;
+            // doing this may mean some curve-specific optimizations can't be used but idk if OpenSSL even
+            // has curve-specific optimizations
+            PKCS8::useSpecifiedCurve();
+
+            $signature = '';
+            // altho PHP's OpenSSL bindings only supported ECDSA key creation in PHP 7.1 they've long
+            // supported signing / verification
+            $result = openssl_sign($message, $signature, $this->getPrivateKey(), $this->hash->getHash());
+
+            if ($namedCurves) {
+                PKCS8::useNamedCurve();
+            }
+
+            if ($result) {
+                if ($shortFormat == 'ASN1') {
+                    return $signature;
+                }
+
+                extract(ASN1Signature::load($signature));
+
+                return $shortFormat == 'SSH2' ? $format::save($r, $s, $this->getCurve()) : $format::save($r, $s);
+            }
+        }
+
+        $e = $this->hash->hash($message);
+        $e = new BigInteger($e, 256);
+
+        $Ln = $this->hash->getLength() - $order->getLength();
+        $z = $Ln > 0 ? $e->bitwise_rightShift($Ln) : $e;
+
+        while (true) {
+            $k = BigInteger::randomRange(self::$one, $order->subtract(self::$one));
+            list($x, $y) = $this->curve->multiplyPoint($this->curve->getBasePoint(), $this->curve->convertInteger($k));
+            $x = $x->toBigInteger();
+            list(, $r) = $x->divide($order);
+            if ($r->equals(self::$zero)) {
+                continue;
+            }
+            $kinv = $k->modInverse($order);
+            $temp = $z->add($dA->multiply($r));
+            $temp = $kinv->multiply($temp);
+            list(, $s) = $temp->divide($order);
+            if (!$s->equals(self::$zero)) {
+                break;
+            }
+        }
+
+        // the following is an RFC6979 compliant implementation of deterministic ECDSA
+        // it's unused because it's mainly intended for use when a good CSPRNG isn't
+        // available. if phpseclib's CSPRNG isn't good then even key generation is
+        // suspect
+        /*
+        // if this were actually being used it'd probably be better if this lived in load() and createKey()
+        $this->q = $this->curve->getOrder();
+        $dA = $this->dA->toBigInteger();
+        $this->x = $dA;
+
+        $h1 = $this->hash->hash($message);
+        $k = $this->computek($h1);
+        list($x, $y) = $this->curve->multiplyPoint($this->curve->getBasePoint(), $this->curve->convertInteger($k));
+        $x = $x->toBigInteger();
+        list(, $r) = $x->divide($this->q);
+        $kinv = $k->modInverse($this->q);
+        $h1 = $this->bits2int($h1);
+        $temp = $h1->add($dA->multiply($r));
+        $temp = $kinv->multiply($temp);
+        list(, $s) = $temp->divide($this->q);
+        */
+
+        return $shortFormat == 'SSH2' ? $format::save($r, $s, $this->getCurve()) : $format::save($r, $s);
+    }
+
+    /**
+     * Verify a signature
+     *
+     * @see self::verify()
+     * @access public
+     * @param string $message
+     * @param string $format optional
+     * @return mixed
+     */
+    public function verify($message, $signature, $format = 'ASN1')
+    {
+        if (!isset($this->QA)) {
+            if (!isset($this->dA)) {
+                throw new NoKeyLoadedException('No key has been loaded');
+            }
+            throw new UnsupportedOperationException('A private key cannot be used to verify data');
+        }
+
+        $order = $this->curve->getOrder();
+
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            if ($this->curve instanceof Ed25519 && self::$engines['libsodium'] && !isset($this->context)) {
+                return sodium_crypto_sign_verify_detached($signature, $message, $this->getPublicKey('libsodium'));
+            }
+
+            $curve = $this->curve;
+            if (strlen($signature) != 2 * $curve::SIZE) {
+                return false;
+            }
+
+            $R = substr($signature, 0, $curve::SIZE);
+            $S = substr($signature, $curve::SIZE);
+
+            try {
+                $R = PKCS1::extractPoint($R, $curve);
+                $R = $this->curve->convertToInternal($R);
+            } catch (\Exception $e) {
+                return false;
+            }
+
+            $S = strrev($S);
+            $S = new BigInteger($S, 256);
+
+            if ($S->compare($order) >= 0) {
+                return false;
+            }
+
+            $A = $curve->encodePoint($this->QA);
+
+            if ($curve instanceof Ed25519) {
+                $dom2 = !isset($this->context) ? '' :
+                    'SigEd25519 no Ed25519 collisions' . "\0" . chr(strlen($this->context)) . $this->context;
+            } else {
+                $context = isset($this->context) ? $this->context : '';
+                $dom2 = 'SigEd448' . "\0" . chr(strlen($context)) . $context;
+            }
+
+            $hash = new Hash($curve::HASH);
+            $k = $hash->hash($dom2 . substr($signature, 0, $curve::SIZE) . $A . $message);
+            $k = strrev($k);
+            $k = new BigInteger($k, 256);
+            list(, $k) = $k->divide($order);
+
+            $qa = $curve->convertToInternal($this->QA);
+
+            $lhs = $curve->multiplyPoint($curve->getBasePoint(), $curve->convertInteger($S));
+            $rhs = $curve->multiplyPoint($qa, $curve->convertInteger($k));
+            $rhs = $curve->addPoint($rhs, $R);
+            $rhs = $curve->convertToAffine($rhs);
+
+            return $lhs[0]->equals($rhs[0]) && $lhs[1]->equals($rhs[1]);
+        }
+
+        $format = self::validatePlugin('Signature', $format);
+        if ($format === false) {
+            return false;
+        }
+
+        $params = $format::load($signature);
+        if ($params === false || count($params) != 2) {
+            return false;
+        }
+        extract($params);
+
+        if (self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods())) {
+            $namedCurves = PKCS8::isUsingNamedCurves();
+
+            PKCS8::useSpecifiedCurve();
+
+            $sig = $format != 'ASN1' ? ASN1Signature::save($r, $s) : $signature;
+
+            $result = openssl_verify($message, $sig, $this->getPublicKey(), $this->hash->getHash());
+
+            if ($namedCurves) {
+                PKCS8::useNamedCurve();
+            }
+
+            if ($result != -1) {
+                return (bool) $result;
+            }
+        }
+
+        $n_1 = $order->subtract(self::$one);
+        if (!$r->between(self::$one, $n_1) || !$s->between(self::$one, $n_1)) {
+            return false;
+        }
+
+        $e = $this->hash->hash($message);
+        $e = new BigInteger($e, 256);
+
+        $Ln = $this->hash->getLength() - $order->getLength();
+        $z = $Ln > 0 ? $e->bitwise_rightShift($Ln) : $e;
+
+        $w = $s->modInverse($order);
+        list(, $u1) = $z->multiply($w)->divide($order);
+        list(, $u2) = $r->multiply($w)->divide($order);
+
+        $u1 = $this->curve->convertInteger($u1);
+        $u2 = $this->curve->convertInteger($u2);
+
+        list($x1, $y1) = $this->curve->multiplyAddPoints(
+            [$this->curve->getBasePoint(), $this->QA],
+            [$u1, $u2]
+        );
+
+        $x1 = $x1->toBigInteger();
+        list(, $x1) = $x1->divide($order);
+
+        return $x1->equals($r);
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/BaseCurves/Base.php b/phpseclib/Crypt/ECDSA/BaseCurves/Base.php
new file mode 100644
index 00000000..53cd59c5
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/BaseCurves/Base.php
@@ -0,0 +1,220 @@
+<?php
+
+/**
+ * Curve methods common to all curves
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\BaseCurves;
+
+use phpseclib\Math\Common\FiniteField;
+use phpseclib\Math\BigInteger;
+
+/**
+ * Base
+ *
+ * @package Prime
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Base
+{
+    /**
+     * Doubles
+     *
+     * @var object[]
+     */
+    protected $doubles;
+
+    /**
+     * NAF Points
+     *
+     * @var int[]
+     */
+    private $naf;
+
+    /**
+     * The Order
+     *
+     * @var BigInteger
+     */
+    protected $order;
+
+    /**
+     * Finite Field Integer factory
+     *
+     * @var \phpseclib\Math\FiniteField\Integer
+     */
+    protected $factory;
+
+    /**
+     * Returns a random integer
+     *
+     * @return object
+     */
+    public function randomInteger()
+    {
+        return $this->factory->randomInteger();
+    }
+
+    /**
+     * Converts a BigInteger to a FiniteField integer
+     *
+     * @return object
+     */
+    public function convertInteger(BigInteger $x)
+    {
+        return $this->factory->newInteger($x);
+    }
+
+    /**
+     * Returns the length, in bytes, of the modulo
+     *
+     * @return integer
+     */
+    public function getLengthInBytes()
+    {
+        return $this->factory->getLengthInBytes();
+    }
+
+    /**
+     * Returns the length, in bits, of the modulo
+     *
+     * @return integer
+     */
+    public function getLength()
+    {
+        return $this->factory->getLength();
+    }
+
+    /**
+     * Multiply a point on the curve by a scalar
+     *
+     * Uses the montgomery ladder technique as described here:
+     *
+     * https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder
+     * https://github.com/phpecc/phpecc/issues/16#issuecomment-59176772
+     *
+     * @return array
+     */
+    public function multiplyPoint(array $p, FiniteField\Integer $d)
+    {
+        $alreadyInternal = isset($p[2]);
+        $r = $alreadyInternal ?
+            [[], $p] :
+            [[], $this->convertToInternal($p)];
+
+        $d = $d->toBits();
+        for ($i = 0; $i < strlen($d); $i++) {
+            $d_i = (int) $d[$i];
+            $r[1 - $d_i] = $this->addPoint($r[0], $r[1]);
+            $r[$d_i] = $this->doublePoint($r[$d_i]);
+        }
+
+        return $alreadyInternal ? $r[0] : $this->convertToAffine($r[0]);
+    }
+
+    /**
+     * Creates a random scalar multiplier
+     *
+     * @return FiniteField
+     */
+    public function createRandomMultiplier()
+    {
+        static $one;
+        if (!isset($one)) {
+            $one = new BigInteger(1);
+        }
+
+        $dA = BigInteger::randomRange($one, $this->order->subtract($one));
+        return $this->factory->newInteger($dA);
+    }
+
+    /**
+     * Sets the Order
+     */
+    public function setOrder(BigInteger $order)
+    {
+        $this->order = $order;
+    }
+
+    /**
+     * Returns the Order
+     *
+     * @return \phpseclib\Math\BigInteger
+     */
+    public function getOrder()
+    {
+        return $this->order;
+    }
+
+    /**
+     * Use a custom defined modular reduction function
+     *
+     * @return object
+     */
+    public function setReduction(callable $func)
+    {
+        $this->factory->setReduction($func);
+    }
+
+    /**
+     * Returns the affine point
+     *
+     * @return object[]
+     */
+    public function convertToAffine(array $p)
+    {
+        return $p;
+    }
+
+    /**
+     * Converts an affine point to a jacobian coordinate
+     *
+     * @return object[]
+     */
+    public function convertToInternal(array $p)
+    {
+        return $p;
+    }
+
+    /**
+     * Negates a point
+     *
+     * @return object[]
+     */
+    public function negatePoint(array $p)
+    {
+        $temp = [
+            $p[0],
+            $p[1]->negate()
+        ];
+        if (isset($p[2])) {
+            $temp[] = $p[2];
+        }
+        return $temp;
+    }
+
+    /**
+     * Multiply and Add Points
+     *
+     * @return int[]
+     */
+    public function multiplyAddPoints(array $points, array $scalars)
+    {
+        $p1 = $this->convertToInternal($points[0]);
+        $p2 = $this->convertToInternal($points[1]);
+        $p1 = $this->multiplyPoint($p1, $scalars[0]);
+        $p2 = $this->multiplyPoint($p2, $scalars[1]);
+        $r = $this->addPoint($p1, $p2);
+        return $this->convertToAffine($r);
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/BaseCurves/Binary.php b/phpseclib/Crypt/ECDSA/BaseCurves/Binary.php
new file mode 100644
index 00000000..bbfeb8c1
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/BaseCurves/Binary.php
@@ -0,0 +1,378 @@
+<?php
+
+/**
+ * Curves over y^2 + x*y = x^3 + a*x^2 + b
+ *
+ * These are curves used in SEC 2 over prime fields: http://www.secg.org/SEC2-Ver-1.0.pdf
+ * The curve is a weierstrass curve with a[3] and a[2] set to 0.
+ *
+ * Uses Jacobian Coordinates for speed if able:
+ *
+ * https://en.wikipedia.org/wiki/Jacobian_curve
+ * https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\BaseCurves;
+
+use phpseclib\Common\Functions\Strings;
+use phpseclib\Math\BinaryField;
+use phpseclib\Math\BigInteger;
+use phpseclib\Math\BinaryField\Integer as BinaryInteger;
+
+/**
+ * Curves over y^2 + x*y = x^3 + a*x^2 + b
+ *
+ * @package Binary
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class Binary extends Base
+{
+    /**
+     * Binary Field Integer factory
+     *
+     * @var \phpseclib\Math\BinaryFields
+     */
+    protected $factory;
+
+    /**
+     * Cofficient for x^1
+     *
+     * @var object
+     */
+    protected $a;
+
+    /**
+     * Cofficient for x^0
+     *
+     * @var object
+     */
+    protected $b;
+
+    /**
+     * Base Point
+     *
+     * @var object
+     */
+    protected $p;
+
+    /**
+     * The number one over the specified finite field
+     *
+     * @var object
+     */
+    protected $one;
+
+    /**
+     * The modulo
+     *
+     * @var BigInteger
+     */
+    protected $modulo;
+
+    /**
+     * The Order
+     *
+     * @var BigInteger
+     */
+    protected $order;
+
+    /**
+     * Sets the modulo
+     */
+    public function setModulo(...$modulo)
+    {
+        $this->modulo = $modulo;
+        $this->factory = new BinaryField(...$modulo);
+
+        $this->one = $this->factory->newInteger("\1");
+    }
+
+    /**
+     * Set coefficients a and b
+     *
+     * @param string $a
+     * @param string $b
+     */
+    public function setCoefficients($a, $b)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->a = $this->factory->newInteger(pack('H*', $a));
+        $this->b = $this->factory->newInteger(pack('H*', $b));
+    }
+
+    /**
+     * Set x and y coordinates for the base point
+     *
+     * @param string|BinaryInteger $x
+     * @param string|BinaryInteger $y
+     */
+    public function setBasePoint($x, $y)
+    {
+        switch (true) {
+            case !is_string($x) && !$x instanceof BinaryInteger:
+                throw new \UnexpectedValueException('Argument 1 passed to Binary::setBasePoint() must be a string or an instance of BinaryField\Integer');
+            case !is_string($y) && !$y instanceof BinaryInteger:
+                throw new \UnexpectedValueException('Argument 2 passed to Binary::setBasePoint() must be a string or an instance of BinaryField\Integer');
+        }
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->p = [
+            is_string($x) ? $this->factory->newInteger(pack('H*', $x)) : $x,
+            is_string($y) ? $this->factory->newInteger(pack('H*', $y)) : $y
+        ];
+    }
+
+    /**
+     * Retrieve the base point as an array
+     *
+     * @return array
+     */
+    public function getBasePoint()
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        /*
+        if (!isset($this->p)) {
+            throw new \RuntimeException('setBasePoint needs to be called before this method');
+        }
+        */
+        return $this->p;
+    }
+
+    /**
+     * Adds two points on the curve
+     *
+     * @return FiniteField[]
+     */
+    public function addPoint(array $p, array $q)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p) || !count($q)) {
+            if (count($q)) {
+                return $q;
+            }
+            if (count($p)) {
+                return $p;
+            }
+            return [];
+        }
+
+        if (!isset($p[2]) || !isset($q[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
+        }
+
+        if ($p[0]->equals($q[0])) {
+            return !$p[1]->equals($q[1]) ? [] : $this->doublePoint($p);
+        }
+
+        // formulas from http://hyperelliptic.org/EFD/g12o/auto-shortw-jacobian.html
+
+        list($x1, $y1, $z1) = $p;
+        list($x2, $y2, $z2) = $q;
+
+        $o1 = $z1->multiply($z1);
+        $b = $x2->multiply($o1);
+
+        if ($z2->equals($this->one)) {
+            $d = $y2->multiply($o1)->multiply($z1);
+            $e = $x1->add($b);
+            $f = $y1->add($d);
+            $z3 = $e->multiply($z1);
+            $h = $f->multiply($x2)->add($z3->multiply($y2));
+            $i = $f->add($z3);
+            $g = $z3->multiply($z3);
+            $p1 = $this->a->multiply($g);
+            $p2 = $f->multiply($i);
+            $p3 = $e->multiply($e)->multiply($e);
+            $x3 = $p1->add($p2)->add($p3);
+            $y3 = $i->multiply($x3)->add($g->multiply($h));
+
+            return [$x3, $y3, $z3];
+        }
+
+        $o2 = $z2->multiply($z2);
+        $a = $x1->multiply($o2);
+        $c = $y1->multiply($o2)->multiply($z2);
+        $d = $y2->multiply($o1)->multiply($z1);
+        $e = $a->add($b);
+        $f = $c->add($d);
+        $g = $e->multiply($z1);
+        $h = $f->multiply($x2)->add($g->multiply($y2));
+        $z3 = $g->multiply($z2);
+        $i = $f->add($z3);
+        $p1 = $this->a->multiply($z3->multiply($z3));
+        $p2 = $f->multiply($i);
+        $p3 = $e->multiply($e)->multiply($e);
+        $x3 = $p1->add($p2)->add($p3);
+        $y3 = $i->multiply($x3)->add($g->multiply($g)->multiply($h));
+
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Doubles a point on a curve
+     *
+     * @return FiniteField[]
+     */
+    public function doublePoint(array $p)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p)) {
+            return [];
+        }
+
+        if (!isset($p[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
+        }
+
+        // formulas from http://hyperelliptic.org/EFD/g12o/auto-shortw-jacobian.html
+
+        list($x1, $y1, $z1) = $p;
+
+        $a = $x1->multiply($x1);
+        $b = $a->multiply($a);
+
+        if ($z1->equals($this->one)) {
+            $x3 = $b->add($this->b);
+            $z3 = clone $x1;
+            $p1 = $a->add($y1)->add($z3)->multiply($this->b);
+            $p2 = $a->add($y1)->multiply($b);
+            $y3 = $p1->add($p2);
+
+            return [$x3, $y3, $z3];
+        }
+
+        $c = $z1->multiply($z1);
+        $d = $c->multiply($c);
+        $x3 = $b->add($this->b->multiply($d->multiply($d)));
+        $z3 = $x1->multiply($c);
+        $p1 = $b->multiply($z3);
+        $p2 = $a->add($y1->multiply($z1))->add($z3)->multiply($x3);
+        $y3 = $p1->add($p2);
+
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Returns the X coordinate and the derived Y coordinate
+     *
+     * Not supported because it is covered by patents.
+     * Quoting https://www.openssl.org/docs/man1.1.0/apps/ecparam.html ,
+     * 
+     * "Due to patent issues the compressed option is disabled by default for binary curves
+     *  and can be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at
+     *  compile time."
+     *
+     * @return array
+     */
+    public function derivePoint($m)
+    {
+        throw new \RuntimeException('Point compression on binary finite field elliptic curves is not supported');
+    }
+
+    /**
+     * Tests whether or not the x / y values satisfy the equation
+     *
+     * @return boolean
+     */
+    public function verifyPoint(array $p)
+    {
+        list($x, $y) = $p;
+        $lhs = $y->multiply($y);
+        $lhs = $lhs->add($x->multiply($y));
+        $x2 = $x->multiply($x);
+        $x3 = $x2->multiply($x);
+        $rhs = $x3->add($this->a->multiply($x2))->add($this->b);
+
+        return $lhs->equals($rhs);
+    }
+
+    /**
+     * Returns the modulo
+     *
+     * @return \phpseclib\Math\BigInteger
+     */
+    public function getModulo()
+    {
+        return $this->modulo;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function getB()
+    {
+        return $this->b;
+    }
+
+    /**
+     * Returns the affine point
+     *
+     * A Jacobian Coordinate is of the form (x, y, z).
+     * To convert a Jacobian Coordinate to an Affine Point
+     * you do (x / z^2, y / z^3)
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToAffine(array $p)
+    {
+        if (!isset($p[2])) {
+            return $p;
+        }
+        list($x, $y, $z) = $p;
+        $z = $this->one->divide($z);
+        $z2 = $z->multiply($z);
+        return [
+            $x->multiply($z2),
+            $y->multiply($z2)->multiply($z)
+        ];
+    }
+
+    /**
+     * Converts an affine point to a jacobian coordinate
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (isset($p[2])) {
+            return $p;
+        }
+ 
+        $p[2] = clone $this->one;
+        $p['fresh'] = true;
+        return $p;
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/BaseCurves/KoblitzPrime.php b/phpseclib/Crypt/ECDSA/BaseCurves/KoblitzPrime.php
new file mode 100644
index 00000000..f6a680a0
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/BaseCurves/KoblitzPrime.php
@@ -0,0 +1,324 @@
+<?php
+
+/**
+ * Generalized Koblitz Curves over y^2 = x^3 + b.
+ *
+ * According to http://www.secg.org/SEC2-Ver-1.0.pdf Koblitz curves are over the GF(2**m)
+ * finite field. Both the $a$ and $b$ coefficients are either 0 or 1. However, SEC2
+ * generalizes the definition to include curves over GF(P) "which possess an efficiently
+ * computable endomorphism".
+ *
+ * For these generalized Koblitz curves $b$ doesn't have to be 0 or 1. Whether or not $a$
+ * has any restrictions on it is unclear, however, for all the GF(P) Koblitz curves defined
+ * in SEC2 v1.0 $a$ is $0$ so all of the methods defined herein will assume that it is.
+ *
+ * I suppose we could rename the $b$ coefficient to $a$, however, the documentation refers
+ * to $b$ so we'll just keep it.
+ *
+ * If a later version of SEC2 comes out wherein some $a$ values are non-zero we can create a
+ * new method for those. eg. KoblitzA1Prime.php or something.
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\BaseCurves;
+
+use phpseclib\Common\Functions\Strings;
+use phpseclib\Math\PrimeField;
+use phpseclib\Math\BigInteger;
+use phpseclib\Math\PrimeField\Integer as PrimeInteger;
+
+/**
+ * Curves over y^2 = x^3 + b
+ *
+ * @package KoblitzPrime
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class KoblitzPrime extends Prime
+{
+    // don't overwrite setCoefficients() with one that only accepts one parameter so that
+    // one might be able to switch between KoblitzPrime and Prime more easily (for benchmarking
+    // purposes).
+
+    /**
+     * Multiply and Add Points
+     *
+     * Uses a efficiently computable endomorphism to achieve a slight speedup
+     *
+     * Adapted from https://git.io/vxbrP
+     *
+     * @return int[]
+     */
+    public function multiplyAddPoints(array $points, array $scalars)
+    {
+        static $zero, $one, $two;
+        if (!isset($two)) {
+            $two = new BigInteger(2);
+            $one = new BigInteger(1);
+        }
+
+        if (!isset($this->beta)) {
+            // get roots
+            $inv = $this->one->divide($this->two)->negate();
+            $s = $this->three->negate()->squareRoot()->multiply($inv);
+            $betas = [
+                $inv->add($s),
+                $inv->subtract($s)
+            ];
+            $this->beta = $betas[0]->compare($betas[1]) < 0 ? $betas[0] : $betas[1];
+            //echo strtoupper($this->beta->toHex(true)) . "\n"; exit;
+        }
+
+        if (!isset($this->basis)) {
+            $factory = new PrimeField($this->order);
+            $tempOne = $factory->newInteger($one);
+            $tempTwo = $factory->newInteger($two);
+            $tempThree = $factory->newInteger(new BigInteger(3));
+
+            $inv = $tempOne->divide($tempTwo)->negate();
+            $s = $tempThree->negate()->squareRoot()->multiply($inv);
+
+            $lambdas = [
+                $inv->add($s),
+                $inv->subtract($s)
+            ];
+
+            $lhs = $this->multiplyPoint($this->p, $lambdas[0])[0];
+            $rhs = $this->p[0]->multiply($this->beta);
+            $lambda = $lhs->equals($rhs) ? $lambdas[0] : $lambdas[1];
+
+            $this->basis = static::extendedGCD($lambda->toBigInteger(), $this->order);
+            ///*
+            foreach ($this->basis as $basis) {
+                echo strtoupper($basis['a']->toHex(true)) . "\n";
+                echo strtoupper($basis['b']->toHex(true)) . "\n\n";
+            }
+            exit;
+            //*/
+        }
+
+        $npoints = $nscalars = [];
+        for ($i = 0; $i < count($points); $i++) {
+            $p = $points[$i];
+            $k = $scalars[$i]->toBigInteger();
+
+            // begin split
+            list($v1, $v2) = $this->basis;
+
+            $c1 = $v2['b']->multiply($k);
+            list($c1, $r) = $c1->divide($this->order);
+            if ($this->order->compare($r->multiply($two)) <= 0) {
+                $c1 = $c1->add($one);
+            }
+
+            $c2 = $v1['b']->negate()->multiply($k);
+            list($c2, $r) = $c2->divide($this->order);
+            if ($this->order->compare($r->multiply($two)) <= 0) {
+                $c2 = $c2->add($one);
+            }
+
+            $p1 = $c1->multiply($v1['a']);
+            $p2 = $c2->multiply($v2['a']);
+            $q1 = $c1->multiply($v1['b']);
+            $q2 = $c2->multiply($v2['b']);
+
+            $k1 = $k->subtract($p1)->subtract($p2);
+            $k2 = $q1->add($q2)->negate();
+            // end split
+
+            $beta = [
+                $p[0]->multiply($this->beta),
+                $p[1],
+                clone $this->one
+            ];
+
+            if (isset($p['naf'])) {
+                $beta['naf'] = array_map(function($p) {
+                    return [
+                        $p[0]->multiply($this->beta),
+                        $p[1],
+                        clone $this->one
+                    ];
+                }, $p['naf']);
+                $beta['nafwidth'] = $p['nafwidth'];
+            }
+
+            if ($k1->isNegative()) {
+                $k1 = $k1->negate();
+                $p = $this->negatePoint($p);
+            }
+
+            if ($k2->isNegative()) {
+                $k2 = $k2->negate();
+                $beta = $this->negatePoint($beta);
+            }
+
+            $pos = 2 * $i;
+            $npoints[$pos] = $p;
+            $nscalars[$pos] = $this->factory->newInteger($k1);
+
+            $pos++;
+            $npoints[$pos] = $beta;
+            $nscalars[$pos] = $this->factory->newInteger($k2);
+        }
+
+        return parent::multiplyAddPoints($npoints, $nscalars);
+    }
+
+    /**
+     * Returns the numerator and denominator of the slope
+     *
+     * @return FiniteField[]
+     */
+    protected function doublePointHelper(array $p)
+    {
+        $numerator = $this->three->multiply($p[0])->multiply($p[0]);
+        $denominator = $this->two->multiply($p[1]);
+        return [$numerator, $denominator];
+    }
+
+    /**
+     * Doubles a jacobian coordinate on the curve
+     *
+     * See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianDoublePoint(array $p)
+    {
+        list($x1, $y1, $z1) = $p;
+        $a = $x1->multiply($x1);
+        $b = $y1->multiply($y1);
+        $c = $b->multiply($b);
+        $d = $x1->add($b);
+        $d = $d->multiply($d)->subtract($a)->subtract($c)->multiply($this->two);
+        $e = $this->three->multiply($a);
+        $f = $e->multiply($e);
+        $x3 = $f->subtract($this->two->multiply($d));
+        $y3 = $e->multiply($d->subtract($x3))->subtract(
+              $this->eight->multiply($c));
+        $z3 = $this->two->multiply($y1)->multiply($z1);
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Doubles a "fresh" jacobian coordinate on the curve
+     *
+     * See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-mdbl-2007-bl
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianDoublePointMixed(array $p)
+    {
+        list($x1, $y1) = $p;
+        $xx = $x1->multiply($x1);
+        $yy = $y1->multiply($y1);
+        $yyyy = $yy->multiply($yy);
+        $s = $x1->add($yy);
+        $s = $s->multiply($s)->subtract($xx)->subtract($yyyy)->multiply($this->two);
+        $m = $this->three->multiply($xx);
+        $t = $m->multiply($m)->subtract($this->two->multiply($s));
+        $x3 = $t;
+        $y3 = $s->subtract($t);
+        $y3 = $m->multiply($y3)->subtract($this->eight->multiply($yyyy));
+        $z3 = $this->two->multiply($y1);
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Tests whether or not the x / y values satisfy the equation
+     *
+     * @return boolean
+     */
+    public function verifyPoint(array $p)
+    {
+        list($x, $y) = $p;
+        $lhs = $y->multiply($y);
+        $temp = $x->multiply($x)->multiply($x);
+        $rhs = $temp->add($this->b);
+
+        return $lhs->equals($rhs);
+    }
+
+    /**
+     * Calculates the parameters needed from the Euclidean algorithm as discussed at
+     * http://diamond.boisestate.edu/~liljanab/MATH308/GuideToECC.pdf#page=148
+     *
+     * @param BigInteger $n
+     * @return BigInteger[]
+     */
+    protected static function extendedGCD(BigInteger $u, BigInteger $v)
+    {
+        $one = new BigInteger(1);
+        $zero = new BigInteger();
+
+        $a = clone $one;
+        $b = clone $zero;
+        $c = clone $zero;
+        $d = clone $one;
+
+        $stop = $v->bitwise_rightShift($v->getLength() >> 1);
+
+        $a1 = clone $zero;
+        $b1 = clone $zero;
+        $a2 = clone $zero;
+        $b2 = clone $zero;
+
+        $postGreatestIndex = 0;
+
+        while (!$v->equals($zero)) {
+            list($q) = $u->divide($v);
+
+            $temp = $u;
+            $u = $v;
+            $v = $temp->subtract($v->multiply($q));
+
+            $temp = $a;
+            $a = $c;
+            $c = $temp->subtract($a->multiply($q));
+
+            $temp = $b;
+            $b = $d;
+            $d = $temp->subtract($b->multiply($q));
+
+            if ($v->compare($stop) > 0) {
+                $a0 = $v;
+                $b0 = $c;
+            } else {
+                $postGreatestIndex++;
+            }
+
+            if ($postGreatestIndex == 1) {
+                $a1 = $v;
+                $b1 = $c->negate();
+            }
+
+            if ($postGreatestIndex == 2) {
+                $rhs = $a0->multiply($a0)->add($b0->multiply($b0));
+                $lhs = $v->multiply($v)->add($b->multiply($b));
+                if ($lhs->compare($rhs) <= 0) {
+                    $a2 = $a0;
+                    $b2 = $b0->negate();
+                } else {
+                    $a2 = $v;
+                    $b2 = $c->negate();
+                }
+
+                break;
+            }
+        }
+
+        return [
+            ['a' => $a1, 'b' => $b1],
+            ['a' => $a2, 'b' => $b2]
+        ];
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/BaseCurves/Prime.php b/phpseclib/Crypt/ECDSA/BaseCurves/Prime.php
new file mode 100644
index 00000000..dde84ce7
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/BaseCurves/Prime.php
@@ -0,0 +1,774 @@
+<?php
+
+/**
+ * Curves over y^2 = x^3 + a*x + b
+ *
+ * These are curves used in SEC 2 over prime fields: http://www.secg.org/SEC2-Ver-1.0.pdf
+ * The curve is a weierstrass curve with a[1], a[3] and a[2] set to 0.
+ *
+ * Uses Jacobian Coordinates for speed if able:
+ *
+ * https://en.wikipedia.org/wiki/Jacobian_curve
+ * https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\BaseCurves;
+
+use phpseclib\Math\Common\FiniteField\Integer;
+use phpseclib\Common\Functions\Strings;
+use phpseclib\Math\PrimeField;
+use phpseclib\Math\BigInteger;
+use phpseclib\Math\PrimeField\Integer as PrimeInteger;
+
+/**
+ * Curves over y^2 = x^3 + a*x + b
+ *
+ * @package Prime
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class Prime extends Base
+{
+    /**
+     * Prime Field Integer factory
+     *
+     * @var \phpseclib\Math\PrimeFields
+     */
+    protected $factory;
+
+    /**
+     * Cofficient for x^1
+     *
+     * @var object
+     */
+    protected $a;
+
+    /**
+     * Cofficient for x^0
+     *
+     * @var object
+     */
+    protected $b;
+
+    /**
+     * Base Point
+     *
+     * @var object
+     */
+    protected $p;
+
+    /**
+     * The number one over the specified finite field
+     *
+     * @var object
+     */
+    protected $one;
+
+    /**
+     * The number two over the specified finite field
+     *
+     * @var object
+     */
+    protected $two;
+
+    /**
+     * The number three over the specified finite field
+     *
+     * @var object
+     */
+    protected $three;
+
+    /**
+     * The number four over the specified finite field
+     *
+     * @var object
+     */
+    protected $four;
+
+    /**
+     * The number eight over the specified finite field
+     *
+     * @var object
+     */
+    protected $eight;
+
+    /**
+     * The modulo
+     *
+     * @var BigInteger
+     */
+    protected $modulo;
+
+    /**
+     * The Order
+     *
+     * @var BigInteger
+     */
+    protected $order;
+
+    /**
+     * Sets the modulo
+     */
+    public function setModulo(BigInteger $modulo)
+    {
+        $this->modulo = $modulo;
+        $this->factory = new PrimeField($modulo);
+        $this->two = $this->factory->newInteger(new BigInteger(2));
+        $this->three = $this->factory->newInteger(new BigInteger(3));
+        // used by jacobian coordinates
+        $this->one = $this->factory->newInteger(new BigInteger(1));
+        $this->four = $this->factory->newInteger(new BigInteger(4));
+        $this->eight = $this->factory->newInteger(new BigInteger(8));
+    }
+
+    /**
+     * Set coefficients a and b
+     */
+    public function setCoefficients(BigInteger $a, BigInteger $b)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->a = $this->factory->newInteger($a);
+        $this->b = $this->factory->newInteger($b);
+    }
+
+    /**
+     * Set x and y coordinates for the base point
+     *
+     * @param BigInteger|PrimeInteger $x
+     * @param BigInteger|PrimeInteger $y
+     * @return PrimeInteger[]
+     */
+    public function setBasePoint($x, $y)
+    {
+        switch (true) {
+            case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
+                throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
+            case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
+                throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
+        }
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->p = [
+            $x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
+            $y instanceof BigInteger ? $this->factory->newInteger($y) : $y
+        ];
+    }
+
+    /**
+     * Retrieve the base point as an array
+     *
+     * @return array
+     */
+    public function getBasePoint()
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        /*
+        if (!isset($this->p)) {
+            throw new \RuntimeException('setBasePoint needs to be called before this method');
+        }
+        */
+        return $this->p;
+    }
+
+    /**
+     * Adds two "fresh" jacobian form on the curve
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianAddPointMixedXY(array $p, array $q)
+    {
+        list($u1, $s1) = $p;
+        list($u2, $s2) = $q;
+        if ($u1->equals($u2)) {
+            if (!$s1->equals($s2)) {
+                return [];
+            } else {
+                return $this->doublePoint($p);
+            }
+        }
+        $h = $u2->subtract($u1);
+        $r = $s2->subtract($s1);
+        $h2 = $h->multiply($h);
+        $h3 = $h2->multiply($h);
+        $v = $u1->multiply($h2);
+        $x3 = $r->multiply($r)->subtract($h3)->subtract($v->multiply($this->two));
+        $y3 = $r->multiply(
+            $v->subtract($x3))->subtract(
+            $s1->multiply($h3));
+        return [$x3, $y3, $h];
+    }
+
+    /**
+     * Adds one "fresh" jacobian form on the curve
+     *
+     * The second parameter should be the "fresh" one
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianAddPointMixedX(array $p, array $q)
+    {
+        list($u1, $s1, $z1) = $p;
+        list($x2, $y2) = $q;
+
+        $z12 = $z1->multiply($z1);
+
+        $u2 = $x2->multiply($z12);
+        $s2 = $y2->multiply($z12->multiply($z1));
+        if ($u1->equals($u2)) {
+            if (!$s1->equals($s2)) {
+                return [];
+            } else {
+                return $this->doublePoint($p);
+            }
+        }
+        $h = $u2->subtract($u1);
+        $r = $s2->subtract($s1);
+        $h2 = $h->multiply($h);
+        $h3 = $h2->multiply($h);
+        $v = $u1->multiply($h2);
+        $x3 = $r->multiply($r)->subtract($h3)->subtract($v->multiply($this->two));
+        $y3 = $r->multiply(
+            $v->subtract($x3))->subtract(
+            $s1->multiply($h3));
+        $z3 = $h->multiply($z1);
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Adds two jacobian coordinates on the curve
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianAddPoint(array $p, array $q)
+    {
+        list($x1, $y1, $z1) = $p;
+        list($x2, $y2, $z2) = $q;
+
+        $z12 = $z1->multiply($z1);
+        $z22 = $z2->multiply($z2);
+
+        $u1 = $x1->multiply($z22);
+        $u2 = $x2->multiply($z12);
+        $s1 = $y1->multiply($z22->multiply($z2));
+        $s2 = $y2->multiply($z12->multiply($z1));
+        if ($u1->equals($u2)) {
+            if (!$s1->equals($s2)) {
+                return [];
+            } else {
+                return $this->doublePoint($p);
+            }
+        }
+        $h = $u2->subtract($u1);
+        $r = $s2->subtract($s1);
+        $h2 = $h->multiply($h);
+        $h3 = $h2->multiply($h);
+        $v = $u1->multiply($h2);
+        $x3 = $r->multiply($r)->subtract($h3)->subtract($v->multiply($this->two));
+        $y3 = $r->multiply(
+            $v->subtract($x3))->subtract(
+            $s1->multiply($h3));
+        $z3 = $h->multiply($z1)->multiply($z2);
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Adds two points on the curve
+     *
+     * @return FiniteField[]
+     */
+    public function addPoint(array $p, array $q)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p) || !count($q)) {
+            if (count($q)) {
+                return $q;
+            }
+            if (count($p)) {
+                return $p;
+            }
+            return [];
+        }
+
+        // use jacobian coordinates
+        if (isset($p[2]) && isset($q[2])) {
+            if (isset($p['fresh']) && isset($q['fresh'])) {
+                return $this->jacobianAddPointMixedXY($p, $q);
+            }
+            if (isset($p['fresh'])) {
+                return $this->jacobianAddPointMixedX($q, $p);
+            }
+            if (isset($q['fresh'])) {
+                return $this->jacobianAddPointMixedX($p, $q);
+            }
+            return $this->jacobianAddPoint($p, $q);
+        }
+
+        if (isset($p[2]) || isset($q[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to Jacobi coordinates or vice versa');
+        }
+
+        if ($p[0]->equals($q[0])) {
+            if (!$p[1]->equals($q[1])) {
+                return [];
+            } else { // eg. doublePoint
+                list($numerator, $denominator) = $this->doublePointHelper($p);
+            }
+        } else {
+            $numerator = $q[1]->subtract($p[1]);
+            $denominator = $q[0]->subtract($p[0]);
+        }
+        $slope = $numerator->divide($denominator);
+        $x = $slope->multiply($slope)->subtract($p[0])->subtract($q[0]);
+        $y = $slope->multiply($p[0]->subtract($x))->subtract($p[1]);
+
+        return [$x, $y];
+    }
+
+    /**
+     * Returns the numerator and denominator of the slope
+     *
+     * @return FiniteField[]
+     */
+    protected function doublePointHelper(array $p)
+    {
+        $numerator = $this->three->multiply($p[0])->multiply($p[0])->add($this->a);
+        $denominator = $this->two->multiply($p[1]);
+        return [$numerator, $denominator];
+    }
+
+    /**
+     * Doubles a jacobian coordinate on the curve
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianDoublePoint(array $p)
+    {
+        list($x, $y, $z) = $p;
+        $x2 = $x->multiply($x);
+        $y2 = $y->multiply($y);
+        $z2 = $z->multiply($z);
+        $s = $this->four->multiply($x)->multiply($y2);
+        $m1 = $this->three->multiply($x2);
+        $m2 = $this->a->multiply($z2->multiply($z2));
+        $m = $m1->add($m2);
+        $x1 = $m->multiply($m)->subtract($this->two->multiply($s));
+        $y1 = $m->multiply($s->subtract($x1))->subtract(
+              $this->eight->multiply($y2->multiply($y2)));
+        $z1 = $this->two->multiply($y)->multiply($z);
+        return [$x1, $y1, $z1];
+    }
+
+    /**
+     * Doubles a "fresh" jacobian coordinate on the curve
+     *
+     * @return FiniteField[]
+     */
+    protected function jacobianDoublePointMixed(array $p)
+    {
+        list($x, $y) = $p;
+        $x2 = $x->multiply($x);
+        $y2 = $y->multiply($y);
+        $s = $this->four->multiply($x)->multiply($y2);
+        $m1 = $this->three->multiply($x2);
+        $m = $m1->add($this->a);
+        $x1 = $m->multiply($m)->subtract($this->two->multiply($s));
+        $y1 = $m->multiply($s->subtract($x1))->subtract(
+              $this->eight->multiply($y2->multiply($y2)));
+        $z1 = $this->two->multiply($y);
+        return [$x1, $y1, $z1];
+    }
+
+    /**
+     * Doubles a point on a curve
+     *
+     * @return FiniteField[]
+     */
+    public function doublePoint(array $p)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p)) {
+            return [];
+        }
+
+        // use jacobian coordinates
+        if (isset($p[2])) {
+            if (isset($p['fresh'])) {
+                return $this->jacobianDoublePointMixed($p);
+            }
+            return $this->jacobianDoublePoint($p);
+        }
+
+        list($numerator, $denominator) = $this->doublePointHelper($p);
+
+        $slope = $numerator->divide($denominator);
+
+        $x = $slope->multiply($slope)->subtract($p[0])->subtract($p[0]);
+        $y = $slope->multiply($p[0]->subtract($x))->subtract($p[1]);
+
+        return [$x, $y];
+    }
+
+    /**
+     * Returns the X coordinate and the derived Y coordinate
+     *
+     * @return array
+     */
+    public function derivePoint($m)
+    {
+        $y = ord(Strings::shift($m));
+        $x = new BigInteger($m, 256);
+        $xp = $this->convertInteger($x);
+        switch ($y) {
+            case 2: $ypn = false; break;
+            case 3: $ypn = true; break;
+            default:
+                throw new \RuntimeException('Coordinate not in recognized format');
+        }
+        $temp = $xp->multiply($this->a);
+        $temp = $xp->multiply($xp)->multiply($xp)->add($temp);
+        $temp = $temp->add($this->b);
+        $b = $temp->squareRoot();
+        if (!$b) {
+            throw new \RuntimeException('Unable to derive Y coordinate');
+        }
+        $bn = $b->isOdd();
+        $yp = $ypn == $bn ? $b : $b->negate();
+        return [$xp, $yp];
+    }
+
+    /**
+     * Tests whether or not the x / y values satisfy the equation
+     *
+     * @return boolean
+     */
+    public function verifyPoint(array $p)
+    {
+        list($x, $y) = $p;
+        $lhs = $y->multiply($y);
+        $temp = $x->multiply($this->a);
+        $temp = $x->multiply($x)->multiply($x)->add($temp);
+        $rhs = $temp->add($this->b);
+
+        return $lhs->equals($rhs);
+    }
+
+    /**
+     * Returns the modulo
+     *
+     * @return \phpseclib\Math\BigInteger
+     */
+    public function getModulo()
+    {
+        return $this->modulo;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function getB()
+    {
+        return $this->b;
+    }
+
+    /**
+     * Multiply and Add Points
+     *
+     * Adapted from https://git.io/vxPUH
+     *
+     * @return int[]
+     */
+    public function multiplyAddPoints(array $points, array $scalars)
+    {
+        $length = count($points);
+
+        foreach ($points as &$point) {
+            $point = $this->convertToInternal($point);
+        }
+
+        $wnd = [$this->getNAFPoints($points[0], 7)];
+        $wndWidth = [isset($points[0]['nafwidth']) ? $points[0]['nafwidth'] : 7];
+        for ($i = 1; $i < $length; $i++) {
+            $wnd[] = $this->getNAFPoints($points[$i], 1);
+            $wndWidth[] = isset($points[$i]['nafwidth']) ? $points[$i]['nafwidth'] : 1;
+        }
+
+        $naf = [];
+
+        // comb all window NAFs
+
+        $max = 0;
+        for ($i = $length - 1; $i >= 1; $i-= 2) {
+            $a = $i - 1;
+            $b = $i;
+            if ($wndWidth[$a] != 1 || $wndWidth[$b] != 1) {
+                $naf[$a] = $scalars[$a]->getNAF($wndWidth[$a]);
+                $naf[$b] = $scalars[$b]->getNAF($wndWidth[$b]);
+                $max = max(count($naf[$a]), count($naf[$b]), $max);
+                continue;
+            }
+
+            $comb = [
+                $points[$a], // 1
+                null,        // 3
+                null,        // 5
+                $points[$b]  // 7
+            ];
+
+            $comb[1] = $this->addPoint($points[$a], $points[$b]);
+            $comb[2] = $this->addPoint($points[$a], $this->negatePoint($points[$b]));
+
+            $index = [
+                -3, /* -1 -1 */
+                -1, /* -1  0 */
+                -5, /* -1  1 */
+                -7, /*  0 -1 */
+                 0, /*  0 -1 */
+                 7, /*  0  1 */
+                 5, /*  1 -1 */
+                 1, /*  1  0 */
+                 3  /*  1  1 */
+            ];
+
+            $jsf = self::getJSFPoints($scalars[$a], $scalars[$b]);
+
+            $max = max(count($jsf[0]), $max);
+            if ($max > 0) {
+                $naf[$a] = array_fill(0, $max, 0);
+                $naf[$b] = array_fill(0, $max, 0);
+            } else {
+                $naf[$a] = [];
+                $naf[$b] = [];
+            }
+
+            for ($j = 0; $j < $max; $j++) {
+                $ja = isset($jsf[0][$j]) ? $jsf[0][$j] : 0;
+                $jb = isset($jsf[1][$j]) ? $jsf[1][$j] : 0;
+
+                $naf[$a][$j] = $index[3 * ($ja + 1) + $jb + 1];
+                $naf[$b][$j] = 0;
+                $wnd[$a] = $comb;
+            }
+        }
+
+        $acc = [];
+        $temp = [0, 0, 0, 0];
+        for ($i = $max; $i >= 0; $i--) {
+            $k = 0;
+            while ($i >= 0) {
+                $zero = true;
+                for ($j = 0; $j < $length; $j++) {
+                    $temp[$j] = isset($naf[$j][$i]) ? $naf[$j][$i] : 0;
+                    if ($temp[$j] != 0) {
+                        $zero = false;
+                    }
+                }
+                if (!$zero) {
+                    break;
+                }
+                $k++;
+                $i--;
+            }
+
+            if ($i >= 0) {
+                $k++;
+            }
+            while ($k--) {
+                $acc = $this->doublePoint($acc);
+            }
+
+            if ($i < 0) {
+                break;
+            }
+
+            for ($j = 0; $j < $length; $j++) {
+                $z = $temp[$j];
+                $p = null;
+                if ($z == 0) {
+                    continue;
+                }
+                $p = $z > 0 ?
+                    $wnd[$j][($z - 1) >> 1] :
+                    $this->negatePoint($wnd[$j][(-$z - 1) >> 1]);
+                $acc = $this->addPoint($acc, $p);
+            }
+        }
+
+        return $this->convertToAffine($acc);
+    }
+
+    /**
+     * Precomputes NAF points
+     *
+     * Adapted from https://git.io/vxY1f
+     *
+     * @return int[]
+     */
+    private function getNAFPoints($point, $wnd)
+    {
+        if (isset($point['naf'])) {
+            return $point['naf'];
+        }
+
+        $res = [$point];
+        $max = (1 << $wnd) - 1;
+        $dbl = $max == 1 ? null : $this->doublePoint($point);
+        for ($i = 1; $i < $max; $i++) {
+            $res[] = $this->addPoint($res[$i - 1], $dbl);
+        }
+
+        $point['naf'] = $res;
+
+        /*
+        $str = '';
+        foreach ($res as $re) {
+            $re[0] = bin2hex($re[0]->toBytes());
+            $re[1] = bin2hex($re[1]->toBytes());
+            $str.= "            ['$re[0]', '$re[1]'],\r\n";
+        }
+        file_put_contents('temp.txt', $str);
+        exit;
+        */
+
+        return $res;
+    }
+
+    /**
+     * Precomputes points in Joint Sparse Form
+     *
+     * Adapted from https://git.io/vxrpD
+     *
+     * @return int[]
+     */
+    private static function getJSFPoints(Integer $k1, Integer $k2)
+    {
+        static $three;
+        if (!isset($three)) {
+            $three = new BigInteger(3);
+        }
+
+        $jsf = [[], []];
+        $k1 = $k1->toBigInteger();
+        $k2 = $k2->toBigInteger();
+        $d1 = 0;
+        $d2 = 0;
+
+        while ($k1->compare(new BigInteger(-$d1)) > 0 || $k2->compare(new BigInteger(-$d2)) > 0) {
+            // first phase
+            $m14 = $k1->testBit(0) + 2 * $k1->testBit(1);
+            $m14+= $d1;
+            $m14&= 3;
+
+            $m24 = $k2->testBit(0) + 2 * $k2->testBit(1);
+            $m24+= $d2;
+            $m24&= 3;
+
+            if ($m14 == 3) {
+                $m14 = -1;
+            }
+            if ($m24 == 3) {
+                $m24 = -1;
+            }
+
+            $u1 = 0;
+            if ($m14 & 1) { // if $m14 is odd
+                $m8 = $k1->testBit(0) + 2 * $k1->testBit(1) + 4 * $k1->testBit(2);
+                $m8+= $d1;
+                $m8&= 7;
+                $u1 = ($m8 == 3 || $m8 == 5) && $m24 == 2 ? -$m14 : $m14;
+            }
+            $jsf[0][] = $u1;
+
+            $u2 = 0;
+            if ($m24 & 1) { // if $m24 is odd
+                $m8 = $k2->testBit(0) + 2 * $k2->testBit(1) + 4 * $k2->testBit(2);
+                $m8+= $d2;
+                $m8&= 7;
+                $u2 = ($m8 == 3 || $m8 == 5) && $m14 == 2 ? -$m24 : $m24;
+            }
+            $jsf[1][] = $u2;
+
+            // second phase
+            if (2 * $d1 == $u1 + 1) {
+                $d1 = 1 - $d1;
+            }
+            if (2 * $d2 == $u2 + 1) {
+                $d2 = 1 - $d2;
+            }
+            $k1 = $k1->bitwise_rightShift(1);
+            $k2 = $k2->bitwise_rightShift(1);
+        }
+
+        return $jsf;
+    }
+
+    /**
+     * Returns the affine point
+     *
+     * A Jacobian Coordinate is of the form (x, y, z).
+     * To convert a Jacobian Coordinate to an Affine Point
+     * you do (x / z^2, y / z^3)
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToAffine(array $p)
+    {
+        if (!isset($p[2])) {
+            return $p;
+        }
+        list($x, $y, $z) = $p;
+        $z = $this->one->divide($z);
+        $z2 = $z->multiply($z);
+        return [
+            $x->multiply($z2),
+            $y->multiply($z2)->multiply($z)
+        ];
+    }
+
+    /**
+     * Converts an affine point to a jacobian coordinate
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (isset($p[2])) {
+            return $p;
+        }
+
+        $p[2] = clone $this->one;
+        $p['fresh'] = true;
+        return $p;
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/BaseCurves/TwistedEdwards.php b/phpseclib/Crypt/ECDSA/BaseCurves/TwistedEdwards.php
new file mode 100644
index 00000000..4cd0d246
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/BaseCurves/TwistedEdwards.php
@@ -0,0 +1,236 @@
+<?php
+
+/**
+ * Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
+ *
+ * http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters.
+ * ie. the coefficients can be arbitrary set through specially formatted keys, etc.
+ * As such, Prime.php is built very generically and it's not able to take full
+ * advantage of curves with 0 coefficients to produce simplified point doubling,
+ * point addition. Twisted Edwards curves, in contrast, do not have a way, currently,
+ * to customize them. As such, we can omit the super generic stuff from this class
+ * and let the named curves (Ed25519 and Ed448) define their own custom tailored
+ * point addition and point doubling methods.
+ *
+ * More info:
+ *
+ * https://en.wikipedia.org/wiki/Twisted_Edwards_curve
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\BaseCurves;
+
+use phpseclib\Math\PrimeField;
+use phpseclib\Math\BigInteger;
+use phpseclib\Math\PrimeField\Integer as PrimeInteger;
+
+/**
+ * Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
+ *
+ * @package Prime
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class TwistedEdwards extends Base
+{
+    /**
+     * The modulo
+     *
+     * @var BigInteger
+     */
+    protected $modulo;
+
+    /**
+     * Cofficient for x^2
+     *
+     * @var object
+     */
+    protected $a;
+
+    /**
+     * Cofficient for x^2*y^2
+     *
+     * @var object
+     */
+    protected $d;
+
+    /**
+     * Base Point
+     *
+     * @var object[]
+     */
+    protected $p;
+
+    /**
+     * The number zero over the specified finite field
+     *
+     * @var object
+     */
+    protected $zero;
+
+    /**
+     * The number one over the specified finite field
+     *
+     * @var object
+     */
+    protected $one;
+
+    /**
+     * The number two over the specified finite field
+     *
+     * @var object
+     */
+    protected $two;
+
+    /**
+     * Sets the modulo
+     */
+    public function setModulo(BigInteger $modulo)
+    {
+        $this->modulo = $modulo;
+        $this->factory = new PrimeField($modulo);
+        $this->zero = $this->factory->newInteger(new BigInteger(0));
+        $this->one = $this->factory->newInteger(new BigInteger(1));
+        $this->two = $this->factory->newInteger(new BigInteger(2));
+    }
+
+    /**
+     * Set coefficients a and b
+     */
+    public function setCoefficients(BigInteger $a, BigInteger $d)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->a = $this->factory->newInteger($a);
+        $this->d = $this->factory->newInteger($d);
+    }
+
+    /**
+     * Set x and y coordinates for the base point
+     */
+    public function setBasePoint($x, $y)
+    {
+        switch (true) {
+            case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
+                throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
+            case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
+                throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
+        }
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->p = [
+            $x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
+            $y instanceof BigInteger ? $this->factory->newInteger($y) : $y
+        ];
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function getD()
+    {
+        return $this->d;
+    }
+
+    /**
+     * Retrieve the base point as an array
+     *
+     * @return array
+     */
+    public function getBasePoint()
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        /*
+        if (!isset($this->p)) {
+            throw new \RuntimeException('setBasePoint needs to be called before this method');
+        }
+        */
+        return $this->p;
+    }
+
+    /**
+     * Returns the affine point
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToAffine(array $p)
+    {
+        if (!isset($p[2])) {
+            return $p;
+        }
+        list($x, $y, $z) = $p;
+        $z = $this->one->divide($z);
+        return [
+            $x->multiply($z),
+            $y->multiply($z)
+        ];
+    }
+
+    /**
+     * Returns the modulo
+     *
+     * @return \phpseclib\Math\BigInteger
+     */
+    public function getModulo()
+    {
+        return $this->modulo;
+    }
+
+    /**
+     * Tests whether or not the x / y values satisfy the equation
+     *
+     * @return boolean
+     */
+    public function verifyPoint(array $p)
+    {
+        list($x, $y) = $p;
+        $x2 = $x->multiply($x);
+        $y2 = $y->multiply($y);
+
+        $lhs = $this->a->multiply($x2)->add($y2);
+        $rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
+
+        return $lhs->equals($rhs);
+    }
+
+    /**
+     * Tests whether or not the x / y values satisfy the equation
+     *
+     * @return boolean
+     */
+    public function get(array $p)
+    {
+        list($x, $y) = $p;
+        $x2 = $x->multiply($x);
+        $y2 = $y->multiply($y);
+
+        $lhs = $this->a->multiply($x2)->add($y2);
+        $rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
+
+        return $lhs->equals($rhs);
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/Ed25519.php b/phpseclib/Crypt/ECDSA/Curves/Ed25519.php
new file mode 100644
index 00000000..837a0053
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/Ed25519.php
@@ -0,0 +1,334 @@
+<?php
+
+/**
+ * Ed25519
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards;
+use phpseclib\Math\BigInteger;
+use phpseclib\Crypt\Hash;
+use phpseclib\Crypt\Random;
+
+class Ed25519 extends TwistedEdwards
+{
+    const HASH = 'sha512';
+    /*
+      Per https://tools.ietf.org/html/rfc8032#page-6 EdDSA has several parameters, one of which is b:
+
+      2.   An integer b with 2^(b-1) > p.  EdDSA public keys have exactly b
+           bits, and EdDSA signatures have exactly 2*b bits.  b is
+           recommended to be a multiple of 8, so public key and signature
+           lengths are an integral number of octets.
+
+      SIZE corresponds to b
+    */
+    const SIZE = 32;
+
+    public function __construct()
+    {
+        // 2^255 - 19
+        $this->setModulo(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED', 16));
+        $this->setCoefficients(
+            // -1
+            new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC', 16), // a
+            // -121665/121666
+            new BigInteger('52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3', 16)  // d
+        );
+        $this->setBasePoint(
+            new BigInteger('216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A', 16),
+            new BigInteger('6666666666666666666666666666666666666666666666666666666666666658', 16)
+        );
+        $this->setOrder(new BigInteger('1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED', 16));
+        // algorithm 14.47 from http://cacr.uwaterloo.ca/hac/about/chap14.pdf#page=16
+        /*
+        $this->setReduction(function($x) {
+            $parts = $x->bitwise_split(255);
+            $className = $this->className;
+
+            if (count($parts) > 2) {
+                list(, $r) = $x->divide($className::$modulo);
+                return $r;
+            }
+
+            $zero = new BigInteger();
+            $c = new BigInteger(19);
+
+            switch (count($parts)) {
+                case 2:
+                    list($qi, $ri) = $parts;
+                    break;
+                case 1:
+                    $qi = $zero;
+                    list($ri) = $parts;
+                    break;
+                case 0:
+                    return $zero;
+            }
+            $r = $ri;
+
+            while ($qi->compare($zero) > 0) {
+                $temp = $qi->multiply($c)->bitwise_split(255);
+                if (count($temp) == 2) {
+                    list($qi, $ri) = $temp;
+                } else {
+                    $qi = $zero;
+                    list($ri) = $temp;
+                }
+                $r = $r->add($ri);
+            }
+
+            while ($r->compare($className::$modulo) > 0) {
+                $r = $r->subtract($className::$modulo);
+            }
+            return $r;
+        });
+        */
+    }
+
+    /**
+     * Recover X from Y
+     *
+     * Implements steps 2-4 at https://tools.ietf.org/html/rfc8032#section-5.1.3
+     *
+     * Used by ECDSA\Keys\Common.php
+     *
+     * @param BigInteger $x
+     * @param boolean $sign
+     * @return object[]
+     */
+    public function recoverX(BigInteger $y, $sign)
+    {
+        $y = $this->factory->newInteger($y);
+
+        $y2 = $y->multiply($y);
+        $u = $y2->subtract($this->one);
+        $v = $this->d->multiply($y2)->add($this->one);
+        $x2 = $u->divide($v);
+        if ($x2->equals($this->zero)) {
+            if ($sign) {
+                throw new \RuntimeException('Unable to recover X coordinate (x2 = 0)');
+            }
+            return clone $this->zero;
+        }
+        // find the square root
+        /* we don't do $x2->squareRoot() because, quoting from
+           https://tools.ietf.org/html/rfc8032#section-5.1.1:
+
+           "For point decoding or "decompression", square roots modulo p are
+            needed.  They can be computed using the Tonelli-Shanks algorithm or
+            the special case for p = 5 (mod 8).  To find a square root of a,
+            first compute the candidate root x = a^((p+3)/8) (mod p)."
+         */
+        $exp = $this->getModulo()->add(new BigInteger(3));
+        $exp = $exp->bitwise_rightShift(3);
+        $x = $x2->pow($exp);
+
+        // If v x^2 = -u (mod p), set x <-- x * 2^((p-1)/4), which is a square root.
+        if (!$x->multiply($x)->subtract($x2)->equals($this->zero)) {
+            $temp = $this->getModulo()->subtract(new BigInteger(1));
+            $temp = $temp->bitwise_rightShift(2);
+            $temp = $this->two->pow($temp);
+            $x = $x->multiply($temp);
+            if (!$x->multiply($x)->subtract($x2)->equals($this->zero)) {
+                throw new \RuntimeException('Unable to recover X coordinate');
+            }
+        }
+        if ($x->isOdd() != $sign) {
+            $x = $x->negate();
+        }
+
+        return [$x, $y];
+    }
+
+    /**
+     * Extract Secret Scalar
+     *
+     * Implements steps 1-3 at https://tools.ietf.org/html/rfc8032#section-5.1.5
+     *
+     * Used by the various key handlers
+     *
+     * @param string $str
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function extractSecret($str)
+    {
+        if (strlen($str) != 32) {
+            throw new \LengthException('Private Key should be 32-bytes long');
+        }
+        // 1.  Hash the 32-byte private key using SHA-512, storing the digest in
+        //     a 64-octet large buffer, denoted h.  Only the lower 32 bytes are
+        //     used for generating the public key.
+        $hash = new Hash('sha512');
+        $h = $hash->hash($str);
+        $h = substr($h, 0, 32);
+        // 2.  Prune the buffer: The lowest three bits of the first octet are
+        //     cleared, the highest bit of the last octet is cleared, and the
+        //     second highest bit of the last octet is set.
+        $h[0] = $h[0] & chr(0xF8);
+        $h = strrev($h);
+        $h[0] = ($h[0] & chr(0x3F)) | chr(0x40);
+        // 3.  Interpret the buffer as the little-endian integer, forming a
+        //     secret scalar s.
+        $dA = new BigInteger($h, 256);
+        $dA = $this->factory->newInteger($dA);
+
+        $dA->secret = $str;
+        return $dA;
+    }
+
+    /**
+     * Encode a point as a string
+     *
+     * @param string $str
+     * @return string
+     */
+    public function encodePoint($point)
+    {
+        list($x, $y) = $point;
+        $y = $y->toBytes();
+        $y[0] = $y[0] & chr(0x7F);
+        if ($x->isOdd()) {
+            $y[0] = $y[0] | chr(0x80);
+        }
+        $y = strrev($y);
+
+        return $y;
+    }
+
+    /**
+     * Creates a random scalar multiplier
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function createRandomMultiplier()
+    {
+        return $this->extractSecret(Random::string(32));
+    }
+
+    /**
+     * Converts an affine point to an extended homogeneous coordinate
+     *
+     * From https://tools.ietf.org/html/rfc8032#section-5.1.4 :
+     *
+     * A point (x,y) is represented in extended homogeneous coordinates (X, Y, Z, T),
+     * with x = X/Z, y = Y/Z, x * y = T/Z.
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (empty($p)) {
+            return [clone $this->zero, clone $this->one, clone $this->one, clone $this->zero];
+        }
+
+        if (isset($p[2])) {
+            return $p;
+        }
+
+        $p[2] = clone $this->one;
+        $p[3] = $p[0]->multiply($p[1]);
+
+        return $p;
+    }
+
+    /**
+     * Doubles a point on a curve
+     *
+     * @return FiniteField[]
+     */
+    public function doublePoint(array $p)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p)) {
+            return [];
+        }
+
+        if (!isset($p[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
+        }
+
+        // from https://tools.ietf.org/html/rfc8032#page-12
+
+        list($x1, $y1, $z1, $t1) = $p;
+
+        $a = $x1->multiply($x1);
+        $b = $y1->multiply($y1);
+        $c = $this->two->multiply($z1)->multiply($z1);
+        $h = $a->add($b);
+        $temp = $x1->add($y1);
+        $e = $h->subtract($temp->multiply($temp));
+        $g = $a->subtract($b);
+        $f = $c->add($g);
+
+        $x3 = $e->multiply($f);
+        $y3 = $g->multiply($h);
+        $t3 = $e->multiply($h);
+        $z3 = $f->multiply($g);
+
+        return [$x3, $y3, $z3, $t3];
+    }
+
+    /**
+     * Adds two points on the curve
+     *
+     * @return FiniteField[]
+     */
+    public function addPoint(array $p, array $q)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p) || !count($q)) {
+            if (count($q)) {
+                return $q;
+            }
+            if (count($p)) {
+                return $p;
+            }
+            return [];
+        }
+
+        if (!isset($p[2]) || !isset($q[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
+        }
+
+        if ($p[0]->equals($q[0])) {
+            return !$p[1]->equals($q[1]) ? [] : $this->doublePoint($p);
+        }
+
+        // from https://tools.ietf.org/html/rfc8032#page-12
+
+        list($x1, $y1, $z1, $t1) = $p;
+        list($x2, $y2, $z2, $t2) = $q;
+
+        $a = $y1->subtract($x1)->multiply($y2->subtract($x2));
+        $b = $y1->add($x1)->multiply($y2->add($x2));
+        $c = $t1->multiply($this->two)->multiply($this->d)->multiply($t2);
+        $d = $z1->multiply($this->two)->multiply($z2);
+        $e = $b->subtract($a);
+        $f = $d->subtract($c);
+        $g = $d->add($c);
+        $h = $b->add($a);
+
+        $x3 = $e->multiply($f);
+        $y3 = $g->multiply($h);
+        $t3 = $e->multiply($h);
+        $z3 = $f->multiply($g);
+
+        return [$x3, $y3, $z3, $t3];
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/Ed448.php b/phpseclib/Crypt/ECDSA/Curves/Ed448.php
new file mode 100644
index 00000000..554c5d03
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/Ed448.php
@@ -0,0 +1,267 @@
+<?php
+
+/**
+ * Ed448
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards;
+use phpseclib\Math\BigInteger;
+use phpseclib\Crypt\Hash;
+use phpseclib\Crypt\Random;
+
+class Ed448 extends TwistedEdwards
+{
+    const HASH = 'shake256-912';
+    const SIZE = 57;
+
+    public function __construct()
+    {
+        // 2^448 - 2^224 - 1
+        $this->setModulo(new BigInteger(
+            'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE' .
+            'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger(1),
+            // -39081
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE' . 
+                           'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6756', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('4F1970C66BED0DED221D15A622BF36DA9E146570470F1767EA6DE324' .
+                           'A3D3A46412AE1AF72AB66511433B80E18B00938E2626A82BC70CC05E', 16),
+            new BigInteger('693F46716EB6BC248876203756C9C7624BEA73736CA3984087789C1E' .
+                           '05A0C2D73AD3FF1CE67C39C4FDBD132C4ED7C8AD9808795BF230FA14', 16)
+        );
+        $this->setOrder(new BigInteger(
+            '3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+            '7CCA23E9C44EDB49AED63690216CC2728DC58F552378C292AB5844F3', 16));
+    }
+
+    /**
+     * Recover X from Y
+     *
+     * Implements steps 2-4 at https://tools.ietf.org/html/rfc8032#section-5.2.3
+     *
+     * Used by ECDSA\Keys\Common.php
+     *
+     * @param BigInteger $x
+     * @param boolean $sign
+     * @return object[]
+     */
+    public function recoverX(BigInteger $y, $sign)
+    {
+        $y = $this->factory->newInteger($y);
+
+        $y2 = $y->multiply($y);
+        $u = $y2->subtract($this->one);
+        $v = $this->d->multiply($y2)->subtract($this->one);
+        $x2 = $u->divide($v);
+        if ($x2->equals($this->zero)) {
+            if ($sign) {
+                throw new \RuntimeException('Unable to recover X coordinate (x2 = 0)');
+            }
+            return clone $this->zero;
+        }
+        // find the square root
+        $exp = $this->getModulo()->add(new BigInteger(1));
+        $exp = $exp->bitwise_rightShift(2);
+        $x = $x2->pow($exp);
+
+        if (!$x->multiply($x)->subtract($x2)->equals($this->zero)) {
+            throw new \RuntimeException('Unable to recover X coordinate');
+        }
+        if ($x->isOdd() != $sign) {
+            $x = $x->negate();
+        }
+
+        return [$x, $y];
+    }
+
+    /**
+     * Extract Secret Scalar
+     *
+     * Implements steps 1-3 at https://tools.ietf.org/html/rfc8032#section-5.2.5
+     *
+     * Used by the various key handlers
+     *
+     * @param string $str
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function extractSecret($str)
+    {
+        if (strlen($str) != 57) {
+            throw new \LengthException('Private Key should be 57-bytes long');
+        }
+        // 1.  Hash the 57-byte private key using SHAKE256(x, 114), storing the
+        //     digest in a 114-octet large buffer, denoted h.  Only the lower 57
+        //     bytes are used for generating the public key.
+        $hash = new Hash('shake256-912');
+        $h = $hash->hash($str);
+        $h = substr($h, 0, 57);
+        // 2.  Prune the buffer: The two least significant bits of the first
+        //     octet are cleared, all eight bits the last octet are cleared, and
+        //     the highest bit of the second to last octet is set.
+        $h[0] = $h[0] & chr(0xFC);
+        $h = strrev($h);
+        $h[0] = "\0";
+        $h[1] = $h[1] | chr(0x80);
+        // 3.  Interpret the buffer as the little-endian integer, forming a
+        //     secret scalar s.
+        $dA = new BigInteger($h, 256);
+        $dA = $this->factory->newInteger($dA);
+
+        $dA->secret = $str;
+        return $dA;
+    }
+
+    /**
+     * Encode a point as a string
+     *
+     * @param string $str
+     * @return string
+     */
+    public function encodePoint($point)
+    {
+        list($x, $y) = $point;
+        $y = "\0" . $y->toBytes();
+        if ($x->isOdd()) {
+            $y[0] = $y[0] | chr(0x80);
+        }
+        $y = strrev($y);
+
+        return $y;
+    }
+
+    /**
+     * Creates a random scalar multiplier
+     *
+     * @return \phpseclib\Math\PrimeField\Integer
+     */
+    public function createRandomMultiplier()
+    {
+        return $this->extractSecret(Random::string(57));
+    }
+
+    /**
+     * Converts an affine point to an extended homogeneous coordinate
+     *
+     * From https://tools.ietf.org/html/rfc8032#section-5.2.4 :
+     *
+     * A point (x,y) is represented in extended homogeneous coordinates (X, Y, Z, T),
+     * with x = X/Z, y = Y/Z, x * y = T/Z.
+     *
+     * @return \phpseclib\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (empty($p)) {
+            return [clone $this->zero, clone $this->one, clone $this->one];
+        }
+
+        if (isset($p[2])) {
+            return $p;
+        }
+
+        $p[2] = clone $this->one;
+
+        return $p;
+    }
+
+    /**
+     * Doubles a point on a curve
+     *
+     * @return FiniteField[]
+     */
+    public function doublePoint(array $p)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p)) {
+            return [];
+        }
+
+        if (!isset($p[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
+        }
+
+        // from https://tools.ietf.org/html/rfc8032#page-18
+
+        list($x1, $y1, $z1) = $p;
+
+        $b = $x1->add($y1);
+        $b = $b->multiply($b);
+        $c = $x1->multiply($x1);
+        $d = $y1->multiply($y1);
+        $e = $c->add($d);
+        $h = $z1->multiply($z1);
+        $j = $e->subtract($this->two->multiply($h));
+
+        $x3 = $b->subtract($e)->multiply($j);
+        $y3 = $c->subtract($d)->multiply($e);
+        $z3 = $e->multiply($j);
+
+        return [$x3, $y3, $z3];
+    }
+
+    /**
+     * Adds two points on the curve
+     *
+     * @return FiniteField[]
+     */
+    public function addPoint(array $p, array $q)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p) || !count($q)) {
+            if (count($q)) {
+                return $q;
+            }
+            if (count($p)) {
+                return $p;
+            }
+            return [];
+        }
+
+        if (!isset($p[2]) || !isset($q[2])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
+        }
+
+        if ($p[0]->equals($q[0])) {
+            return !$p[1]->equals($q[1]) ? [] : $this->doublePoint($p);
+        }
+
+        // from https://tools.ietf.org/html/rfc8032#page-17
+
+        list($x1, $y1, $z1) = $p;
+        list($x2, $y2, $z2) = $q;
+
+        $a = $z1->multiply($z2);
+        $b = $a->multiply($a);
+        $c = $x1->multiply($x2);
+        $d = $y1->multiply($y2);
+        $e = $this->d->multiply($c)->multiply($d);
+        $f = $b->subtract($e);
+        $g = $b->add($e);
+        $h = $x1->add($y1)->multiply($x2->add($y2));
+
+        $x3 = $a->multiply($f)->multiply($h->subtract($c)->subtract($d));
+        $y3 = $a->multiply($g)->multiply($d->subtract($c));
+        $z3 = $f->multiply($g);
+
+        return [$x3, $y3, $z3];
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP160r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP160r1.php
new file mode 100644
index 00000000..bc07369b
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP160r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP160r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP160r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('E95E4A5F737059DC60DFC7AD95B3D8139515620F', 16));
+        $this->setCoefficients(
+            new BigInteger('340E7BE2A280EB74E2BE61BADA745D97E8F7C300', 16),
+            new BigInteger('1E589A8595423412134FAA2DBDEC95C8D8675E58', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('BED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3', 16),
+            new BigInteger('1667CB477A1A8EC338F94741669C976316DA6321', 16)
+        );
+        $this->setOrder(new BigInteger('E95E4A5F737059DC60DF5991D45029409E60FC09', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP160t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP160t1.php
new file mode 100644
index 00000000..55ac37fa
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP160t1.php
@@ -0,0 +1,49 @@
+<?php
+
+/**
+ * brainpoolP160t1
+ *
+ * This curve is a twisted version of brainpoolP160r1 with A = -3. With brainpool,
+ * the curves ending in r1 are the "regular" curves and the curves ending in "t1"
+ * are the twisted version of the r1 curves. Per https://tools.ietf.org/html/rfc5639#page-7
+ * you can convert a point on an r1 curve to a point on a t1 curve thusly:
+ *
+ *     F(x,y) := (x*Z^2, y*Z^3)
+ *
+ * The advantage of A = -3 is that some of the point doubling and point addition can be
+ * slightly optimized. See http://hyperelliptic.org/EFD/g1p/auto-shortw-projective-3.html
+ * vs http://hyperelliptic.org/EFD/g1p/auto-shortw-projective.html for example.
+ *
+ * phpseclib does not currently take advantage of this optimization opportunity
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP160t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('E95E4A5F737059DC60DFC7AD95B3D8139515620F', 16));
+        $this->setCoefficients(
+            new BigInteger('E95E4A5F737059DC60DFC7AD95B3D8139515620C', 16), // eg. -3
+            new BigInteger('7A556B6DAE535B7B51ED2C4D7DAA7A0B5C55F380', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('B199B13B9B34EFC1397E64BAEB05ACC265FF2378', 16),
+            new BigInteger('ADD6718B7C7C1961F0991B842443772152C9E0AD', 16)
+        );
+        $this->setOrder(new BigInteger('E95E4A5F737059DC60DF5991D45029409E60FC09', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP192r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP192r1.php
new file mode 100644
index 00000000..c6308d4a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP192r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP192r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP192r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('C302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297', 16));
+        $this->setCoefficients(
+            new BigInteger('6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF', 16),
+            new BigInteger('469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('C0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD6', 16),
+            new BigInteger('14B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F', 16)
+        );
+        $this->setOrder(new BigInteger('C302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP192t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP192t1.php
new file mode 100644
index 00000000..89d8f0c2
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP192t1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP192t1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP192t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('C302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297', 16));
+        $this->setCoefficients(
+            new BigInteger('C302F41D932A36CDA7A3463093D18DB78FCE476DE1A86294', 16), // eg. -3
+            new BigInteger('13D56FFAEC78681E68F9DEB43B35BEC2FB68542E27897B79', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('3AE9E58C82F63C30282E1FE7BBF43FA72C446AF6F4618129', 16),
+            new BigInteger('097E2C5667C2223A902AB5CA449D0084B7E5B3DE7CCC01C9', 16)
+        );
+        $this->setOrder(new BigInteger('C302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP224r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP224r1.php
new file mode 100644
index 00000000..d74bddcc
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP224r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP224r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP224r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF', 16));
+        $this->setCoefficients(
+            new BigInteger('68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43', 16),
+            new BigInteger('2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('0D9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D', 16),
+            new BigInteger('58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD', 16)
+        );
+        $this->setOrder(new BigInteger('D7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP224t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP224t1.php
new file mode 100644
index 00000000..7293b693
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP224t1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP224t1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP224t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF', 16));
+        $this->setCoefficients(
+            new BigInteger('D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FC', 16), // eg. -3
+            new BigInteger('4B337D934104CD7BEF271BF60CED1ED20DA14C08B3BB64F18A60888D', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('6AB1E344CE25FF3896424E7FFE14762ECB49F8928AC0C76029B4D580', 16),
+            new BigInteger('0374E9F5143E568CD23F3F4D7C0D4B1E41C8CC0D1C6ABD5F1A46DB4C', 16)
+        );
+        $this->setOrder(new BigInteger('D7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP256r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP256r1.php
new file mode 100644
index 00000000..f9307800
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP256r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP256r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP256r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377', 16));
+        $this->setCoefficients(
+            new BigInteger('7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9', 16),
+            new BigInteger('26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262', 16),
+            new BigInteger('547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997', 16)
+        );
+        $this->setOrder(new BigInteger('A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP256t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP256t1.php
new file mode 100644
index 00000000..deef2eba
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP256t1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * brainpoolP256t1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP256t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377', 16));
+        $this->setCoefficients(
+            new BigInteger('A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5374', 16), // eg. -3
+            new BigInteger('662C61C430D84EA4FE66A7733D0B76B7BF93EBC4AF2F49256AE58101FEE92B04', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('A3E8EB3CC1CFE7B7732213B23A656149AFA142C47AAFBC2B79A191562E1305F4', 16),
+            new BigInteger('2D996C823439C56D7F7B22E14644417E69BCB6DE39D027001DABE8F35B25C9BE', 16)
+        );
+        $this->setOrder(new BigInteger('A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7', 16));
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP320r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP320r1.php
new file mode 100644
index 00000000..d9469a06
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP320r1.php
@@ -0,0 +1,42 @@
+<?php
+
+/**
+ * brainpoolP320r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP320r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F9' .
+                                        '2B9EC7893EC28FCD412B1F1B32E27', 16));
+        $this->setCoefficients(
+            new BigInteger('3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9F4' .
+                           '92F375A97D860EB4', 16),
+            new BigInteger('520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD88453981' .
+                           '6F5EB4AC8FB1F1A6', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('43BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599C7' .
+                           '10AF8D0D39E20611', 16),
+            new BigInteger('14FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6AC7' .
+                           'D35245D1692E8EE1', 16)
+        );
+        $this->setOrder(new BigInteger('D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D4' .
+                                       '82EC7EE8658E98691555B44C59311', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP320t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP320t1.php
new file mode 100644
index 00000000..54bb626a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP320t1.php
@@ -0,0 +1,42 @@
+<?php
+
+/**
+ * brainpoolP320t1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP320t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F9' .
+                                        '2B9EC7893EC28FCD412B1F1B32E27', 16));
+        $this->setCoefficients(
+            new BigInteger('D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC28' .
+                           'FCD412B1F1B32E24', 16), // eg. -3
+            new BigInteger('A7F561E038EB1ED560B3D147DB782013064C19F27ED27C6780AAF77FB8A547CE' .
+                           'B5B4FEF422340353', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('925BE9FB01AFC6FB4D3E7D4990010F813408AB106C4F09CB7EE07868CC136FFF' .
+                           '3357F624A21BED52', 16),
+            new BigInteger('63BA3A7A27483EBF6671DBEF7ABB30EBEE084E58A0B077AD42A5A0989D1EE71B' .
+                           '1B9BC0455FB0D2C3', 16)
+        );
+        $this->setOrder(new BigInteger('D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D4' .
+                                       '82EC7EE8658E98691555B44C59311', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP384r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP384r1.php
new file mode 100644
index 00000000..534f1c67
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP384r1.php
@@ -0,0 +1,48 @@
+<?php
+
+/**
+ * brainpoolP384r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP384r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger(
+            '8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A7' .
+            '1874700133107EC53', 16));
+        $this->setCoefficients(
+            new BigInteger(
+                '7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F90F8AA5814A503' .
+                'AD4EB04A8C7DD22CE2826', 16),
+            new BigInteger(
+                '4A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62D57CB4390295DB' .
+                'C9943AB78696FA504C11', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger(
+                '1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D' .
+                '646AAEF87B2E247D4AF1E', 16),
+            new BigInteger(
+                '8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E464621779' .
+                '1811142820341263C5315', 16)
+        );
+        $this->setOrder(new BigInteger(
+            '8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC31' .
+            '03B883202E9046565', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP384t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP384t1.php
new file mode 100644
index 00000000..85e1885a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP384t1.php
@@ -0,0 +1,48 @@
+<?php
+
+/**
+ * brainpoolP384t1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP384t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger(
+            '8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A7' .
+            '1874700133107EC53', 16));
+        $this->setCoefficients(
+            new BigInteger(
+                '8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901' .
+                'D1A71874700133107EC50', 16), // eg. -3
+            new BigInteger(
+                '7F519EADA7BDA81BD826DBA647910F8C4B9346ED8CCDC64E4B1ABD11756DCE1D2074AA263B8' .
+                '8805CED70355A33B471EE', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger(
+                '18DE98B02DB9A306F2AFCD7235F72A819B80AB12EBD653172476FECD462AABFFC4FF191B946' .
+                'A5F54D8D0AA2F418808CC', 16),
+            new BigInteger(
+                '25AB056962D30651A114AFD2755AD336747F93475B7A1FCA3B88F2B6A208CCFE469408584DC' .
+                '2B2912675BF5B9E582928', 16)
+        );
+        $this->setOrder(new BigInteger(
+            '8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC31' .
+            '03B883202E9046565', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP512r1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP512r1.php
new file mode 100644
index 00000000..140f6205
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP512r1.php
@@ -0,0 +1,48 @@
+<?php
+
+/**
+ * brainpoolP512r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP512r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger(
+            'AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC' .
+            '66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3', 16));
+        $this->setCoefficients(
+            new BigInteger(
+                '7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863BC2DED5D5AA82' .
+                '53AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA', 16),
+            new BigInteger(
+                '3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C' .
+                '1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger(
+                '81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D' .
+                '0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822', 16),
+            new BigInteger(
+                '7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5' .
+                'F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892', 16)
+        );
+        $this->setOrder(new BigInteger(
+            'AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA' .
+            '92619418661197FAC10471DB1D381085DDADDB58796829CA90069', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/brainpoolP512t1.php b/phpseclib/Crypt/ECDSA/Curves/brainpoolP512t1.php
new file mode 100644
index 00000000..50432b07
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/brainpoolP512t1.php
@@ -0,0 +1,48 @@
+<?php
+
+/**
+ * brainpoolP512t1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class brainpoolP512t1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger(
+            'AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC' .
+            '66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3', 16));
+        $this->setCoefficients(
+            new BigInteger(
+                'AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC' .
+                '66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F0', 16), // eg. -3
+            new BigInteger(
+                '7CBBBCF9441CFAB76E1890E46884EAE321F70C0BCB4981527897504BEC3E36A62BCDFA23049' .
+                '76540F6450085F2DAE145C22553B465763689180EA2571867423E', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger(
+                '640ECE5C12788717B9C1BA06CBC2A6FEBA85842458C56DDE9DB1758D39C0313D82BA51735CD' .
+                'B3EA499AA77A7D6943A64F7A3F25FE26F06B51BAA2696FA9035DA', 16),
+            new BigInteger(
+                '5B534BD595F5AF0FA2C892376C84ACE1BB4E3019B71634C01131159CAE03CEE9D9932184BEE' .
+                'F216BD71DF2DADF86A627306ECFF96DBB8BACE198B61E00F8B332', 16)
+        );
+        $this->setOrder(new BigInteger(
+            'AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA' .
+            '92619418661197FAC10471DB1D381085DDADDB58796829CA90069', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistb233.php b/phpseclib/Crypt/ECDSA/Curves/nistb233.php
new file mode 100644
index 00000000..db93276e
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistb233.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistb233
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistb233 extends sect233r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistb409.php b/phpseclib/Crypt/ECDSA/Curves/nistb409.php
new file mode 100644
index 00000000..79e1f2a9
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistb409.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistb409
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistb409 extends sect409r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistk163.php b/phpseclib/Crypt/ECDSA/Curves/nistk163.php
new file mode 100644
index 00000000..57bd4950
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistk163.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistk163
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistk163 extends sect163k1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistk233.php b/phpseclib/Crypt/ECDSA/Curves/nistk233.php
new file mode 100644
index 00000000..a6b1ab80
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistk233.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistk233
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistk233 extends sect233k1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistk283.php b/phpseclib/Crypt/ECDSA/Curves/nistk283.php
new file mode 100644
index 00000000..c4ce0f92
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistk283.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * sect283k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistk283 extends sect283k1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistk409.php b/phpseclib/Crypt/ECDSA/Curves/nistk409.php
new file mode 100644
index 00000000..03a56cb5
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistk409.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistk409
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistk409 extends sect409k1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistp192.php b/phpseclib/Crypt/ECDSA/Curves/nistp192.php
new file mode 100644
index 00000000..bcb9c7dd
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistp192.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistp192
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistp192 extends secp192r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistp224.php b/phpseclib/Crypt/ECDSA/Curves/nistp224.php
new file mode 100644
index 00000000..e7598e8a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistp224.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistp224
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistp224 extends secp224r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistp256.php b/phpseclib/Crypt/ECDSA/Curves/nistp256.php
new file mode 100644
index 00000000..73613bcb
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistp256.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistp256
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistp256 extends secp256r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistp384.php b/phpseclib/Crypt/ECDSA/Curves/nistp384.php
new file mode 100644
index 00000000..a30e88ee
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistp384.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistp384
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistp384 extends secp384r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistp521.php b/phpseclib/Crypt/ECDSA/Curves/nistp521.php
new file mode 100644
index 00000000..22a53758
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistp521.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistp521
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistp521 extends secp521r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/nistt571.php b/phpseclib/Crypt/ECDSA/Curves/nistt571.php
new file mode 100644
index 00000000..9f30686b
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/nistt571.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * nistt571
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class nistt571 extends sect571k1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime192v1.php b/phpseclib/Crypt/ECDSA/Curves/prime192v1.php
new file mode 100644
index 00000000..4a5ef8a6
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime192v1.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * prime192v1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class prime192v1 extends secp192r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime192v2.php b/phpseclib/Crypt/ECDSA/Curves/prime192v2.php
new file mode 100644
index 00000000..f3aa260f
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime192v2.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * prime192v2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class prime192v2 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC', 16),
+            new BigInteger('CC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('EEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A', 16),
+            new BigInteger('6574D11D69B6EC7A672BB82A083DF2F2B0847DE970B2DE15', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime192v3.php b/phpseclib/Crypt/ECDSA/Curves/prime192v3.php
new file mode 100644
index 00000000..4b0855d4
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime192v3.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * prime192v3
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class prime192v3 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC', 16),
+            new BigInteger('22123DC2395A05CAA7423DAECCC94760A7D462256BD56916', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896', 16),
+            new BigInteger('38A90F22637337334B49DCB66A6DC8F9978ACA7648A943B0', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime239v1.php b/phpseclib/Crypt/ECDSA/Curves/prime239v1.php
new file mode 100644
index 00000000..2ee69197
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime239v1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * prime239v1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class prime239v1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC', 16),
+            new BigInteger('6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('0FFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF', 16),
+            new BigInteger('7DEBE8E4E90A5DAE6E4054CA530BA04654B36818CE226B39FCCB7B02F1AE', 16)
+        );
+        $this->setOrder(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime239v2.php b/phpseclib/Crypt/ECDSA/Curves/prime239v2.php
new file mode 100644
index 00000000..4d32a2b6
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime239v2.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * prime239v2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class prime239v2 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC', 16),
+            new BigInteger('617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7', 16),
+            new BigInteger('5B0125E4DBEA0EC7206DA0FC01D9B081329FB555DE6EF460237DFF8BE4BA', 16)
+        );
+        $this->setOrder(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime239v3.php b/phpseclib/Crypt/ECDSA/Curves/prime239v3.php
new file mode 100644
index 00000000..0afbfee4
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime239v3.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * prime239v3
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class prime239v3 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC', 16),
+            new BigInteger('255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A', 16),
+            new BigInteger('1607E6898F390C06BC1D552BAD226F3B6FCFE48B6E818499AF18E3ED6CF3', 16)
+        );
+        $this->setOrder(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/prime256v1.php b/phpseclib/Crypt/ECDSA/Curves/prime256v1.php
new file mode 100644
index 00000000..29fb1ab4
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/prime256v1.php
@@ -0,0 +1,20 @@
+<?php
+
+/**
+ * prime256v1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+final class prime256v1 extends secp256r1
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp112r1.php b/phpseclib/Crypt/ECDSA/Curves/secp112r1.php
new file mode 100644
index 00000000..dfbabe89
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp112r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * secp112r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp112r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('DB7C2ABF62E35E668076BEAD208B', 16));
+        $this->setCoefficients(
+            new BigInteger('DB7C2ABF62E35E668076BEAD2088', 16),
+            new BigInteger('659EF8BA043916EEDE8911702B22', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('09487239995A5EE76B55F9C2F098', 16),
+            new BigInteger('A89CE5AF8724C0A23E0E0FF77500', 16)
+        );
+        $this->setOrder(new BigInteger('DB7C2ABF62E35E7628DFAC6561C5', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp112r2.php b/phpseclib/Crypt/ECDSA/Curves/secp112r2.php
new file mode 100644
index 00000000..f536a02b
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp112r2.php
@@ -0,0 +1,37 @@
+<?php
+
+/**
+ * secp112r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp112r2 extends Prime
+{
+    public function __construct()
+    {
+        // same modulo as secp112r1
+        $this->setModulo(new BigInteger('DB7C2ABF62E35E668076BEAD208B', 16));
+        $this->setCoefficients(
+            new BigInteger('6127C24C05F38A0AAAF65C0EF02C', 16),
+            new BigInteger('51DEF1815DB5ED74FCC34C85D709', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('4BA30AB5E892B4E1649DD0928643', 16),
+            new BigInteger('ADCD46F5882E3747DEF36E956E97', 16)
+        );
+        $this->setOrder(new BigInteger('36DF0AAFD8B8D7597CA10520D04B', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp128r1.php b/phpseclib/Crypt/ECDSA/Curves/secp128r1.php
new file mode 100644
index 00000000..b73eec7f
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp128r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * secp128r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp128r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC', 16),
+            new BigInteger('E87579C11079F43DD824993C2CEE5ED3', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('161FF7528B899B2D0C28607CA52C5B86', 16),
+            new BigInteger('CF5AC8395BAFEB13C02DA292DDED7A83', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFE0000000075A30D1B9038A115', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp128r2.php b/phpseclib/Crypt/ECDSA/Curves/secp128r2.php
new file mode 100644
index 00000000..18d92b0d
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp128r2.php
@@ -0,0 +1,37 @@
+<?php
+
+/**
+ * secp128r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp128r2 extends Prime
+{
+    public function __construct()
+    {
+        // same as secp128r1
+        $this->setModulo(new BigInteger('FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('D6031998D1B3BBFEBF59CC9BBFF9AEE1', 16),
+            new BigInteger('5EEEFCA380D02919DC2C6558BB6D8A5D', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('7B6AA5D85E572983E6FB32A7CDEBC140', 16),
+            new BigInteger('27B6916A894D3AEE7106FE805FC34B44', 16)
+        );
+        $this->setOrder(new BigInteger('3FFFFFFF7FFFFFFFBE0024720613B5A3', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp160k1.php b/phpseclib/Crypt/ECDSA/Curves/secp160k1.php
new file mode 100644
index 00000000..41acc4e7
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp160k1.php
@@ -0,0 +1,48 @@
+<?php
+
+/**
+ * secp160k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\KoblitzPrime;
+use phpseclib\Math\BigInteger;
+
+class secp160k1 extends KoblitzPrime
+{
+    public function __construct()
+    {
+        // same as secp160r2
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73', 16));
+        $this->setCoefficients(
+            new BigInteger('0000000000000000000000000000000000000000', 16),
+            new BigInteger('0000000000000000000000000000000000000007', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('3B4C382CE37AA192A4019E763036F4F5DD4D7EBB', 16),
+            new BigInteger('938CF935318FDCED6BC28286531733C3F03C4FEE', 16)
+        );
+        $this->setOrder(new BigInteger('0100000000000000000001B8FA16DFAB9ACA16B6B3', 16));
+
+        $this->basis = [];
+        $this->basis[] = [
+            'a' => new BigInteger('0096341F1138933BC2F505', -16),
+            'b' => new BigInteger('FF6E9D0418C67BB8D5F562', -16)
+        ];
+        $this->basis[] = [
+            'a' => new BigInteger('01BDCB3A09AAAABEAFF4A8', -16),
+            'b' => new BigInteger('04D12329FF0EF498EA67', -16)
+        ];
+        $this->beta = $this->factory->newInteger(new BigInteger('645B7345A143464942CC46D7CF4D5D1E1E6CBB68', -16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp160r1.php b/phpseclib/Crypt/ECDSA/Curves/secp160r1.php
new file mode 100644
index 00000000..175f5e8b
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp160r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * secp160r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp160r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC', 16),
+            new BigInteger('1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('4A96B5688EF573284664698968C38BB913CBFC82', 16),
+            new BigInteger('23A628553168947D59DCC912042351377AC5FB32', 16)
+        );
+        $this->setOrder(new BigInteger('0100000000000000000001F4C8F927AED3CA752257', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp160r2.php b/phpseclib/Crypt/ECDSA/Curves/secp160r2.php
new file mode 100644
index 00000000..fcf9591a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp160r2.php
@@ -0,0 +1,37 @@
+<?php
+
+/**
+ * secp160r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp160r2 extends Prime
+{
+    public function __construct()
+    {
+        // same as secp160k1
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70', 16),
+            new BigInteger('B4E134D3FB59EB8BAB57274904664D5AF50388BA', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('52DCB034293A117E1F4FF11B30F7199D3144CE6D', 16),
+            new BigInteger('FEAFFEF2E331F296E071FA0DF9982CFEA7D43F2E', 16)
+        );
+        $this->setOrder(new BigInteger('0100000000000000000000351EE786A818F3A1A16B', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp192k1.php b/phpseclib/Crypt/ECDSA/Curves/secp192k1.php
new file mode 100644
index 00000000..acc10f59
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp192k1.php
@@ -0,0 +1,47 @@
+<?php
+
+/**
+ * secp192k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\KoblitzPrime;
+use phpseclib\Math\BigInteger;
+
+class secp192k1 extends KoblitzPrime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37', 16));
+        $this->setCoefficients(
+            new BigInteger('000000000000000000000000000000000000000000000000', 16),
+            new BigInteger('000000000000000000000000000000000000000000000003', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D', 16),
+            new BigInteger('9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D', 16));
+
+        $this->basis = [];
+        $this->basis[] = [
+            'a' => new BigInteger('00B3FB3400DEC5C4ADCEB8655C', -16),
+            'b' => new BigInteger('8EE96418CCF4CFC7124FDA0F', -16)
+        ];
+        $this->basis[] = [
+            'a' => new BigInteger('01D90D03E8F096B9948B20F0A9', -16),
+            'b' => new BigInteger('42E49819ABBA9474E1083F6B', -16)
+        ];
+        $this->beta = $this->factory->newInteger(new BigInteger('447A96E6C647963E2F7809FEAAB46947F34B0AA3CA0BBA74', -16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp192r1.php b/phpseclib/Crypt/ECDSA/Curves/secp192r1.php
new file mode 100644
index 00000000..48ad6dcb
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp192r1.php
@@ -0,0 +1,80 @@
+<?php
+
+/**
+ * secp192r1
+ *
+ * This is the NIST P-192 curve
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp192r1 extends Prime
+{
+    public function __construct()
+    {
+        $modulo = new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF', 16);
+        $this->setModulo($modulo);
+
+        // algorithm 2.27 from http://diamond.boisestate.edu/~liljanab/MATH308/GuideToECC.pdf#page=66
+        /* in theory this should be faster than regular modular reductions save for one small issue.
+           to convert to / from base-2**8 with BCMath you have to call bcmul() and bcdiv() a lot.
+           to convert to / from base-2**8 with PHP64 you have to call base256_rshift() a lot.
+           in short, converting to / from base-2**8 is pretty expensive and that expense is
+           enough to offset whatever else might be gained by a simplified reduction algorithm.
+           now, if PHP supported unsigned integers things might be different. no bit-shifting
+           would be required for the PHP engine and it'd be a lot faster. but as is, BigInteger
+           uses base-2**31 or base-2**26 depending on whether or not the system is has a 32-bit
+           or a 64-bit OS.           
+        */
+        /*
+        $m_length = $this->getLengthInBytes();
+        $this->setReduction(function($c) use ($m_length) {
+            $cBytes = $c->toBytes();
+            $className = $this->className;
+
+            if (strlen($cBytes) > 2 * $m_length) {
+                list(, $r) = $c->divide($className::$modulo);
+                return $r;
+            }
+
+            $c = str_pad($cBytes, 48, "\0", STR_PAD_LEFT);
+            $c = array_reverse(str_split($c, 8));
+
+            $null = "\0\0\0\0\0\0\0\0";
+            $s1 = new BigInteger($c[2] . $c[1] . $c[0], 256);
+            $s2 = new BigInteger($null . $c[3] . $c[3], 256);
+            $s3 = new BigInteger($c[4] . $c[4] . $null, 256);
+            $s4 = new BigInteger($c[5] . $c[5] . $c[5], 256);
+
+            $r = $s1->add($s2)->add($s3)->add($s4);
+            while ($r->compare($className::$modulo) >= 0) {
+                $r = $r->subtract($className::$modulo);
+            }
+
+            return $r;
+        });
+        */
+
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC', 16),
+            new BigInteger('64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012', 16),
+            new BigInteger('07192B95FFC8DA78631011ED6B24CDD573F977A11E794811', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp224k1.php b/phpseclib/Crypt/ECDSA/Curves/secp224k1.php
new file mode 100644
index 00000000..e590ea0d
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp224k1.php
@@ -0,0 +1,47 @@
+<?php
+
+/**
+ * secp224k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\KoblitzPrime;
+use phpseclib\Math\BigInteger;
+
+class secp224k1 extends KoblitzPrime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D', 16));
+        $this->setCoefficients(
+            new BigInteger('00000000000000000000000000000000000000000000000000000000', 16),
+            new BigInteger('00000000000000000000000000000000000000000000000000000005', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C', 16),
+            new BigInteger('7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5', 16)
+        );
+        $this->setOrder(new BigInteger('010000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7', 16));
+
+        $this->basis = [];
+        $this->basis[] = [
+            'a' => new BigInteger('00B8ADF1378A6EB73409FA6C9C637D', -16),
+            'b' => new BigInteger('94730F82B358A3776A826298FA6F', -16)
+        ];
+        $this->basis[] = [
+            'a' => new BigInteger('01DCE8D2EC6184CAF0A972769FCC8B', -16),
+            'b' => new BigInteger('4D2100BA3DC75AAB747CCF355DEC', -16)
+        ];
+        $this->beta = $this->factory->newInteger(new BigInteger('01F178FFA4B17C89E6F73AECE2AAD57AF4C0A748B63C830947B27E04', -16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp224r1.php b/phpseclib/Crypt/ECDSA/Curves/secp224r1.php
new file mode 100644
index 00000000..21125546
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp224r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * secp224r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp224r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE', 16),
+            new BigInteger('B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21', 16),
+            new BigInteger('BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D', 16));
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp256k1.php b/phpseclib/Crypt/ECDSA/Curves/secp256k1.php
new file mode 100644
index 00000000..3d90d35f
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp256k1.php
@@ -0,0 +1,51 @@
+<?php
+
+/**
+ * secp256k1
+ *
+ * This is the curve used in Bitcoin
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+//use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Crypt\ECDSA\BaseCurves\KoblitzPrime;
+use phpseclib\Math\BigInteger;
+
+//class secp256k1 extends Prime
+class secp256k1 extends KoblitzPrime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F', 16));
+        $this->setCoefficients(
+            new BigInteger('0000000000000000000000000000000000000000000000000000000000000000', 16),
+            new BigInteger('0000000000000000000000000000000000000000000000000000000000000007', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141', 16));
+        $this->setBasePoint(
+            new BigInteger('79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798', 16),
+            new BigInteger('483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8', 16)
+        );
+
+        $this->basis = [];
+        $this->basis[] = [
+            'a' => new BigInteger('3086D221A7D46BCDE86C90E49284EB15', -16),
+            'b' => new BigInteger('FF1BBC8129FEF177D790AB8056F5401B3D', -16)
+        ];
+        $this->basis[] = [
+            'a' => new BigInteger('114CA50F7A8E2F3F657C1108D9D44CFD8', -16),
+            'b' => new BigInteger('3086D221A7D46BCDE86C90E49284EB15', -16)
+        ];
+        $this->beta = $this->factory->newInteger(new BigInteger('7AE96A2B657C07106E64479EAC3434E99CF0497512F58995C1396C28719501EE', -16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp256r1.php b/phpseclib/Crypt/ECDSA/Curves/secp256r1.php
new file mode 100644
index 00000000..67e162d8
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp256r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * secp256r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp256r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC', 16),
+            new BigInteger('5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296', 16),
+            new BigInteger('4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5', 16)
+        );
+        $this->setOrder(new BigInteger('FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551', 16));
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp384r1.php b/phpseclib/Crypt/ECDSA/Curves/secp384r1.php
new file mode 100644
index 00000000..f30bf24f
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp384r1.php
@@ -0,0 +1,54 @@
+<?php
+
+/**
+ * secp384r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp384r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger(
+            'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF',
+            16
+        ));
+        $this->setCoefficients(
+            new BigInteger(
+                'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC',
+                16
+            ),
+            new BigInteger(
+                'B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF',
+                16
+            )
+        );
+        $this->setBasePoint(
+            new BigInteger(
+                'AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7',
+                16
+            ),
+            new BigInteger(
+                '3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F',
+                16
+            )
+        );
+        $this->setOrder(new BigInteger(
+            'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973',
+            16
+        ));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/secp521r1.php b/phpseclib/Crypt/ECDSA/Curves/secp521r1.php
new file mode 100644
index 00000000..f37d59ef
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/secp521r1.php
@@ -0,0 +1,48 @@
+<?php
+
+/**
+ * secp521r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime;
+use phpseclib\Math\BigInteger;
+
+class secp521r1 extends Prime
+{
+    public function __construct()
+    {
+        $this->setModulo(new BigInteger('01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+                                        'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+                                        'FFFF', 16));
+        $this->setCoefficients(
+            new BigInteger('01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+                           'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+                           'FFFC', 16),
+            new BigInteger('0051953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF1' .
+                           '09E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B50' .
+                           '3F00', 16)
+        );
+        $this->setBasePoint(
+            new BigInteger('00C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D' .
+                           '3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5' .
+                           'BD66', 16),
+            new BigInteger('011839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E' .
+                           '662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD1' .
+                           '6650', 16)
+        );
+        $this->setOrder(new BigInteger('01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+                                       'FFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E9138' .
+                                       '6409', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect113r1.php b/phpseclib/Crypt/ECDSA/Curves/sect113r1.php
new file mode 100644
index 00000000..992b5945
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect113r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect113r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect113r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(113, 9, 0);
+        $this->setCoefficients(
+            '003088250CA6E7C7FE649CE85820F7',
+            '00E8BEE4D3E2260744188BE0E9C723'
+        );
+        $this->setBasePoint(
+            '009D73616F35F4AB1407D73562C10F',
+            '00A52830277958EE84D1315ED31886'
+        );
+        $this->setOrder(new BigInteger('0100000000000000D9CCEC8A39E56F', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect113r2.php b/phpseclib/Crypt/ECDSA/Curves/sect113r2.php
new file mode 100644
index 00000000..140b94f3
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect113r2.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect113r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect113r2 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(113, 9, 0);
+        $this->setCoefficients(
+            '00689918DBEC7E5A0DD6DFC0AA55C7',
+            '0095E9A9EC9B297BD4BF36E059184F'
+        );
+        $this->setBasePoint(
+            '01A57A6A7B26CA5EF52FCDB8164797',
+            '00B3ADC94ED1FE674C06E695BABA1D'
+        );
+        $this->setOrder(new BigInteger('010000000000000108789B2496AF93', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect131r1.php b/phpseclib/Crypt/ECDSA/Curves/sect131r1.php
new file mode 100644
index 00000000..ba41413a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect131r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect131r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect131r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(131, 8, 3, 2, 0);
+        $this->setCoefficients(
+            '07A11B09A76B562144418FF3FF8C2570B8',
+            '0217C05610884B63B9C6C7291678F9D341'
+        );
+        $this->setBasePoint(
+            '0081BAF91FDF9833C40F9C181343638399',
+            '078C6E7EA38C001F73C8134B1B4EF9E150'
+        );
+        $this->setOrder(new BigInteger('0400000000000000023123953A9464B54D', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect131r2.php b/phpseclib/Crypt/ECDSA/Curves/sect131r2.php
new file mode 100644
index 00000000..8b1d88bf
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect131r2.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect131r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect131r2 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(131, 8, 3, 2, 0);
+        $this->setCoefficients(
+            '03E5A88919D7CAFCBF415F07C2176573B2',
+            '04B8266A46C55657AC734CE38F018F2192'
+        );
+        $this->setBasePoint(
+            '0356DCD8F2F95031AD652D23951BB366A8',
+            '0648F06D867940A5366D9E265DE9EB240F'
+        );
+        $this->setOrder(new BigInteger('0400000000000000016954A233049BA98F', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect163k1.php b/phpseclib/Crypt/ECDSA/Curves/sect163k1.php
new file mode 100644
index 00000000..562eb144
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect163k1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect163k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect163k1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(163, 7, 6, 3, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000001',
+            '000000000000000000000000000000000000000001'
+        );
+        $this->setBasePoint(
+            '02FE13C0537BBC11ACAA07D793DE4E6D5E5C94EEE8',
+            '0289070FB05D38FF58321F2E800536D538CCDAA3D9'
+        );
+        $this->setOrder(new BigInteger('04000000000000000000020108A2E0CC0D99F8A5EF', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect163r1.php b/phpseclib/Crypt/ECDSA/Curves/sect163r1.php
new file mode 100644
index 00000000..634e300c
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect163r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect163r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect163r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(163, 7, 6, 3, 0);
+        $this->setCoefficients(
+            '07B6882CAAEFA84F9554FF8428BD88E246D2782AE2',
+            '0713612DCDDCB40AAB946BDA29CA91F73AF958AFD9'
+        );
+        $this->setBasePoint(
+            '0369979697AB43897789566789567F787A7876A654',
+            '00435EDB42EFAFB2989D51FEFCE3C80988F41FF883'
+        );
+        $this->setOrder(new BigInteger('03FFFFFFFFFFFFFFFFFFFF48AAB689C29CA710279B', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect163r2.php b/phpseclib/Crypt/ECDSA/Curves/sect163r2.php
new file mode 100644
index 00000000..87ec5afc
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect163r2.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect163r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect163r2 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(163, 7, 6, 3, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000001',
+            '020A601907B8C953CA1481EB10512F78744A3205FD'
+        );

+        $this->setBasePoint(
+            '03F0EBA16286A2D57EA0991168D4994637E8343E36',
+            '00D51FBC6C71A0094FA2CDD545B11C5C0C797324F1'
+        );
+        $this->setOrder(new BigInteger('040000000000000000000292FE77E70C12A4234C33', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect193r1.php b/phpseclib/Crypt/ECDSA/Curves/sect193r1.php
new file mode 100644
index 00000000..e424229c
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect193r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect193r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect193r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(193, 15, 0);
+        $this->setCoefficients(
+            '0017858FEB7A98975169E171F77B4087DE098AC8A911DF7B01',
+            '00FDFB49BFE6C3A89FACADAA7A1E5BBC7CC1C2E5D831478814'
+        );

+        $this->setBasePoint(
+            '01F481BC5F0FF84A74AD6CDF6FDEF4BF6179625372D8C0C5E1',
+            '0025E399F2903712CCF3EA9E3A1AD17FB0B3201B6AF7CE1B05'
+        );
+        $this->setOrder(new BigInteger('01000000000000000000000000C7F34A778F443ACC920EBA49', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect193r2.php b/phpseclib/Crypt/ECDSA/Curves/sect193r2.php
new file mode 100644
index 00000000..334d86db
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect193r2.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect193r2
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect193r2 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(193, 15, 0);
+        $this->setCoefficients(
+            '0163F35A5137C2CE3EA6ED8667190B0BC43ECD69977702709B',
+            '00C9BB9E8927D4D64C377E2AB2856A5B16E3EFB7F61D4316AE'
+        );

+        $this->setBasePoint(
+            '00D9B67D192E0367C803F39E1A7E82CA14A651350AAE617E8F',
+            '01CE94335607C304AC29E7DEFBD9CA01F596F927224CDECF6C'
+        );
+        $this->setOrder(new BigInteger('010000000000000000000000015AAB561B005413CCD4EE99D5', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect233k1.php b/phpseclib/Crypt/ECDSA/Curves/sect233k1.php
new file mode 100644
index 00000000..1e171f46
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect233k1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect233k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect233k1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(233, 74, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000000',
+            '000000000000000000000000000000000000000000000000000000000001'
+        );

+        $this->setBasePoint(
+            '017232BA853A7E731AF129F22FF4149563A419C26BF50A4C9D6EEFAD6126',
+            '01DB537DECE819B7F70F555A67C427A8CD9BF18AEB9B56E0C11056FAE6A3'
+        );
+        $this->setOrder(new BigInteger('8000000000000000000000000000069D5BB915BCD46EFB1AD5F173ABDF', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect233r1.php b/phpseclib/Crypt/ECDSA/Curves/sect233r1.php
new file mode 100644
index 00000000..066e7865
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect233r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect233r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect233r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(233, 74, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000001',
+            '0066647EDE6C332C7F8C0923BB58213B333B20E9CE4281FE115F7D8F90AD'
+        );

+        $this->setBasePoint(
+            '00FAC9DFCBAC8313BB2139F1BB755FEF65BC391F8B36F8F8EB7371FD558B',
+            '01006A08A41903350678E58528BEBF8A0BEFF867A7CA36716F7E01F81052'
+        );
+        $this->setOrder(new BigInteger('01000000000000000000000000000013E974E72F8A6922031D2603CFE0D7', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect239k1.php b/phpseclib/Crypt/ECDSA/Curves/sect239k1.php
new file mode 100644
index 00000000..92e00f6a
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect239k1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect239k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect239k1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(239, 158, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000000',
+            '000000000000000000000000000000000000000000000000000000000001'
+        );

+        $this->setBasePoint(
+            '29A0B6A887A983E9730988A68727A8B2D126C44CC2CC7B2A6555193035DC',
+            '76310804F12E549BDB011C103089E73510ACB275FC312A5DC6B76553F0CA'
+        );
+        $this->setOrder(new BigInteger('2000000000000000000000000000005A79FEC67CB6E91F1C1DA800E478A5', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect283k1.php b/phpseclib/Crypt/ECDSA/Curves/sect283k1.php
new file mode 100644
index 00000000..b4408009
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect283k1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect283k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect283k1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(283, 12, 7, 5, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000000000000000000',
+            '000000000000000000000000000000000000000000000000000000000000000000000001'
+        );

+        $this->setBasePoint(
+            '0503213F78CA44883F1A3B8162F188E553CD265F23C1567A16876913B0C2AC2458492836',
+            '01CCDA380F1C9E318D90F95D07E5426FE87E45C0E8184698E45962364E34116177DD2259'
+        );
+        $this->setOrder(new BigInteger('01FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE9AE2ED07577265DFF7F94451E061E163C61', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect283r1.php b/phpseclib/Crypt/ECDSA/Curves/sect283r1.php
new file mode 100644
index 00000000..090a6401
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect283r1.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * sect283r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect283r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(283, 12, 7, 5, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000000000000000001',
+            '027B680AC8B8596DA5A4AF8A19A0303FCA97FD7645309FA2A581485AF6263E313B79A2F5'
+        );

+        $this->setBasePoint(
+            '05F939258DB7DD90E1934F8C70B0DFEC2EED25B8557EAC9C80E2E198F8CDBECD86B12053',
+            '03676854FE24141CB98FE6D4B20D02B4516FF702350EDDB0826779C813F0DF45BE8112F4'
+        );
+        $this->setOrder(new BigInteger('03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEF90399660FC938A90165B042A7CEFADB307', 16));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect409k1.php b/phpseclib/Crypt/ECDSA/Curves/sect409k1.php
new file mode 100644
index 00000000..bdc779c9
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect409k1.php
@@ -0,0 +1,39 @@
+<?php
+
+/**
+ * sect409k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect409k1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(409, 87, 0);
+        $this->setCoefficients(
+            '00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000',
+            '00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001'
+        );

+        $this->setBasePoint(
+            '0060F05F658F49C1AD3AB1890F7184210EFD0987E307C84C27ACCFB8F9F67CC2C460189EB5AAAA62EE222EB1B35540CFE9023746',
+            '01E369050B7C4E42ACBA1DACBF04299C3460782F918EA427E6325165E9EA10E3DA5F6C42E9C55215AA9CA27A5863EC48D8E0286B'
+        );
+        $this->setOrder(new BigInteger(
+            '7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE5F' .
+            '83B2D4EA20400EC4557D5ED3E3E7CA5B4B5C83B8E01E5FCF', 16
+        ));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect409r1.php b/phpseclib/Crypt/ECDSA/Curves/sect409r1.php
new file mode 100644
index 00000000..86f5999d
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect409r1.php
@@ -0,0 +1,39 @@
+<?php
+
+/**
+ * sect409r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect409r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(409, 87, 0);
+        $this->setCoefficients(
+            '00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001',
+            '0021A5C2C8EE9FEB5C4B9A753B7B476B7FD6422EF1F3DD674761FA99D6AC27C8A9A197B272822F6CD57A55AA4F50AE317B13545F'
+        );

+        $this->setBasePoint(
+            '015D4860D088DDB3496B0C6064756260441CDE4AF1771D4DB01FFE5B34E59703DC255A868A1180515603AEAB60794E54BB7996A7',
+            '0061B1CFAB6BE5F32BBFA78324ED106A7636B9C5A7BD198D0158AA4F5488D08F38514F1FDF4B4F40D2181B3681C364BA0273C706'
+        );
+        $this->setOrder(new BigInteger(
+            '010000000000000000000000000000000000000000000000000001E2' .
+            'AAD6A612F33307BE5FA47C3C9E052F838164CD37D9A21173', 16
+        ));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect571k1.php b/phpseclib/Crypt/ECDSA/Curves/sect571k1.php
new file mode 100644
index 00000000..77a112c0
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect571k1.php
@@ -0,0 +1,43 @@
+<?php
+
+/**
+ * sect571k1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect571k1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(571, 10, 5, 2, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000000000000000000' .
+            '000000000000000000000000000000000000000000000000000000000000000000000000',
+            '000000000000000000000000000000000000000000000000000000000000000000000000' .
+            '000000000000000000000000000000000000000000000000000000000000000000000001'
+        );

+        $this->setBasePoint(
+            '026EB7A859923FBC82189631F8103FE4AC9CA2970012D5D46024804801841CA443709584' .
+            '93B205E647DA304DB4CEB08CBBD1BA39494776FB988B47174DCA88C7E2945283A01C8972',
+            '0349DC807F4FBF374F4AEADE3BCA95314DD58CEC9F307A54FFC61EFC006D8A2C9D4979C0' .
+            'AC44AEA74FBEBBB9F772AEDCB620B01A7BA7AF1B320430C8591984F601CD4C143EF1C7A3'
+        );
+        $this->setOrder(new BigInteger(
+            '020000000000000000000000000000000000000000000000000000000000000000000000' .
+            '131850E1F19A63E4B391A8DB917F4138B630D84BE5D639381E91DEB45CFE778F637C1001
', 16
+        ));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Curves/sect571r1.php b/phpseclib/Crypt/ECDSA/Curves/sect571r1.php
new file mode 100644
index 00000000..020d4d77
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Curves/sect571r1.php
@@ -0,0 +1,43 @@
+<?php
+
+/**
+ * sect571r1
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wiggint  on <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\ECDSA\Curves;
+
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary;
+use phpseclib\Math\BigInteger;
+
+class sect571r1 extends Binary
+{
+    public function __construct()
+    {
+        $this->setModulo(571, 10, 5, 2, 0);
+        $this->setCoefficients(
+            '000000000000000000000000000000000000000000000000000000000000000000000000' .
+            '000000000000000000000000000000000000000000000000000000000000000000000001',
+            '02F40E7E2221F295DE297117B7F3D62F5C6A97FFCB8CEFF1CD6BA8CE4A9A18AD84FFABBD' .
+            '8EFA59332BE7AD6756A66E294AFD185A78FF12AA520E4DE739BACA0C7FFEFF7F2955727A'
+        );

+        $this->setBasePoint(
+            '0303001D34B856296C16C0D40D3CD7750A93D1D2955FA80AA5F40FC8DB7B2ABDBDE53950' .
+            'F4C0D293CDD711A35B67FB1499AE60038614F1394ABFA3B4C850D927E1E7769C8EEC2D19',
+            '037BF27342DA639B6DCCFFFEB73D69D78C6C27A6009CBBCA1980F8533921E8A684423E43' .
+            'BAB08A576291AF8F461BB2A8B3531D2F0485C19B16E2F1516E23DD3C1A4827AF1B8AC15B'
+        );
+        $this->setOrder(new BigInteger(
+            '03FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+            'E661CE18FF55987308059B186823851EC7DD9CA1161DE93D5174D66E8382E9BB2FE84E47
', 16
+        ));
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Keys/Common.php b/phpseclib/Crypt/ECDSA/Keys/Common.php
new file mode 100644
index 00000000..196a3348
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/Common.php
@@ -0,0 +1,558 @@
+<?php
+
+/**
+ * Generic ECDSA Key Parsing Helper functions
+ *
+ * PHP version 5
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use ParagonIE\ConstantTime\Hex;
+use phpseclib\Crypt\ECDSA\BaseCurves\Base as BaseCurve;
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime as PrimeCurve;
+use phpseclib\Crypt\ECDSA\BaseCurves\Binary as BinaryCurve;
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+use phpseclib\Common\Functions\Strings;
+use phpseclib\Math\BigInteger;
+use phpseclib\Math\PrimeField;
+use phpseclib\File\ASN1;
+use phpseclib\File\ASN1\Maps;
+use phpseclib\Exception\UnsupportedCurveException;
+
+/**
+ * Generic ECDSA Key Parsing Helper functions
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+trait Common
+{
+    /**
+     * Curve OIDs
+     *
+     * @var array
+     */
+    private static $curveOIDs = [];
+
+    /**
+     * Child OIDs loaded
+     *
+     * @var bool
+     */
+    protected static $childOIDsLoaded = false;
+
+    /**
+     * Use Named Curves
+     *
+     * @var bool
+     */
+    private static $useNamedCurves = true;
+
+    /**
+     * Initialize static variables
+     */
+    private static function initialize_static_variables()
+    {
+        if (empty(self::$curveOIDs)) {
+            // the sec* curves are from the standards for efficient cryptography group
+            // sect* curves are curves over binary finite fields
+            // secp* curves are curves over prime finite fields
+            // sec*r* curves are regular curves; sec*k* curves are koblitz curves
+            // brainpool*r* curves are regular prime finite field curves
+            // brainpool*t* curves are twisted versions of the brainpool*r* curves
+            self::$curveOIDs = [
+                // from https://tools.ietf.org/html/rfc5915
+                'secp192r1' => '1.2.840.10045.3.1.1', // aka prime192v1
+                'sect163k1' => '1.3.132.0.1',
+                'sect163r2' => '1.3.132.0.15',
+                'secp224r1' => '1.3.132.0.33',
+                'sect233k1'=> '1.3.132.0.26',
+                'sect233r1'=> '1.3.132.0.27',
+                'secp256r1' => '1.2.840.10045.3.1.7', // aka prime256v1
+                'sect283k1' => '1.3.132.0.16',
+                'sect283r1' => '1.3.132.0.17',
+                'secp384r1' => '1.3.132.0.34',
+                'sect409k1' => '1.3.132.0.36',
+                'sect409r1' => '1.3.132.0.37',
+                'secp521r1' => '1.3.132.0.35',
+                'sect571k1' => '1.3.132.0.38',
+                'sect571r1' => '1.3.132.0.39',
+                // from http://www.secg.org/SEC2-Ver-1.0.pdf
+                'secp112r1' => '1.3.132.0.6',
+                'secp112r2' => '1.3.132.0.7',
+                'secp128r1' => '1.3.132.0.28',
+                'secp128r2' => '1.3.132.0.29',
+                'secp160k1' => '1.3.132.0.9',
+                'secp160r1' => '1.3.132.0.8',
+                'secp160r2' => '1.3.132.0.30',
+                'secp192k1' => '1.3.132.0.31',
+                'secp224k1' => '1.3.132.0.32',
+                'secp256k1' => '1.3.132.0.10',
+
+                'sect113r1' => '1.3.132.0.4',
+                'sect113r2' => '1.3.132.0.5',
+                'sect131r1' => '1.3.132.0.22',
+                'sect131r2' => '1.3.132.0.23',
+                'sect163r1' => '1.3.132.0.2',
+                'sect193r1' => '1.3.132.0.24',
+                'sect193r2' => '1.3.132.0.25',
+                'sect239k1' => '1.3.132.0.3',
+
+                // from http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.202.2977&rep=rep1&type=pdf#page=36
+                /*
+                'c2pnb163v1' => '1.2.840.10045.3.0.1', // J.4.1, example 1
+                'c2pnb163v2' => '1.2.840.10045.3.0.2', // J.4.1, example 2
+                'c2pnb163v3' => '1.2.840.10045.3.0.3', // J.4.1, example 3
+                'c2pnb172w1' => '1.2.840.10045.3.0.4', // J.4.2, example 1
+                'c2tnb191v1' => '1.2.840.10045.3.0.5', // J.4.3, example 1
+                'c2tnb191v2' => '1.2.840.10045.3.0.6', // J.4.3, example 2
+                'c2tnb191v3' => '1.2.840.10045.3.0.7', // J.4.3, example 3
+                'c2onb191v4' => '1.2.840.10045.3.0.8', // J.4.3, example 4
+                'c2onb191v5' => '1.2.840.10045.3.0.9', // J.4.3, example 5
+                'c2pnb208w1' => '1.2.840.10045.3.0.10', // J.4.4, example 1
+                'c2tnb239v1' => '1.2.840.10045.3.0.11', // J.4.5, example 1
+                'c2tnb239v2' => '1.2.840.10045.3.0.12', // J.4.5, example 2
+                'c2tnb239v3' => '1.2.840.10045.3.0.13', // J.4.5, example 3
+                'c2onb239v4' => '1.2.840.10045.3.0.14', // J.4.5, example 4
+                'c2onb239v5' => '1.2.840.10045.3.0.15', // J.4.5, example 5
+                'c2pnb272w1' => '1.2.840.10045.3.0.16', // J.4.6, example 1
+                'c2pnb304w1' => '1.2.840.10045.3.0.17', // J.4.7, example 1
+                'c2tnb359v1' => '1.2.840.10045.3.0.18', // J.4.8, example 1
+                'c2pnb368w1' => '1.2.840.10045.3.0.19', // J.4.9, example 1
+                'c2tnb431r1' => '1.2.840.10045.3.0.20', // J.4.10, example 1
+                */
+
+                'prime192v1' => '1.2.840.10045.3.1.1', // J.5.1, example 1 (aka secp192r1)
+                'prime192v2' => '1.2.840.10045.3.1.2', // J.5.1, example 2
+                'prime192v3' => '1.2.840.10045.3.1.3', // J.5.1, example 3
+                'prime239v1' => '1.2.840.10045.3.1.4', // J.5.2, example 1
+                'prime239v2' => '1.2.840.10045.3.1.5', // J.5.2, example 2
+                'prime239v3' => '1.2.840.10045.3.1.6', // J.5.2, example 3
+                'prime256v1' => '1.2.840.10045.3.1.7', // J.5.3, example 1 (aka secp256r1)
+
+                // https://tools.ietf.org/html/rfc5656#section-10
+                'nistp256' => '1.2.840.10045.3.1.7', // aka secp256r1
+                'nistp384' => '1.3.132.0.34', // aka secp384r1
+                'nistp521' => '1.3.132.0.35', // aka secp521r1
+
+                'nistk163' => '1.3.132.0.1', // aka sect163k1
+                'nistp192' => '1.2.840.10045.3.1.1', // aka secp192r1
+                'nistp224' => '1.3.132.0.33', // aka secp224r1
+                'nistk233' => '1.3.132.0.26', // aka sect233k1
+                'nistb233' => '1.3.132.0.27', // aka sect233r1
+                'nistk283' => '1.3.132.0.16', // aka sect283k1
+                'nistk409' => '1.3.132.0.36', // aka sect409k1
+                'nistb409' => '1.3.132.0.37', // aka sect409r1
+                'nistt571' => '1.3.132.0.38', // aka sect571k1
+
+                // http://www.ecc-brainpool.org/download/Domain-parameters.pdf
+                // https://tools.ietf.org/html/rfc5639
+                'brainpoolP160r1' => '1.3.36.3.3.2.8.1.1.1',
+                'brainpoolP160t1' => '1.3.36.3.3.2.8.1.1.2',
+                'brainpoolP192r1' => '1.3.36.3.3.2.8.1.1.3',
+                'brainpoolP192t1' => '1.3.36.3.3.2.8.1.1.4',
+                'brainpoolP224r1' => '1.3.36.3.3.2.8.1.1.5',
+                'brainpoolP224t1' => '1.3.36.3.3.2.8.1.1.6',
+                'brainpoolP256r1' => '1.3.36.3.3.2.8.1.1.7',
+                'brainpoolP256t1' => '1.3.36.3.3.2.8.1.1.8',
+                'brainpoolP320r1' => '1.3.36.3.3.2.8.1.1.9',
+                'brainpoolP320t1' => '1.3.36.3.3.2.8.1.1.10',
+                'brainpoolP384r1' => '1.3.36.3.3.2.8.1.1.11',
+                'brainpoolP384t1' => '1.3.36.3.3.2.8.1.1.12',
+                'brainpoolP512r1' => '1.3.36.3.3.2.8.1.1.13',
+                'brainpoolP512t1' => '1.3.36.3.3.2.8.1.1.14'
+            ];
+            ASN1::loadOIDs([
+                'prime-field' => '1.2.840.10045.1.1',
+                'characteristic-two-field' => '1.2.840.10045.1.2',
+                'characteristic-two-basis' => '1.2.840.10045.1.2.3',
+                // per http://www.secg.org/SEC1-Ver-1.0.pdf#page=84, gnBasis "not used here"
+                'gnBasis' => '1.2.840.10045.1.2.3.1', // NULL
+                'tpBasis' => '1.2.840.10045.1.2.3.2', // Trinomial
+                'ppBasis' => '1.2.840.10045.1.2.3.3'  // Pentanomial
+            ] + self::$curveOIDs);
+        }
+    }
+
+    /**
+     * Explicitly set the curve
+     *
+     * If the key contains an implicit curve phpseclib needs the curve
+     * to be explicitly provided
+     *
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     */
+    public static function setImplicitCurve(BaseCurve $curve)
+    {
+        self::$implicitCurve = $curve;
+    }
+
+    /**
+     * Returns an instance of \phpseclib\Crypt\ECDSA\BaseCurves\Base based
+     * on the curve parameters
+     *
+     * @param array $params
+     * @return \phpseclib\Crypt\ECDSA\BaseCurves\Base|false
+     */
+    protected static function loadCurveByParam(array $params)
+    {
+        if (count($params) > 1) {
+            throw new \RuntimeException('No parameters are present');
+        }
+        if (isset($params['namedCurve'])) {
+            $curve = '\phpseclib\Crypt\ECDSA\Curves\\' . $params['namedCurve'];
+            if (!class_exists($curve)) {
+                throw new UnsupportedCurveException('Named Curve of ' . $params['namedCurve'] . ' is not supported');
+            }
+            return new $curve();
+        }
+        if (isset($params['implicitCurve'])) {
+            if (!isset(self::$implicitCurve)) {
+                throw new \RuntimeException('Implicit curves can be provided by calling setImplicitCurve');
+            }
+            return self::$implicitCurve;
+        }
+        if (isset($params['specifiedCurve'])) {
+            $data = $params['specifiedCurve'];
+            switch ($data['fieldID']['fieldType']) {
+                case 'prime-field':
+                    $curve = new PrimeCurve();
+                    $curve->setModulo($data['fieldID']['parameters']);
+                    $curve->setCoefficients(
+                        new BigInteger($data['curve']['a'], 256),
+                        new BigInteger($data['curve']['b'], 256)
+                    );
+                    $point = self::extractPoint("\0" . $data['base'], $curve);
+                    $curve->setBasePoint(...$point);
+                    $curve->setOrder($data['order']);
+                    return $curve;
+                case 'characteristic-two-field':
+                    $curve = new BinaryCurve();
+                    $params = ASN1::decodeBER($data['fieldID']['parameters']);
+                    $params = ASN1::asn1map($params[0], Maps\Characteristic_two::MAP);
+                    $modulo = [(int) $params['m']->toString()];
+                    switch ($params['basis']) {
+                        case 'tpBasis':
+                            $modulo[] = (int) $params['parameters']->toString();
+                            break;
+                        case 'ppBasis':
+                            $temp = ASN1::decodeBER($params['parameters']);
+                            $temp = ASN1::asn1map($temp[0], Maps\Pentanomial::MAP);
+                            $modulo[] = (int) $temp['k3']->toString();
+                            $modulo[] = (int) $temp['k2']->toString();
+                            $modulo[] = (int) $temp['k1']->toString();
+                    }
+                    $modulo[] = 0;
+                    $curve->setModulo(...$modulo);
+                    $len = ceil($modulo[0] / 8);
+                    $curve->setCoefficients(
+                        Hex::encode($data['curve']['a']),
+                        Hex::encode($data['curve']['b'])
+                    );
+                    $point = self::extractPoint("\0" . $data['base'], $curve);
+                    $curve->setBasePoint(...$point);
+                    $curve->setOrder($data['order']);
+                    return $curve;
+                default:
+                    throw new UnsupportedCurveException('Field Type of ' . $data['fieldID']['fieldType'] . ' is not supported');
+            }
+        }
+        throw new \RuntimeException('No valid parameters are present');
+    }
+
+    /**
+     * Extract points from a string
+     *
+     * Supports both compressed and uncompressed points
+     *
+     * @param string $str
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @return object[]
+     */
+    public static function extractPoint($str, BaseCurve $curve)
+    {
+        if ($curve instanceof TwistedEdwardsCurve) {
+            // first step of point deciding as discussed at the following URL's:
+            // https://tools.ietf.org/html/rfc8032#section-5.1.3
+            // https://tools.ietf.org/html/rfc8032#section-5.2.3
+            $y = $str;
+            $y = strrev($y);
+            $sign = (bool) (ord($y[0]) & 0x80);
+            $y[0] = $y[0] & chr(0x7F);
+            $y = new BigInteger($y, 256);
+            if ($y->compare($curve->getModulo()) >= 0) {
+                throw new \RuntimeException('The Y coordinate should not be >= the modulo');
+            }
+            $point = $curve->recoverX($y, $sign);
+            if (!$curve->verifyPoint($point)) {
+                throw new \RuntimeException('Unable to verify that point exists on curve');
+            }
+            return $point;
+        }
+
+        // the first byte of a bit string represents the number of bits in the last byte that are to be ignored but,
+        // currently, bit strings wanting a non-zero amount of bits trimmed are not supported
+        if (($val = Strings::shift($str)) != "\0") {
+            throw new \UnexpectedValueException('extractPoint expects the first byte to be null - not ' . Hex::encode($val));
+        }
+        if ($str == "\0") {
+            return [];
+        }
+
+        $keylen = strlen($str);
+        $order = $curve->getLengthInBytes();
+        // point compression is being used
+        if ($keylen == $order + 1) {
+            return $curve->derivePoint($str);
+        }
+
+        // point compression is not being used
+        if ($keylen == 2 * $order + 1) {
+            preg_match("#(.)(.{{$order}})(.{{$order}})#s", $str, $matches);
+            list(, $w, $x, $y) = $matches;
+            if ($w != "\4") {
+                throw new \UnexpectedValueException('The first byte of an uncompressed point should be 04 - not ' . Hex::encode($val));
+            }
+            $point = [
+                $curve->convertInteger(new BigInteger($x, 256)),
+                $curve->convertInteger(new BigInteger($y, 256))
+            ];
+
+            if (!$curve->verifyPoint($point)) {
+                throw new \RuntimeException('Unable to verify that point exists on curve');
+            }
+
+            return $point;
+        }
+
+        throw new \UnexpectedValueException('The string representation of the points is not of an appropriate length');
+    }
+
+    /**
+     * Encode Parameters
+     *
+     * @todo Maybe at some point this could be moved to __toString() for each of the curves?
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param bool $returnArray
+     * @return string|false
+     */
+    private static function encodeParameters(BaseCurve $curve, $returnArray = false)
+    {
+        $reflect = new \ReflectionClass($curve);
+        $name = $reflect->getShortName();
+        if (isset(self::$curveOIDs[$name]) && self::$useNamedCurves) {
+            return $returnArray ?
+                ['namedCurve' => $name] :
+                ASN1::encodeDER(['namedCurve' => $name], Maps\ECParameters::MAP);
+        }
+        if (self::$useNamedCurves) {
+            foreach (new \DirectoryIterator(__DIR__ . '/../Curves/') as $file) {
+                if ($file->getExtension() != 'php') {
+                    continue;
+                }
+                $testName = $file->getBasename('.php');
+                $class = 'phpseclib\Crypt\ECDSA\Curves\\' . $testName;
+                $reflect = new \ReflectionClass($class);
+                if ($reflect->isFinal()) {
+                    continue;
+                }
+                $candidate = new $class();
+                switch ($name) {
+                    case 'Prime':
+                        if (!$candidate instanceof PrimeCurve) {
+                            break;
+                        }
+                        if (!$candidate->getModulo()->equals($curve->getModulo())) {
+                            break;
+                        }
+                        if ($candidate->getA()->toBytes() != $curve->getA()->toBytes()) {
+                            break;
+                        }
+                        if ($candidate->getB()->toBytes() != $curve->getB()->toBytes()) {
+                            break;
+                        }
+
+                        list($candidateX, $candidateY) = $candidate->getBasePoint();
+                        list($curveX, $curveY) = $curve->getBasePoint();
+                        if ($candidateX->toBytes() != $curveX->toBytes()) {
+                            break;
+                        }
+                        if ($candidateY->toBytes() != $curveY->toBytes()) {
+                            break;
+                        }
+
+                        return $returnArray ?
+                            ['namedCurve' => $testName] :
+                            ASN1::encodeDER(['namedCurve' => $testName], Maps\ECParameters::MAP);
+                    case 'Binary':
+                        if (!$candidate instanceof BinaryCurve) {
+                            break;
+                        }
+                        if ($candidate->getModulo() != $curve->getModulo()) {
+                            break;
+                        }
+                        if ($candidate->getA()->toBytes() != $curve->getA()->toBytes()) {
+                            break;
+                        }
+                        if ($candidate->getB()->toBytes() != $curve->getB()->toBytes()) {
+                            break;
+                        }
+
+                        list($candidateX, $candidateY) = $candidate->getBasePoint();
+                        list($curveX, $curveY) = $curve->getBasePoint();
+                        if ($candidateX->toBytes() != $curveX->toBytes()) {
+                            break;
+                        }
+                        if ($candidateY->toBytes() != $curveY->toBytes()) {
+                            break;
+                        }
+
+                        return $returnArray ?
+                            ['namedCurve' => $testName] :
+                            ASN1::encodeDER(['namedCurve' => $testName], Maps\ECParameters::MAP);
+                }
+            }
+        }
+
+        $order = $curve->getOrder();
+        // we could try to calculate the order thusly:
+        // https://crypto.stackexchange.com/a/27914/4520
+        // https://en.wikipedia.org/wiki/Schoof%E2%80%93Elkies%E2%80%93Atkin_algorithm
+        if (!$order) {
+            throw new \RuntimeException('Specified Curves need the order to be specified');
+        }
+        $point = $curve->getBasePoint();
+        $x = $point[0]->toBytes();
+        $y = $point[1]->toBytes();
+
+        if ($curve instanceof PrimeCurve) {
+            /*
+             * valid versions are:
+             *
+             * ecdpVer1:
+             *   - neither the curve or the base point are generated verifiably randomly.
+             * ecdpVer2:
+             *   - curve and base point are generated verifiably at random and curve.seed is present
+             * ecdpVer3: 
+             *   - base point is generated verifiably at random but curve is not. curve.seed is present
+             */
+            // other (optional) parameters can be calculated using the methods discused at
+            // https://crypto.stackexchange.com/q/28947/4520
+            $data = [
+                'version' => 'ecdpVer1',
+                'fieldID' => [
+                    'fieldType' => 'prime-field',
+                    'parameters' => $curve->getModulo()
+                ],
+                'curve' => [
+                    'a' => $curve->getA()->toBytes(),
+                    'b' => $curve->getB()->toBytes()
+                ],
+                'base' => "\4" . $x . $y,
+                'order' => $order
+            ];
+
+            return $returnArray ?
+                ['specifiedCurve' => $data] :
+                ASN1::encodeDER(['specifiedCurve' => $data], Maps\ECParameters::MAP);
+        }
+        if ($curve instanceof BinaryCurve) {
+            $modulo = $curve->getModulo();
+            $basis = count($modulo);
+            $m = array_shift($modulo);
+            array_pop($modulo); // the last parameter should always be 0
+            //rsort($modulo);
+            switch ($basis) {
+                case 3:
+                    $basis = 'tpBasis';
+                    $modulo = new BigInteger($modulo[0]);
+                    break;
+                case 5:
+                    $basis = 'ppBasis';
+                    // these should be in strictly ascending order (hence the commented out rsort above)
+                    $modulo = [
+                        'k1' => new BigInteger($modulo[2]),
+                        'k2' => new BigInteger($modulo[1]),
+                        'k3' => new BigInteger($modulo[0])
+                    ];
+                    $modulo = ASN1::encodeDER($modulo, Maps\Pentanomial::MAP);
+                    $modulo = new ASN1\Element($modulo);
+            }
+            $params = ASN1::encodeDER([
+                'm' => new BigInteger($m),
+                'basis' => $basis,
+                'parameters' => $modulo
+            ], Maps\Characteristic_two::MAP);
+            $params = new ASN1\Element($params);
+            $a = ltrim($curve->getA()->toBytes(), "\0");
+            if (!strlen($a)) {
+                $a = "\0";
+            }
+            $b = ltrim($curve->getB()->toBytes(), "\0");
+            if (!strlen($b)) {
+                $b = "\0";
+            }
+            $data = [
+                'version' => 'ecdpVer1',
+                'fieldID' => [
+                    'fieldType' => 'characteristic-two-field',
+                    'parameters' => $params
+                ],
+                'curve' => [
+                    'a' => $a,
+                    'b' => $b
+                ],
+                'base' => "\4" . $x . $y,
+                'order' => $order
+            ];
+
+            return $returnArray ?
+                ['specifiedCurve' => $data] :
+                ASN1::encodeDER(['specifiedCurve' => $data], Maps\ECParameters::MAP);
+        }
+
+        throw new UnsupportedCurveException('Curve cannot be serialized');
+    }
+
+    /**
+     * Use Specified Curve
+     *
+     * A specified curve has all the coefficients, the base points, etc, explicitely included.
+     * A specified curve is a more verbose way of representing a curve
+     */
+    public static function useSpecifiedCurve()
+    {
+        self::$useNamedCurves = false;
+    }
+
+    /**
+     * Use Named Curve
+     *
+     * A named curve does not include any parameters. It is up to the ECDSA parameters to
+     * know what the coefficients, the base points, etc, are from the name of the curve.
+     * A named curve is a more concise way of representing a curve
+     */
+    public static function useNamedCurve()
+    {
+        self::$useNamedCurves = true;
+    }
+
+    /**
+     * Returns true if named curves are being used by default
+     *
+     * If a named curve is not being used by default than specified curves are being utilized
+     */
+    public static function isUsingNamedCurves()
+    {
+        return self::$useNamedCurves;
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/ECDSA/Keys/OpenSSH.php b/phpseclib/Crypt/ECDSA/Keys/OpenSSH.php
new file mode 100644
index 00000000..7027acd8
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/OpenSSH.php
@@ -0,0 +1,275 @@
+<?php
+
+/**
+ * OpenSSH Formatted ECDSA Key Handler
+ *
+ * PHP version 5
+ *
+ * Place in $HOME/.ssh/authorized_keys
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use ParagonIE\ConstantTime\Base64;
+use phpseclib\Math\BigInteger;
+use phpseclib\Common\Functions\Strings;
+use phpseclib\Crypt\Common\Keys\OpenSSH as Progenitor;
+use phpseclib\Crypt\ECDSA\BaseCurves\Base as BaseCurve;
+use phpseclib\Exception\UnsupportedCurveException;
+use phpseclib\Crypt\ECDSA\Curves\Ed25519;
+use phpseclib\Math\Common\FiniteField\Integer;
+use phpseclib\Crypt\Random;
+
+/**
+ * OpenSSH Formatted ECDSA Key Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class OpenSSH extends Progenitor
+{
+    use Common;
+
+    /**
+     * Supported Key Types
+     *
+     * @var array
+     */
+    private static $types = [
+        'ecdsa-sha2-nistp256',
+        'ecdsa-sha2-nistp384',
+        'ecdsa-sha2-nistp521',
+        'ssh-ed25519'
+    ];
+
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @access public
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        /*
+           key format is described here:
+           https://cvsweb.openbsd.org/cgi-bin/cvsweb/src/usr.bin/ssh/PROTOCOL.key?annotate=HEAD
+
+           this is only supported for ECDSA because of Ed25519. ssh-keygen doesn't generate a
+           PKCS1/8 formatted private key for Ed25519 - it generates an OpenSSH formatted
+           private key. probably because, at the time of this writing, there's not an actual
+           IETF RFC describing an Ed25519 format
+        */
+        if (strpos($key, 'BEGIN OPENSSH PRIVATE KEY') !== false) {
+            $key = preg_replace('#(?:^-.*?-[\r\n]*$)|\s#ms', '', $key);
+            $key = Base64::decode($key);
+            $magic = Strings::shift($key, 15);
+            if ($magic != "openssh-key-v1\0") {
+                throw new \RuntimeException('Expected openssh-key-v1');
+            }
+            list($ciphername, $kdfname, $kdfoptions, $numKeys) = Strings::unpackSSH2('sssN', $key);
+            if ($numKeys != 1) {
+                throw new \RuntimeException('Although the OpenSSH private key format supports multiple keys phpseclib does not');
+            }
+            if (strlen($kdfoptions) || $kdfname != 'none' || $ciphername != 'none') {
+                /*
+                  OpenSSH private keys use a customized version of bcrypt. specifically, instead of encrypting
+                  OrpheanBeholderScryDoubt 64 times OpenSSH's bcrypt variant encrypts
+                  OxychromaticBlowfishSwatDynamite 64 times. so we can't use crypt().
+
+                  bcrypt is basically Blowfish with an altered key expansion. whereas Blowfish just runs the
+                  key through the key expansion bcrypt interleaves the key expansion with the salt and
+                  password. this renders openssl / mcrypt unusuable. this forces us to use a pure-PHP implementation
+                  of bcrypt. the problem with that is that pure-PHP is too slow to be practically useful.
+
+                  in addition to encrypting a different string 64 times the OpenSSH also performs bcrypt from
+                  scratch $rounds times. calling crypt() 64x with bcrypt takes 0.7s. PHP is going to be naturally
+                  slower. pure-PHP is 215x slower than OpenSSL for AES and pure-PHP is 43x slower for bcrypt.
+                  43 * 0.7 = 30s. no one wants to wait 30s to load a private key.
+
+                  another way to think about this..  according to wikipedia's article on Blowfish,
+                  "Each new key requires pre-processing equivalent to encrypting about 4 kilobytes of text".
+                  key expansion is done (9+64*2)*160 times. multiply that by 4 and it turns out that Blowfish,
+                  OpenSSH style, is the equivalent of encrypting ~80mb of text.
+
+                  more supporting evidence: sodium_compat does not implement Argon2 (another password hashing
+                  algorithm) because "It's not feasible to polyfill scrypt or Argon2 into PHP and get reasonable
+                  performance. Users would feel motivated to select parameters that downgrade security to avoid
+                  denial of service (DoS) attacks. The only winning move is not to play"
+                    -- https://github.com/paragonie/sodium_compat/blob/master/README.md
+                */
+                throw new \RuntimeException('Encrypted OpenSSH private keys are not supported');
+                //list($salt, $rounds) = Strings::unpackSSH2('sN', $kdfoptions);
+            }
+
+            list($publicKey, $paddedKey) = Strings::unpackSSH2('ss', $key);
+            list($type, $publicKey) = Strings::unpackSSH2('ss', $publicKey);
+            if ($type != 'ssh-ed25519') {
+                throw new UnsupportedCurveException('ssh-ed25519 is the only supported curve for OpenSSH public keys');
+            }
+            list($checkint1, $checkint2, $type, $publicKey2, $privateKey, $comment) = Strings::unpackSSH2('NNssss', $paddedKey);
+            // any leftover bytes in $paddedKey are for padding? but they should be sequential bytes. eg. 1, 2, 3, etc.
+            if ($checkint1 != $checkint2) {
+                throw new \RuntimeException('The two checkints do not match');
+            }
+            if ($type != 'ssh-ed25519') {
+                throw new UnsupportedCurveException('ssh-ed25519 is the only supported curve for OpenSSH private keys');
+            }
+            if ($publicKey != $publicKey2 || $publicKey2 != substr($privateKey, 32)) {
+                throw new \RuntimeException('The public keys do not match up');
+            }
+            $privateKey = substr($privateKey, 0, 32);
+            $curve = new Ed25519();
+            return [
+                'curve' => $curve,
+                'dA' => $curve->extractSecret($privateKey),
+                'QA' => self::extractPoint($publicKey, $curve),
+                'comment' => $comment
+            ];
+        }
+
+        $parts = explode(' ', $key, 3);
+
+        if (!isset($parts[1])) {
+            $key = Base64::decode($parts[0]);
+            $comment = isset($parts[1]) ? $parts[1] : false;
+        } else {
+            $asciiType = $parts[0];
+            if (!in_array($asciiType, self::$types)) {
+                throw new \RuntimeException('Keys of type ' . $asciiType . ' are not supported');
+            }
+            $key = Base64::decode($parts[1]);
+            $comment = isset($parts[2]) ? $parts[2] : false;
+        }
+
+        list($binaryType) = Strings::unpackSSH2('s', $key);
+        if (isset($asciiType) && $asciiType != $binaryType) {
+            throw new \RuntimeException('Two different types of keys are claimed: ' . $asciiType . ' and ' . $binaryType);
+        } elseif (!isset($asciiType) && !in_array($binaryType, self::$types)) {
+            throw new \RuntimeException('Keys of type ' . $binaryType . ' are not supported');
+        }
+
+        if ($binaryType == 'ssh-ed25519') {
+            if (Strings::shift($key, 4) != "\0\0\0\x20") {
+                throw new \RuntimeException('Length of ssh-ed25519 key should be 32');
+            }
+
+            $curve = new Ed25519();
+            $qa = self::extractPoint($key, $curve);
+        } else {
+            list($curveName, $publicKey) = Strings::unpackSSH2('ss', $key);
+            $curveName = '\phpseclib\Crypt\ECDSA\Curves\\' . $curveName;
+            $curve = new $curveName();
+
+            $qa = self::extractPoint("\0" . $publicKey, $curve);
+        }
+
+        return [
+            'curve' => $curve,
+            'QA' => $qa,
+            'comment' => $comment
+        ];
+    }
+
+    /**
+     * Convert an ECDSA public key to the appropriate format
+     *
+     * @access public
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @return string
+     */
+    public static function savePublicKey(BaseCurve $curve, array $publicKey)
+    {
+        if ($curve instanceof Ed25519) {
+            $key = Strings::packSSH2('ss', 'ssh-ed25519', $curve->encodePoint($publicKey));
+            $key = 'ssh-ed25519 ' . Base64::encode($key) . ' ' . self::$comment;
+            return $key;
+        }
+
+        self::initialize_static_variables();
+
+        $reflect = new \ReflectionClass($curve);
+        $name = $reflect->getShortName();
+
+        $oid = self::$curveOIDs[$name];
+        $aliases = array_filter(self::$curveOIDs, function($v) use ($oid) {
+            return $v == $oid;
+        });
+        $aliases = array_keys($aliases);
+
+        for ($i = 0; $i < count($aliases); $i++) {
+            if (in_array('ecdsa-sha2-' . $aliases[$i], self::$types)) {
+                $alias = $aliases[$i];
+                break;
+            }
+        }
+
+        if (!isset($alias)) {
+            throw new UnsupportedCurveException($name . ' is not a curve that the OpenSSH plugin supports');
+        }
+
+        $points = "\4" . $publicKey[0]->toBytes() . $publicKey[1]->toBytes();
+        $key = Strings::packSSH2('sss', 'ecdsa-sha2-' . $alias, $alias, $points);
+
+        if (self::$binary) {
+            return $key;
+        }
+
+        $key = 'ecdsa-sha2-' . $alias . ' ' . Base64::encode($key) . ' ' . self::$comment;
+
+        return $key;
+    }
+
+    /**
+     * Convert a private key to the appropriate format.
+     *
+     * @access public
+     * @param \phpseclib\Math\Common\FiniteField\Integer $privateKey
+     * @param \phpseclib\Crypt\ECDSA\Curves\Ed25519 $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @param string $password optional
+     * @return string
+     */
+    public static function savePrivateKey(Integer $privateKey, Ed25519 $curve, array $publicKey, $password = '')
+    {
+        if (!isset($privateKey->secret)) {
+            throw new \RuntimeException('Private Key does not have a secret set');
+        }
+        if (strlen($privateKey->secret) != 32) {
+            throw new \RuntimeException('Private Key secret is not of the correct length');
+        }
+
+        list(, $checkint) = unpack('N', Random::string(4));
+        $pubKey = $curve->encodePoint($publicKey);
+
+        $publicKey = Strings::packSSH2('ss', 'ssh-ed25519', $pubKey);
+        $paddedKey = Strings::packSSH2('NNssss', $checkint, $checkint, 'ssh-ed25519', $pubKey, $privateKey->secret . $pubKey, self::$comment);
+        /*
+           from http://tools.ietf.org/html/rfc4253#section-6 :
+
+           Note that the length of the concatenation of 'packet_length',
+           'padding_length', 'payload', and 'random padding' MUST be a multiple
+           of the cipher block size or 8, whichever is larger.
+         */
+        $paddingLength = (7 * strlen($paddedKey)) % 8;
+        for ($i = 1; $i <= $paddingLength; $i++) {
+            $paddedKey.= chr($i);
+        }
+        $key = Strings::packSSH2('sssNss', 'none', 'none', '', 1, $publicKey, $paddedKey);
+        $key = "openssh-key-v1\0$key";
+
+        return "-----BEGIN OPENSSH PRIVATE KEY-----\r\n" .
+               chunk_split(Base64::encode($key), 70) . 
+               "-----END OPENSSH PRIVATE KEY-----";
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Keys/PKCS1.php b/phpseclib/Crypt/ECDSA/Keys/PKCS1.php
new file mode 100644
index 00000000..aebc84eb
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/PKCS1.php
@@ -0,0 +1,141 @@
+<?php
+
+/**
+ * "PKCS1" (RFC5915) Formatted ECDSA Key Handler
+ *
+ * PHP version 5
+ *
+ * Used by File/X509.php
+ *
+ * Processes keys with the following headers:
+ *
+ * -----BEGIN EC PRIVATE KEY-----
+ * -----BEGIN EC PARAMETERS-----
+ *
+ * Technically, PKCS1 is for RSA keys, only, but we're using PKCS1 to describe
+ * DSA, whose format isn't really formally described anywhere, so might as well
+ * use it to describe this, too. PKCS1 is easier to remember than RFC5915, after
+ * all. I suppose this could also be named IETF but idk
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use phpseclib\Math\Common\FiniteField\Integer;
+use phpseclib\Crypt\Common\Keys\PKCS1 as Progenitor;
+use phpseclib\File\ASN1;
+use phpseclib\File\ASN1\Maps;
+use phpseclib\Crypt\ECDSA\BaseCurves\Base as BaseCurve;
+use phpseclib\Math\BigInteger;
+use ParagonIE\ConstantTime\Base64;
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+use phpseclib\Exception\UnsupportedCurveException;
+
+/**
+ * "PKCS1" (RFC5915) Formatted ECDSA Key Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class PKCS1 extends Progenitor
+{
+    use Common;
+
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @access public
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        self::initialize_static_variables();
+
+        $key = parent::load($key, $password);
+
+        $decoded = ASN1::decodeBER($key);
+        if (empty($decoded)) {
+            throw new \RuntimeException('Unable to decode BER');
+        }
+
+        $key = ASN1::asn1map($decoded[0], Maps\ECParameters::MAP);
+        if (is_array($key)) {
+            return ['curve' => self::loadCurveByParam($key)];
+        }
+
+        $key = ASN1::asn1map($decoded[0], Maps\ECPrivateKey::MAP);
+        if (!is_array($key)) {
+            throw new \RuntimeException('Unable to perform ASN1 mapping');
+        }
+
+        $components = [];
+        $components['curve'] = self::loadCurveByParam($key['parameters']);
+        $temp = new BigInteger($key['privateKey'], 256);
+        $components['dA'] = $components['curve']->convertInteger($temp);
+        $components['QA'] = self::extractPoint($key['publicKey'], $components['curve']);
+
+        return $components;
+    }
+
+    /**
+     * Convert ECDSA parameters to the appropriate format
+     *
+     * @access public
+     * @return string
+     */
+    public static function saveParameters(BaseCurve $curve)
+    {
+        self::initialize_static_variables();
+
+        if ($curve instanceof TwistedEdwardsCurve) {
+            throw new UnsupportedCurveException('TwistedEdwards Curves are not supported');
+        }
+
+        $key = self::encodeParameters($curve);
+
+        return "-----BEGIN EC PARAMETERS-----\r\n" .
+               chunk_split(Base64::encode($key), 64) .
+               "-----END EC PARAMETERS-----\r\n";
+    }
+
+    /**
+     * Convert a private key to the appropriate format.
+     *
+     * @access public
+     * @param \phpseclib\Math\Common\FiniteField\Integer $privateKey
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @param string $password optional
+     * @return string
+     */
+    public static function savePrivateKey(Integer $privateKey, BaseCurve $curve, array $publicKey, $password = '')
+    {
+        self::initialize_static_variables();
+
+        if ($curve instanceof TwistedEdwardsCurve) {
+            throw new UnsupportedCurveException('TwistedEdwards Curves are not supported');
+        }
+
+        $publicKey = "\4" . $publicKey[0]->toBytes() . $publicKey[1]->toBytes();
+
+        $key = [
+            'version' => 'ecPrivkeyVer1',
+            'privateKey' => $privateKey->toBytes(),
+            'parameters' => new ASN1\Element(self::encodeParameters($curve)),
+            'publicKey' => "\0" . $publicKey
+        ];
+
+        $key = ASN1::encodeDER($key, Maps\ECPrivateKey::MAP);
+
+        return self::wrapPrivateKey($key, 'EC', $password);
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Keys/PKCS8.php b/phpseclib/Crypt/ECDSA/Keys/PKCS8.php
new file mode 100644
index 00000000..89f31671
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/PKCS8.php
@@ -0,0 +1,233 @@
+<?php
+
+/**
+ * PKCS#8 Formatted ECDSA Key Handler
+ *
+ * PHP version 5
+ *
+ * Processes keys with the following headers:
+ *
+ * -----BEGIN ENCRYPTED PRIVATE KEY-----
+ * -----BEGIN PRIVATE KEY-----
+ * -----BEGIN PUBLIC KEY-----
+ *
+ * Analogous to ssh-keygen's pkcs8 format (as specified by -m). Although PKCS8
+ * is specific to private keys it's basically creating a DER-encoded wrapper
+ * for keys. This just extends that same concept to public keys (much like ssh-keygen)
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use phpseclib\Math\BigInteger;
+use phpseclib\Crypt\Common\Keys\PKCS8 as Progenitor;
+use phpseclib\File\ASN1;
+use phpseclib\File\ASN1\Maps;
+use phpseclib\Crypt\ECDSA\BaseCurves\Base as BaseCurve;
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+use phpseclib\Math\Common\FiniteField\Integer;
+use phpseclib\Crypt\ECDSA\Curves\Ed25519;
+use phpseclib\Crypt\ECDSA\Curves\Ed448;
+
+/**
+ * PKCS#8 Formatted ECDSA Key Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class PKCS8 extends Progenitor
+{
+    use Common;
+
+    /**
+     * OID Name
+     *
+     * @var array
+     * @access private
+     */
+    const OID_NAME = ['id-ecPublicKey', 'id-Ed25519', 'id-Ed448'];
+
+    /**
+     * OID Value
+     *
+     * @var string
+     * @access private
+     */
+    const OID_VALUE = ['1.2.840.10045.2.1', '1.3.101.112', '1.3.101.113'];
+
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @access public
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        // initialize_static_variables() is defined in both the trait and the parent class
+        // when it's defined in two places it's the traits one that's called
+        // the parent one is needed, as well, but the parent one is called by other methods
+        // in the parent class as needed and in the context of the parent it's the parent
+        // one that's called
+        self::initialize_static_variables();
+
+        if (!is_string($key)) {
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
+        }
+
+        $isPublic = strpos($key, 'PUBLIC') !== false;
+
+        $key = parent::load($key, $password);
+
+        $type = isset($key['privateKey']) ? 'privateKey' : 'publicKey';
+
+        switch (true) {
+            case !$isPublic && $type == 'publicKey':
+                throw new \UnexpectedValueException('Human readable string claims non-public key but DER encoded string claims public key');
+            case $isPublic && $type == 'privateKey':
+                throw new \UnexpectedValueException('Human readable string claims public key but DER encoded string claims private key');
+        }
+
+        switch ($key[$type . 'Algorithm']['algorithm']) {
+            case 'id-Ed25519':
+            case 'id-Ed448':
+                return self::loadEdDSA($key);
+        }
+
+        $decoded = ASN1::decodeBER($key[$type . 'Algorithm']['parameters']->element);
+        $params = ASN1::asn1map($decoded[0], Maps\ECParameters::MAP);
+
+        $components = [];
+        $components['curve'] = self::loadCurveByParam($params);
+
+        if ($isPublic) {
+            $components['QA'] = self::extractPoint("\0" . $key['publicKey'], $components['curve']);
+
+            return $components;
+        }
+
+        $decoded = ASN1::decodeBER($key['privateKey']);
+        $key = ASN1::asn1map($decoded[0], Maps\ECPrivateKey::MAP);
+        if (isset($key['parameters']) && $params != $key['parameters']) {
+            throw new \RuntimeException('The PKCS8 parameter field does not match the private key parameter field');
+        }
+
+        $temp = new BigInteger($key['privateKey'], 256);
+        $components['dA'] = $components['curve']->convertInteger($temp);
+
+        $components['QA'] = self::extractPoint($key['publicKey'], $components['curve']);
+
+        return $components;
+    }
+
+    /**
+     * Break a public or private EdDSA key down into its constituent components
+     *
+     * @return array
+     */
+    private static function loadEdDSA(array $key)
+    {
+        $components = [];
+
+        if (isset($key['privateKey'])) {
+            $components['curve'] = $key['privateKeyAlgorithm']['algorithm'] == 'id-Ed25519' ? new Ed25519() : new Ed448();
+
+            // 0x04 == octet string
+            // 0x20 == length (32 bytes)
+            if (substr($key['privateKey'], 0, 2) != "\x04\x20") {
+                throw new \RuntimeException('The first two bytes of the private key field should be 0x0420');
+            }
+            $components['dA'] = $components['curve']->extractSecret(substr($key['privateKey'], 2));
+        }
+
+        if (isset($key['publicKey'])) {
+            if (!isset($components['curve'])) {
+                $components['curve'] = $key['publicKeyAlgorithm']['algorithm'] == 'id-Ed25519' ? new Ed25519() : new Ed448();
+            }
+
+            $components['QA'] = self::extractPoint(substr($key['publicKey'], 1), $components['curve']);
+        }
+
+        if (isset($key['privateKey']) && !isset($components['QA'])) {
+            $components['QA'] = $components['curve']->multiplyPoint($components['curve']->getBasePoint(), $components['dA']);
+        }
+
+        return $components;
+    }
+
+    /**
+     * Convert an ECDSA public key to the appropriate format
+     *
+     * @access public
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @return string
+     */
+    public static function savePublicKey(BaseCurve $curve, array $publicKey)
+    {
+        self::initialize_static_variables();
+
+        if ($curve instanceof TwistedEdwardsCurve) {
+            return self::wrapPublicKey(
+                $curve->encodePoint($publicKey),
+                null,
+                $curve instanceof Ed25519 ? 'id-Ed25519' : 'id-Ed448'
+            );
+        }
+
+        $params = new ASN1\Element(self::encodeParameters($curve));
+
+        $key = "\4" . $publicKey[0]->toBytes() . $publicKey[1]->toBytes();
+
+        return self::wrapPublicKey($key, $params, 'id-ecPublicKey');
+    }
+
+    /**
+     * Convert a private key to the appropriate format.
+     *
+     * @access public
+     * @param \phpseclib\Math\Common\FiniteField\Integer $privateKey
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @param string $password optional
+     * @return string
+     */
+    public static function savePrivateKey(Integer $privateKey, BaseCurve $curve, array $publicKey, $password = '')
+    {
+        self::initialize_static_variables();
+
+        if ($curve instanceof TwistedEdwardsCurve) {
+            return self::wrapPrivateKey(
+                "\x04\x20" . $privateKey->secret,
+                [],
+                null,
+                $password,
+                $curve instanceof Ed25519 ? 'id-Ed25519' : 'id-Ed448',
+                $curve->encodePoint($publicKey)
+            );
+        }
+
+        $publicKey = "\4" . $publicKey[0]->toBytes() . $publicKey[1]->toBytes();
+
+        $params = new ASN1\Element(self::encodeParameters($curve));
+
+        $key = [
+            'version' => 'ecPrivkeyVer1',
+            'privateKey' => $privateKey->toBytes(),
+            //'parameters' => $params,
+            'publicKey' => "\0" . $publicKey
+        ];
+
+        $key = ASN1::encodeDER($key, Maps\ECPrivateKey::MAP);
+
+        return self::wrapPrivateKey($key, [], $params, $password, 'id-ecPublicKey');
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Keys/PuTTY.php b/phpseclib/Crypt/ECDSA/Keys/PuTTY.php
new file mode 100644
index 00000000..ce4eb563
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/PuTTY.php
@@ -0,0 +1,145 @@
+<?php
+
+/**
+ * PuTTY Formatted ECDSA Key Handler
+ *
+ * PHP version 5
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use ParagonIE\ConstantTime\Base64;
+use phpseclib\Math\BigInteger;
+use phpseclib\Common\Functions\Strings;
+use phpseclib\Crypt\Common\Keys\PuTTY as Progenitor;
+use phpseclib\Crypt\ECDSA\BaseCurves\Base as BaseCurve;
+use phpseclib\Math\Common\FiniteField\Integer;
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+
+/**
+ * PuTTY Formatted ECDSA Key Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class PuTTY extends Progenitor
+{
+    use Common;
+
+    /**
+     * Public Handler
+     *
+     * @var string
+     * @access private
+     */
+    const PUBLIC_HANDLER = 'phpseclib\Crypt\ECDSA\Keys\OpenSSH';
+
+    /**
+     * Supported Key Types
+     *
+     * @var array
+     * @access private
+     */
+    protected static $types = [
+        'ecdsa-sha2-nistp256',
+        'ecdsa-sha2-nistp384',
+        'ecdsa-sha2-nistp521',
+        'ssh-ed25519'
+    ];
+
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @access public
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        $components = parent::load($key, $password);
+        if (!isset($components['private'])) {
+            return $components;
+        }
+
+        $private = $components['private'];
+
+        $temp = Base64::encode(Strings::packSSH2('s', $components['type']) . $components['public']);
+        $components = OpenSSH::load($components['type'] . ' ' . $temp . ' ' . $components['comment']);
+
+        if ($components['curve'] instanceof TwistedEdwardsCurve) {
+            if (Strings::shift($private, 4) != "\0\0\0\x20") {
+                throw new \RuntimeException('Length of ssh-ed25519 key should be 32');
+            }
+            $components['dA'] = $components['curve']->extractSecret($private);
+        } else {
+            list($temp) = Strings::unpackSSH2('i', $private);
+            $components['dA'] = $components['curve']->convertInteger($temp);
+        }
+
+        return $components;
+    }
+
+    /**
+     * Convert a private key to the appropriate format.
+     *
+     * @access public
+     * @param \phpseclib\Math\Common\FiniteField\Integer $privateKey
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @param string $password optional
+     * @return string
+     */
+    public static function savePrivateKey(Integer $privateKey, BaseCurve $curve, array $publicKey, $password = false)
+    {
+        self::initialize_static_variables();
+
+        $public = explode(' ', OpenSSH::savePublicKey($curve, $publicKey));
+        $name = $public[0];
+        $public = Base64::decode($public[1]);
+        list(, $length) = unpack('N', Strings::shift($public, 4));
+        Strings::shift($public, $length);
+
+        // PuTTY pads private keys with a null byte per the following:
+        // https://github.com/github/putty/blob/a3d14d77f566a41fc61dfdc5c2e0e384c9e6ae8b/sshecc.c#L1926
+        if (!$curve instanceof TwistedEdwardsCurve) {
+            $private = $privateKey->toBytes();
+            if (!(strlen($privateKey->toBits()) & 7)) {
+                $private ="\0$private";
+            }
+        }
+
+        $private = $curve instanceof TwistedEdwardsCurve ?
+            Strings::packSSH2('s', $privateKey->secret) :
+            Strings::packSSH2('s', $private);
+
+        return self::wrapPrivateKey($public, $private, $name, $password);
+    }
+
+    /**
+     * Convert an ECDSA public key to the appropriate format
+     *
+     * @access public
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField[] $publicKey
+     * @return string
+     */
+    public static function savePublicKey(BaseCurve $curve, array $publicKey)
+    {
+        $public = explode(' ', OpenSSH::savePublicKey($curve, $publicKey));
+        $type = $public[0];
+        $public = Base64::decode($public[1]);
+        list(, $length) = unpack('N', Strings::shift($public, 4));
+        Strings::shift($public, $length);
+
+        return self::wrapPublicKey($public, $type);
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Keys/XML.php b/phpseclib/Crypt/ECDSA/Keys/XML.php
new file mode 100644
index 00000000..b846b845
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/XML.php
@@ -0,0 +1,480 @@
+<?php
+
+/**
+ * XML Formatted ECDSA Key Handler
+ *
+ * More info:
+ *
+ * https://www.w3.org/TR/xmldsig-core/#sec-ECKeyValue
+ * http://en.wikipedia.org/wiki/XML_Signature
+ *
+ * PHP version 5
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use ParagonIE\ConstantTime\Base64;
+use phpseclib\Math\BigInteger;
+use phpseclib\Crypt\ECDSA\BaseCurves\Base as BaseCurve;
+use phpseclib\Crypt\ECDSA\BaseCurves\Prime as PrimeCurve;
+use phpseclib\Crypt\ECDSA\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+use phpseclib\Exception\UnsupportedCurveException;
+
+/**
+ * XML Formatted ECDSA Key Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class XML
+{
+    use Common;
+
+    /**
+     * Default namespace
+     *
+     * @var string
+     */
+    private static $namespace;
+
+    /**
+     * Flag for using RFC4050 syntax
+     *
+     * @var bool
+     */
+    private static $rfc4050 = false;
+
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @access public
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        self::initialize_static_variables();
+
+        if (!is_string($key)) {
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
+        }
+
+        $use_errors = libxml_use_internal_errors(true);
+
+        $temp = self::isolateNamespace($key, 'http://www.w3.org/2009/xmldsig11#');
+        if ($temp) {
+            $key = $temp;
+        }
+
+        $temp = self::isolateNamespace($key, 'http://www.w3.org/2001/04/xmldsig-more#');
+        if ($temp) {
+            $key = $temp;
+        }
+
+        $dom = new \DOMDocument();
+        if (substr($key, 0, 5) != '<?xml') {
+            $key = '<xml>' . $key . '</xml>';
+        }
+
+        if (!$dom->loadXML($key)) {
+            libxml_use_internal_errors($use_errors);
+            throw new \UnexpectedValueException('Key does not appear to contain XML');
+        }
+        $xpath = new \DOMXPath($dom);
+        libxml_use_internal_errors($use_errors);
+        $curve = self::loadCurveByParam($xpath);
+
+        $pubkey = self::query($xpath, 'publickey', 'Public Key is not present');
+
+        $QA = self::query($xpath, 'ecdsakeyvalue')->length ?
+            self::extractPointRFC4050($xpath, $curve) :
+            self::extractPoint("\0" . $pubkey, $curve);
+
+        libxml_use_internal_errors($use_errors);
+
+        return compact('curve', 'QA');
+    }
+
+    /**
+     * Case-insensitive xpath query
+     *
+     * @param \DOMXPath $xpath
+     * @param string $name
+     * @param string $error optional
+     * @param bool $decode optional
+     * @return \DOMNodeList
+     */
+    private static function query($xpath, $name, $error = null, $decode = true)
+    {
+        $query = '/';
+        $names = explode('/', $name);
+        foreach ($names as $name) {
+            $query.= "/*[translate(local-name(), 'ABCDEFGHIJKLMNOPQRSTUVWXYZ','abcdefghijklmnopqrstuvwxyz')='$name']";
+        }
+        $result = $xpath->query($query);
+        if (!isset($error)) {
+            return $result;
+        }
+
+        if (!$result->length) {
+            throw new \RuntimeException($error);
+        }
+        return $decode ? self::decodeValue($result->item(0)->textContent) : $result->item(0)->textContent;
+    }
+
+    /**
+     * Finds the first element in the relevant namespace, strips the namespacing and returns the XML for that element.
+     *
+     * @param string $xml
+     * @param string $ns
+     */
+    private static function isolateNamespace($xml, $ns)
+    {
+        $dom = new \DOMDocument();
+        if (!$dom->loadXML($xml)) {
+            return false;
+        }
+        $xpath = new \DOMXPath($dom);
+        $nodes = $xpath->query("//*[namespace::*[.='$ns'] and not(../namespace::*[.='$ns'])]");
+        if (!$nodes->length) {
+            return false;
+        }
+        $node = $nodes->item(0);
+        $ns_name = $node->lookupPrefix($ns);
+        $node->removeAttributeNS($ns, $ns_name);
+        return $dom->saveXML($node);
+    }
+
+    /**
+     * Decodes the value
+     *
+     * @param string $value
+     */
+    private static function decodeValue($value)
+    {
+        return Base64::decode(str_replace(["\r", "\n", ' ', "\t"], '', $value));
+    }
+
+    /**
+     * Extract points from an XML document
+     *
+     * @param \DOMXPath $xpath
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @return object[]
+     */
+    private static function extractPointRFC4050(\DOMXPath $xpath, BaseCurve $curve)
+    {
+        $x = self::query($xpath, 'publickey/x');
+        $y = self::query($xpath, 'publickey/y');
+        if (!$x->length || !$x->item(0)->hasAttribute('Value')) {
+            throw new \RuntimeException('Public Key / X coordinate not found');
+        }
+        if (!$y->length || !$y->item(0)->hasAttribute('Value')) {
+            throw new \RuntimeException('Public Key / Y coordinate not found');
+        }
+        $point = [
+            $curve->convertInteger(new BigInteger($x->item(0)->getAttribute('Value'))),
+            $curve->convertInteger(new BigInteger($y->item(0)->getAttribute('Value')))
+        ];
+        if (!$curve->verifyPoint($point)) {
+            throw new \RuntimeException('Unable to verify that point exists on curve');
+        }
+        return $point;
+    }
+
+    /**
+     * Returns an instance of \phpseclib\Crypt\ECDSA\BaseCurves\Base based
+     * on the curve parameters
+     *
+     * @param \DomXPath $xpath
+     * @return \phpseclib\Crypt\ECDSA\BaseCurves\Base|false
+     */
+    private static function loadCurveByParam(\DOMXPath $xpath)
+    {
+        $namedCurve = self::query($xpath, 'namedcurve');
+        if ($namedCurve->length == 1) {
+            $oid = $namedCurve->item(0)->getAttribute('URN');
+            $oid = preg_replace('#[^\d.]#', '', $oid);
+            $name = array_search($oid, self::$curveOIDs);
+            if ($name === false) {
+                throw new UnsupportedCurveException('Curve with OID of ' . $oid . ' is not supported');
+            }
+
+            $curve = '\phpseclib\Crypt\ECDSA\Curves\\' . $name;
+            if (!class_exists($curve)) {
+                throw new UnsupportedCurveException('Named Curve of ' . $name . ' is not supported');
+            }
+            return new $curve();
+        }
+
+        $params = self::query($xpath, 'explicitparams');
+        if ($params->length) {
+            return self::loadCurveByParamRFC4050($xpath);
+        }
+
+        $params = self::query($xpath, 'ecparameters');
+        if (!$params->length) {
+            throw new \RuntimeException('No parameters are present');
+        }
+
+        $fieldTypes = [
+            'prime-field' => ['fieldid/prime/p'],
+            'gnb' => ['fieldid/gnb/m'],
+            'tnb' => ['fieldid/tnb/k'],
+            'pnb' => ['fieldid/pnb/k1', 'fieldid/pnb/k2', 'fieldid/pnb/k3'],
+            'unknown' => []
+        ];
+
+        foreach ($fieldTypes as $type => $queries) {
+            foreach ($queries as $query) {
+                $result = self::query($xpath, $query);
+                if (!$result->length) {
+                    continue 2;
+                }
+                $param = preg_replace('#.*/#', '', $query);
+                $$param = self::decodeValue($result->item(0)->textContent);
+            }
+            break;
+        }
+
+        $a = self::query($xpath, 'curve/a', 'A coefficient is not present');
+        $b = self::query($xpath, 'curve/b', 'B coefficient is not present');
+        $base = self::query($xpath, 'base', 'Base point is not present');
+        $order = self::query($xpath, 'order', 'Order is not present');
+
+        switch ($type) {
+            case 'prime-field':
+                $curve = new PrimeCurve();
+                $curve->setModulo(new BigInteger($p, 256));
+                $curve->setCoefficients(
+                    new BigInteger($a, 256),
+                    new BigInteger($b, 256)
+                );
+                $point = self::extractPoint("\0" . $base, $curve);
+                $curve->setBasePoint(...$point);
+                $curve->setOrder(new BigInteger($order, 256));
+                return $curve;
+            case 'gnb':
+            case 'tnb':
+            case 'pnb':
+            default:
+                throw new UnsupportedCurveException('Field Type of ' . $type . ' is not supported');
+        }
+    }
+
+    /**
+     * Returns an instance of \phpseclib\Crypt\ECDSA\BaseCurves\Base based
+     * on the curve parameters
+     *
+     * @param \DomXPath $xpath
+     * @return \phpseclib\Crypt\ECDSA\BaseCurves\Base|false
+     */
+    private static function loadCurveByParamRFC4050(\DOMXPath $xpath)
+    {
+        $fieldTypes = [
+            'prime-field' => ['primefieldparamstype/p'],
+            'unknown' => []
+        ];
+
+        foreach ($fieldTypes as $type => $queries) {
+            foreach ($queries as $query) {
+                $result = self::query($xpath, $query);
+                if (!$result->length) {
+                    continue 2;
+                }
+                $param = preg_replace('#.*/#', '', $query);
+                $$param = $result->item(0)->textContent;
+            }
+            break;
+        }
+
+        $a = self::query($xpath, 'curveparamstype/a', 'A coefficient is not present', false);
+        $b = self::query($xpath, 'curveparamstype/b', 'B coefficient is not present', false);
+        $x = self::query($xpath, 'basepointparams/basepoint/ecpointtype/x', 'Base Point X is not present', false);
+        $y = self::query($xpath, 'basepointparams/basepoint/ecpointtype/y', 'Base Point Y is not present', false);
+        $order = self::query($xpath, 'order', 'Order is not present', false);
+
+        switch ($type) {
+            case 'prime-field':
+                $curve = new PrimeCurve();
+
+                $p = str_replace(["\r", "\n", ' ', "\t"], '', $p);
+                $curve->setModulo(new BigInteger($p));
+
+                $a = str_replace(["\r", "\n", ' ', "\t"], '', $a);
+                $b = str_replace(["\r", "\n", ' ', "\t"], '', $b);
+                $curve->setCoefficients(
+                    new BigInteger($a),
+                    new BigInteger($b)
+                );
+
+                $x = str_replace(["\r", "\n", ' ', "\t"], '', $x);
+                $y = str_replace(["\r", "\n", ' ', "\t"], '', $y);
+                $curve->setBasePoint(
+                    new BigInteger($x),
+                    new BigInteger($y)
+                );
+
+                $order = str_replace(["\r", "\n", ' ', "\t"], '', $order);
+                $curve->setOrder(new BigInteger($order));
+                return $curve;
+            default:
+                throw new UnsupportedCurveException('Field Type of ' . $type . ' is not supported');
+        }
+    }
+
+    /**
+     * Sets the namespace. dsig11 is the most common one.
+     *
+     * Set to null to unset. Used only for creating public keys.
+     *
+     * @param string $namespace
+     */
+    public static function setNamespace($namespace)
+    {
+        self::$namespace = $namespace;
+    }
+
+    /**
+     * Uses the XML syntax specified in https://tools.ietf.org/html/rfc4050
+     */
+    public static function enableRFC4050Syntax()
+    {
+        self::$rfc4050 = true;
+    }
+
+    /**
+     * Uses the XML syntax specified in https://www.w3.org/TR/xmldsig-core/#sec-ECParameters
+     */
+    public static function disableRFC4050Syntax()
+    {
+        self::$rfc4050 = false;
+    }
+
+    /**
+     * Convert a public key to the appropriate format
+     *
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @return string
+     */
+    public static function savePublicKey(BaseCurve $curve, array $publicKey)
+    {
+        self::initialize_static_variables();
+
+        if ($curve instanceof TwistedEdwardsCurve) {
+            throw new UnsupportedCurveException('TwistedEdwards Curves are not supported');
+        }
+
+        if (empty(static::$namespace)) {
+            $pre = $post = '';
+        } else {
+            $pre = static::$namespace . ':';
+            $post = ':' . static::$namespace;
+        }
+
+        if (self::$rfc4050) {
+            return '<' . $pre . 'ECDSAKeyValue xmlns' . $post . '="http://www.w3.org/2001/04/xmldsig-more#">' . "\r\n" .
+                   self::encodeXMLParameters($curve, $pre) . "\r\n" .
+                   '<' . $pre . 'PublicKey>' . "\r\n" .
+                   '<' . $pre . 'X Value="' . $publicKey[0] . '" />' . "\r\n" .
+                   '<' . $pre . 'Y Value="' . $publicKey[1] . '" />' . "\r\n" .
+                   '</' . $pre . 'PublicKey>' . "\r\n" .
+                   '</' . $pre . 'ECDSAKeyValue>';
+        }
+
+        $publicKey = "\4" . $publicKey[0]->toBytes() . $publicKey[1]->toBytes();
+
+        return '<' . $pre . 'ECKeyValue xmlns' . $post . '="http://www.w3.org/2009/xmldsig11#">' . "\r\n" .
+               self::encodeXMLParameters($curve, $pre) . "\r\n" .
+               '<' . $pre . 'PublicKey>' . Base64::encode($publicKey) . '</' . $pre . 'PublicKey>' . "\r\n" .
+               '</' . $pre . 'ECKeyValue>';
+    }
+
+    /**
+     * Encode Parameters
+     *
+     * @param \phpseclib\Crypt\ECDSA\BaseCurves\Base $curve
+     * @param string $pre
+     * @return string|false
+     */
+    private static function encodeXMLParameters(BaseCurve $curve, $pre)
+    {
+        $result = self::encodeParameters($curve, true);
+
+        if (isset($result['namedCurve'])) {
+            $namedCurve = '<' . $pre . 'NamedCurve URI="urn:oid:' . self::$curveOIDs[$result['namedCurve']] . '" />';
+            return self::$rfc4050 ?
+                '<DomainParameters>' . str_replace('URI', 'URN', $namedCurve) . '</DomainParameters>' :
+                $namedCurve;
+        }
+
+        if (self::$rfc4050) {
+            $xml = '<' . $pre . 'ExplicitParams>' . "\r\n" .
+                  '<' . $pre . 'FieldParams>' . "\r\n";
+            $temp = $result['specifiedCurve'];
+            switch ($temp['fieldID']['fieldType']) {
+                case 'prime-field':
+                    $xml.= '<' . $pre . 'PrimeFieldParamsType>' . "\r\n" .
+                           '<' . $pre . 'P>' . $temp['fieldID']['parameters'] . '</' . $pre . 'P>' . "\r\n" .
+                           '</' . $pre . 'PrimeFieldParamsType>' . "\r\n";
+                    $a = $curve->getA();
+                    $b = $curve->getB();
+                    list($x, $y) = $curve->getBasePoint();
+                    break;
+                default:
+                    throw new UnsupportedCurveException('Field Type of ' . $temp['fieldID']['fieldType'] . ' is not supported');
+            }
+            $xml.= '</' . $pre . 'FieldParams>' . "\r\n" .
+                   '<' . $pre . 'CurveParamsType>' . "\r\n" .
+                   '<' . $pre . 'A>' . $a . '</' . $pre . 'A>' . "\r\n" .
+                   '<' . $pre . 'B>' . $b . '</' . $pre . 'B>' . "\r\n" .
+                   '</' . $pre . 'CurveParamsType>' . "\r\n" .
+                   '<' . $pre . 'BasePointParams>' . "\r\n" .
+                   '<' . $pre . 'BasePoint>' . "\r\n" .
+                   '<' . $pre . 'ECPointType>' . "\r\n" .
+                   '<' . $pre . 'X>' . $x . '</' . $pre . 'X>' . "\r\n" .
+                   '<' . $pre . 'Y>' . $y . '</' . $pre . 'Y>' . "\r\n" .
+                   '</' . $pre . 'ECPointType>' . "\r\n" .
+                   '</' . $pre . 'BasePoint>' . "\r\n" .
+                   '<' . $pre . 'Order>' . $curve->getOrder() . '</' . $pre . 'Order>' . "\r\n" .
+                   '</' . $pre . 'BasePointParams>' . "\r\n" .
+                   '</' . $pre . 'ExplicitParams>' . "\r\n";
+
+            return $xml;
+        }
+
+        if (isset($result['specifiedCurve'])) {
+            $xml = '<' . $pre . 'ECParameters>' . "\r\n" .
+                   '<' . $pre . 'FieldID>' . "\r\n";
+            $temp = $result['specifiedCurve'];
+            switch ($temp['fieldID']['fieldType']) {
+                case 'prime-field':
+                    $xml.= '<' . $pre . 'Prime>' . "\r\n" .
+                           '<' . $pre . 'P>' . Base64::encode($temp['fieldID']['parameters']->toBytes()) . '</' . $pre . 'P>' . "\r\n" .
+                           '</' . $pre . 'Prime>' . "\r\n" ;
+                    break;
+                default:
+                    throw new UnsupportedCurveException('Field Type of ' . $temp['fieldID']['fieldType'] . ' is not supported');
+            }
+            $xml.= '</' . $pre . 'FieldID>' . "\r\n" .
+                   '<' . $pre . 'Curve>' . "\r\n" .
+                   '<' . $pre . 'A>' . Base64::encode($temp['curve']['a']) . '</' . $pre . 'A>' . "\r\n" .
+                   '<' . $pre . 'B>' . Base64::encode($temp['curve']['b']) . '</' . $pre . 'B>' . "\r\n" .
+                   '</' . $pre . 'Curve>' . "\r\n" .
+                   '<' . $pre . 'Base>' . Base64::encode($temp['base']) . '</' . $pre . 'Base>' . "\r\n" .
+                   '<' . $pre . 'Order>' . Base64::encode($temp['order']) . '</' . $pre . 'Order>' . "\r\n" .
+                   '</' . $pre . 'ECParameters>';
+            return $xml;
+        }
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Keys/libsodium.php b/phpseclib/Crypt/ECDSA/Keys/libsodium.php
new file mode 100644
index 00000000..bf091bc9
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Keys/libsodium.php
@@ -0,0 +1,111 @@
+<?php
+
+/**
+ * libsodium Key Handler
+ *
+ * Different NaCl implementations store the key differently.
+ * https://blog.mozilla.org/warner/2011/11/29/ed25519-keys/ elaborates.
+ * libsodium appears to use the same format as SUPERCOP.
+ *
+ * PHP version 5
+ *
+ * @category  Crypt
+ * @package   ECDSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Keys;
+
+use phpseclib\Crypt\ECDSA\Curves\Ed25519;
+use phpseclib\Math\Common\FiniteField\Integer;
+
+/**
+ * libsodium Key Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class libsodium
+{
+    use Common;
+
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @access public
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        switch (strlen($key)) {
+            case 32:
+                $public = $key;
+                break;
+            case 64:
+                $private = substr($key, 0, 32);
+                $public = substr($key, -32);
+                break;
+            case 96:
+                $public = substr($key, -32);
+                if (substr($key, 32, 32) != $public) {
+                    throw new \RuntimeException('Keys with 96 bytes should have the 2nd and 3rd set of 32 bytes match');
+                }
+                $private = substr($key, 0, 32);
+                break;
+            default:
+                throw new \RuntimeException('libsodium keys need to either be 32 bytes long, 64 bytes long or 96 bytes long');
+        }
+
+        $curve = new Ed25519();
+        $components = ['curve' => $curve];
+        if (isset($private)) {
+            $components['dA'] = $curve->extractSecret($private);
+        }
+        $components['QA'] = isset($public) ?
+            self::extractPoint($public, $curve) :
+            $curve->multiplyPoint($curve->getBasePoint(), $components['dA']);
+        
+
+        return $components;
+    }
+
+    /**
+     * Convert an ECDSA public key to the appropriate format
+     *
+     * @access public
+     * @param \phpseclib\Crypt\ECDSA\Curves\Ed25519 $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @return string
+     */
+    public static function savePublicKey(Ed25519 $curve, array $publicKey)
+    {
+        return $curve->encodePoint($publicKey);
+    }
+
+    /**
+     * Convert a private key to the appropriate format.
+     *
+     * @access public
+     * @param \phpseclib\Math\Common\FiniteField\Integer $privateKey
+     * @param \phpseclib\Crypt\ECDSA\Curves\Ed25519 $curve
+     * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
+     * @param string $password optional
+     * @return string
+     */
+    public static function savePrivateKey(Integer $privateKey, Ed25519 $curve, array $publicKey, $password = '')
+    {
+        if (!isset($privateKey->secret)) {
+            throw new \RuntimeException('Private Key does not have a secret set');
+        }
+        if (strlen($privateKey->secret) != 32) {
+            throw new \RuntimeException('Private Key secret is not of the correct length');
+        }
+        return $privateKey->secret . $curve->encodePoint($publicKey);
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Signature/ASN1.php b/phpseclib/Crypt/ECDSA/Signature/ASN1.php
new file mode 100644
index 00000000..9baa9fd9
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Signature/ASN1.php
@@ -0,0 +1,68 @@
+<?php
+
+/**
+ * ASN1 Signature Handler
+ *
+ * PHP version 5
+ *
+ * Handles signatures in the format described in
+ * https://tools.ietf.org/html/rfc3279#section-2.2.3
+ *
+ * @category  Crypt
+ * @package   Common
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Signature;
+
+use phpseclib\Math\BigInteger;
+use phpseclib\File\ASN1 as Encoder;
+use phpseclib\File\ASN1\Maps\EcdsaSigValue;
+
+/**
+ * ASN1 Signature Handler
+ *
+ * @package Common
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class ASN1
+{
+    /**
+     * Loads a signature
+     *
+     * @access public
+     * @param array $key
+     * @return array
+     */
+    public static function load($sig)
+    {
+        if (!is_string($sig)) {
+            return false;
+        }
+
+        $decoded = Encoder::decodeBER($sig);
+        if (empty($decoded)) {
+            return false;
+        }
+        $components = Encoder::asn1map($decoded[0], EcdsaSigValue::MAP);
+
+        return $components;
+    }
+
+    /**
+     * Returns a signature in the appropriate format
+     *
+     * @access public
+     * @param \phpseclib\Math\BigInteger $r
+     * @param \phpseclib\Math\BigInteger $s
+     * @return string
+     */
+    public static function save(BigInteger $r, BigInteger $s)
+    {
+        return Encoder::encodeDER(compact('r', 's'), EcdsaSigValue::MAP);
+    }
+}
diff --git a/phpseclib/Crypt/ECDSA/Signature/Raw.php b/phpseclib/Crypt/ECDSA/Signature/Raw.php
new file mode 100644
index 00000000..99e03533
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Signature/Raw.php
@@ -0,0 +1,29 @@
+<?php
+
+/**
+ * Raw ECDSA Signature Handler
+ *
+ * PHP version 5
+ *
+ * @category  Crypt
+ * @package   DSA
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Signature;
+
+use phpseclib\Crypt\Common\Signature\Raw as Progenitor;
+
+/**
+ * Raw DSA Signature Handler
+ *
+ * @package ECDSA
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Raw extends Progenitor
+{
+}
diff --git a/phpseclib/Crypt/ECDSA/Signature/SSH2.php b/phpseclib/Crypt/ECDSA/Signature/SSH2.php
new file mode 100644
index 00000000..65045ac7
--- /dev/null
+++ b/phpseclib/Crypt/ECDSA/Signature/SSH2.php
@@ -0,0 +1,95 @@
+<?php
+
+/**
+ * SSH2 Signature Handler
+ *
+ * PHP version 5
+ *
+ * Handles signatures in the format used by SSH2
+ *
+ * @category  Crypt
+ * @package   Common
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Crypt\ECDSA\Signature;
+
+use phpseclib\Math\BigInteger;
+use phpseclib\Common\Functions\Strings;
+
+/**
+ * SSH2 Signature Handler
+ *
+ * @package Common
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class SSH2
+{
+    /**
+     * Loads a signature
+     *
+     * @access public
+     * @param string $sig
+     * @return mixed
+     */
+    public static function load($sig)
+    {
+        if (!is_string($sig)) {
+            return false;
+        }
+
+        $result = Strings::unpackSSH2('ss', $sig);
+        if ($result === false) {
+            return false;
+        }
+        list($type, $blob) = $result;
+        switch ($type) {
+            // see https://tools.ietf.org/html/rfc5656#section-3.1.2
+            case 'ecdsa-sha2-nistp256':
+            case 'ecdsa-sha2-nistp384':
+            case 'ecdsa-sha2-nistp521':
+                break;
+            default:
+                return false;
+        }
+
+        $length = ceil(substr($type, 16) / 8);
+
+        return [
+            'r' => new BigInteger(substr($blob, 0, $length), 256),
+            's' => new BigInteger(substr($blob, $length), 256)
+        ];
+    }
+
+    /**
+     * Returns a signature in the appropriate format
+     *
+     * @access public
+     * @param \phpseclib\Math\BigInteger $r
+     * @param \phpseclib\Math\BigInteger $s
+     * @param string $curve
+     * @return string
+     */
+    public static function save(BigInteger $r, BigInteger $s, $curve)
+    {
+        switch ($curve) {
+            case 'nistp256':
+            case 'nistp384':
+            case 'nistp521':
+                break;
+            default:
+                return false;
+        }
+
+        $length = ceil(substr($curve, 5) / 8);
+
+        return Strings::packSSH2('ss', 'ecdsa-sha2-' . $curve,
+            str_pad($r->toBytes(), $length, "\0", STR_PAD_LEFT) .
+            str_pad($s->toBytes(), $length, "\0", STR_PAD_LEFT)
+        );
+    }
+}
diff --git a/phpseclib/Crypt/RC2.php b/phpseclib/Crypt/RC2.php
index d714e58a..cdaa4ec7 100644
--- a/phpseclib/Crypt/RC2.php
+++ b/phpseclib/Crypt/RC2.php
@@ -152,7 +152,7 @@ class RC2 extends BlockCipher
      * @var array
      * @access private
      */
-    private $pitable = [
+    private static $pitable = [
         0xD9, 0x78, 0xF9, 0xC4, 0x19, 0xDD, 0xB5, 0xED,
         0x28, 0xE9, 0xFD, 0x79, 0x4A, 0xA0, 0xD8, 0x9D,
         0xC6, 0x7E, 0x37, 0x83, 0x2B, 0x76, 0x53, 0x8E,
@@ -226,7 +226,7 @@ class RC2 extends BlockCipher
      * @var array
      * @access private
      */
-    private $invpitable = [
+    private static $invpitable = [
         0xD1, 0xDA, 0xB9, 0x6F, 0x9C, 0xC8, 0x78, 0x66,
         0x80, 0x2C, 0xF8, 0x37, 0xEA, 0xE0, 0x62, 0xA4,
         0xCB, 0x71, 0x50, 0x27, 0x4B, 0x95, 0xD9, 0x20,
@@ -378,7 +378,7 @@ class RC2 extends BlockCipher
         $tm = 0xFF >> (8 * $t8 - $t1);
 
         // Expand key.
-        $pitable = $this->pitable;
+        $pitable = self::$pitable;
         for ($i = $t; $i < 128; $i++) {
             $l[$i] = $pitable[$l[$i - 1] + $l[$i - $t]];
         }
@@ -389,7 +389,7 @@ class RC2 extends BlockCipher
         }
 
         // Prepare the key for mcrypt.
-        $l[0] = $this->invpitable[$l[0]];
+        $l[0] = self::$invpitable[$l[0]];
         array_unshift($l, 'C*');
 
         $this->key = call_user_func_array('pack', $l);
@@ -549,7 +549,7 @@ class RC2 extends BlockCipher
         // Key has already been expanded in \phpseclib\Crypt\RC2::setKey():
         // Only the first value must be altered.
         $l = unpack('Ca/Cb/v*', $this->key);
-        array_unshift($l, $this->pitable[$l['a']] | ($l['b'] << 8));
+        array_unshift($l, self::$pitable[$l['a']] | ($l['b'] << 8));
         unset($l['a']);
         unset($l['b']);
         $this->keys = $l;
diff --git a/phpseclib/Crypt/RSA.php b/phpseclib/Crypt/RSA.php
index 2689b3f3..4df22b1a 100644
--- a/phpseclib/Crypt/RSA.php
+++ b/phpseclib/Crypt/RSA.php
@@ -45,7 +45,6 @@
 
 namespace phpseclib\Crypt;
 
-use ParagonIE\ConstantTime\Base64;
 use phpseclib\File\ASN1;
 use phpseclib\Math\BigInteger;
 use phpseclib\Common\Functions\Strings;
@@ -203,14 +202,6 @@ class RSA extends AsymmetricKey
      */
     private $sLen;
 
-    /**
-     * Comment
-     *
-     * @var string
-     * @access private
-     */
-    private $comment;
-
     /**
      * Hash function for the Mask Generation Function
      *
@@ -332,40 +323,11 @@ class RSA extends AsymmetricKey
      * @return array
      * @access public
      * @param int $bits
-     *
      */
     public static function createKey($bits = 2048)
     {
         self::initialize_static_variables();
 
-        if (!isset(self::$engine)) {
-            self::setPreferredEngine(self::ENGINE_OPENSSL);
-        }
-
-        // OpenSSL uses 65537 as the exponent and requires RSA keys be 384 bits minimum
-
-        if (self::$engine == self::ENGINE_OPENSSL && $bits >= 384 && self::$defaultExponent == 65537) {
-            $config = [];
-            if (isset(self::$configFile)) {
-                $config['config'] = self::$configFile;
-            }
-            $rsa = openssl_pkey_new(['private_key_bits' => $bits] + $config);
-            openssl_pkey_export($rsa, $privatekeystr, null, $config);
-            $privatekey = new RSA();
-            $privatekey->load($privatekeystr);
-
-            $publickeyarr = openssl_pkey_get_details($rsa);
-            $publickey = new RSA();
-            $publickey->load($publickeyarr['key']);
-            $publickey->setPublicKey();
-
-            // clear the buffer of error strings stemming from a minimalistic openssl.cnf
-            while (openssl_error_string() !== false) {
-            }
-
-            return compact('privatekey', 'publickey');
-        }
-
         static $e;
         if (!isset($e)) {
             $e = new BigInteger(self::$defaultExponent);
@@ -488,7 +450,8 @@ class RSA extends AsymmetricKey
             $this->isPublic = $key->isPublic;
 
             if (is_object($key->hash)) {
-                $this->hash = new Hash($key->hash->getHash());
+                $this->hashName = $key->hash->getHash();
+                $this->hash = new Hash($this->hashName);
             }
             if (is_object($key->mgfHash)) {
                 $this->mgfHash = new Hash($key->mgfHash->getHash());
@@ -531,6 +494,7 @@ class RSA extends AsymmetricKey
             $this->exponents = null;
             $this->coefficients = null;
             $this->publicExponent = null;
+            $this->isPublic = false;
 
             return false;
         }
@@ -652,6 +616,19 @@ class RSA extends AsymmetricKey
         return !isset($this->modulus) ? 0 : $this->modulus->getLength();
     }
 
+    /**
+     * Returns the current engine being used
+     *
+     * @see self::useInternalEngine()
+     * @see self::useBestEngine()
+     * @access public
+     * @return string
+     */
+    public function getEngine()
+    {
+        return 'PHP';
+    }
+
     /**
      * Defines the public key
      *
@@ -704,15 +681,25 @@ class RSA extends AsymmetricKey
     }
 
     /**
-     * Does the key self-identify as being a public key or not?
+     * Is the key a public key?
      *
-     * @see self::isPublicKey()
      * @access public
      * @return bool
      */
     public function isPublicKey()
     {
-        return $this->isPublic();
+        return $this->isPublic;
+    }
+
+    /**
+     * Is the key a private key?
+     *
+     * @access public
+     * @return bool
+     */
+    public function isPrivateKey()
+    {
+        return !$this->isPublic && isset($this->modulus);
     }
 
     /**
@@ -735,6 +722,7 @@ class RSA extends AsymmetricKey
     {
         if ($key === false && !empty($this->publicExponent)) {
             $this->publicExponent = false;
+            $this->isPublic = false;
             return true;
         }
 
@@ -743,6 +731,7 @@ class RSA extends AsymmetricKey
             return false;
         }
         $rsa->publicExponent = false;
+        $rsa->isPublic = false;
 
         // don't overwrite the old key if the new key is invalid
         $this->load($rsa);
@@ -761,8 +750,14 @@ class RSA extends AsymmetricKey
      * @param string $type optional
      * @return mixed
      */
-    public function getPublicKey($type = 'PKCS8')
+    public function getPublicKey($type = null)
     {
+        $returnObj = false;
+        if ($type === null) {
+            $returnObj = true;
+            $type = 'PKCS8';
+        }
+
         $type = self::validatePlugin('Keys', $type, 'savePublicKey');
         if ($type === false) {
             return false;
@@ -772,7 +767,15 @@ class RSA extends AsymmetricKey
             return false;
         }
 
-        return $type::savePublicKey($this->modulus, $this->publicExponent);
+        $key = $type::savePublicKey($this->modulus, $this->publicExponent);
+        if (!$returnObj) {
+            return $key;
+        }
+
+        $public = clone $this;
+        $public->load($key, 'PKCS8');
+
+        return $public;
     }
 
     /**
@@ -1704,17 +1707,17 @@ class RSA extends AsymmetricKey
         static $oids;
         if (!isset($oids)) {
             $oids = [
-                '1.2.840.113549.2.2' => 'md2',
-                '1.2.840.113549.2.4' => 'md4', // from PKCS1 v1.5
-                '1.2.840.113549.2.5' => 'md5',
-                '1.3.14.3.2.26' => 'id-sha1',
-                '2.16.840.1.101.3.4.2.1' => 'id-sha256',
-                '2.16.840.1.101.3.4.2.2' => 'id-sha384',
-                '2.16.840.1.101.3.4.2.3' => 'id-sha512',
+                'md2' => '1.2.840.113549.2.2',
+                'md4' => '1.2.840.113549.2.4', // from PKCS1 v1.5
+                'md5' => '1.2.840.113549.2.5',
+                'id-sha1' => '1.3.14.3.2.26',
+                'id-sha256' => '2.16.840.1.101.3.4.2.1',
+                'id-sha384' => '2.16.840.1.101.3.4.2.2',
+                'id-sha512' => '2.16.840.1.101.3.4.2.3',
                 // from PKCS1 v2.2
-                '2.16.840.1.101.3.4.2.4' => 'id-sha224',
-                '2.16.840.1.101.3.4.2.5' => 'id-sha512/224',
-                '2.16.840.1.101.3.4.2.6' => 'id-sha512/256',
+                'id-sha224' => '2.16.840.1.101.3.4.2.4',
+                'id-sha512/224' => '2.16.840.1.101.3.4.2.5',
+                'id-sha512/256' => '2.16.840.1.101.3.4.2.6',
             ];
             ASN1::loadOIDs($oids);
         }
@@ -1724,7 +1727,7 @@ class RSA extends AsymmetricKey
             return false;
         }
 
-        if (!in_array($decoded['digestAlgorithm']['algorithm'], $oids)) {
+        if (!isset($oids[$decoded['digestAlgorithm']['algorithm']])) {
             return false;
         }
 
diff --git a/phpseclib/Crypt/RSA/Keys/MSBLOB.php b/phpseclib/Crypt/RSA/Keys/MSBLOB.php
index 52223ffd..ef4d7ccc 100644
--- a/phpseclib/Crypt/RSA/Keys/MSBLOB.php
+++ b/phpseclib/Crypt/RSA/Keys/MSBLOB.php
@@ -71,18 +71,21 @@ abstract class MSBLOB
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $key = Base64::decode($key);
 
-        if (!is_string($key) || strlen($key) < 20) {
-            return false;
+        if (!is_string($key)) {
+            throw new \UnexpectedValueException('Base64 decoding produced an error');
+        }
+        if (strlen($key) < 20) {
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         // PUBLICKEYSTRUC  publickeystruc
@@ -103,7 +106,7 @@ abstract class MSBLOB
                 $publickey = false;
                 break;
             default:
-                return false;
+                throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         $components = ['isPublicKey' => $publickey];
@@ -114,7 +117,7 @@ abstract class MSBLOB
             case self::CALG_RSA_SIGN:
                 break;
             default:
-                return false;
+                throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         // RSAPUBKEY rsapubkey
@@ -132,12 +135,12 @@ abstract class MSBLOB
             case self::RSA1:
                 break;
             default:
-                return false;
+                throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         $baseLength = $bitlen / 16;
         if (strlen($key) != 2 * $baseLength && strlen($key) != 9 * $baseLength) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
 
         $components[$components['isPublicKey'] ? 'publicExponent' : 'privateExponent'] = new BigInteger(strrev($pubexp), 256);
diff --git a/phpseclib/Crypt/RSA/Keys/OpenSSH.php b/phpseclib/Crypt/RSA/Keys/OpenSSH.php
index b8ba1bb5..77545d25 100644
--- a/phpseclib/Crypt/RSA/Keys/OpenSSH.php
+++ b/phpseclib/Crypt/RSA/Keys/OpenSSH.php
@@ -37,18 +37,15 @@ abstract class OpenSSH extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         $key = parent::load($key, 'ssh-rsa');
-        if ($key === false) {
-            return false;
-        }
 
         $result = Strings::unpackSSH2('ii', $key);
         if ($result === false) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
         list($publicExponent, $modulus) = $result;
 
diff --git a/phpseclib/Crypt/RSA/Keys/PKCS1.php b/phpseclib/Crypt/RSA/Keys/PKCS1.php
index 6c73d65d..6dbb46f4 100644
--- a/phpseclib/Crypt/RSA/Keys/PKCS1.php
+++ b/phpseclib/Crypt/RSA/Keys/PKCS1.php
@@ -44,24 +44,21 @@ abstract class PKCS1 extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $components = ['isPublicKey' => strpos($key, 'PUBLIC') !== false];
 
         $key = parent::load($key, $password);
-        if ($key === false) {
-            return false;
-        }
 
         $decoded = ASN1::decodeBER($key);
         if (empty($decoded)) {
-            return false;
+            throw new \RuntimeException('Unable to decode BER');
         }
 
         $key = ASN1::asn1map($decoded[0], Maps\RSAPrivateKey::MAP);
@@ -86,7 +83,11 @@ abstract class PKCS1 extends Progenitor
 
         $key = ASN1::asn1map($decoded[0], Maps\RSAPublicKey::MAP);
 
-        return is_array($key) ? $components + $key : false;
+        if (!is_array($key)) {
+            throw new \RuntimeException('Unable to perform ASN1 mapping');
+        }
+
+        return $components + $key;
     }
 
     /**
diff --git a/phpseclib/Crypt/RSA/Keys/PKCS8.php b/phpseclib/Crypt/RSA/Keys/PKCS8.php
index 40888020..b50c7c0a 100644
--- a/phpseclib/Crypt/RSA/Keys/PKCS8.php
+++ b/phpseclib/Crypt/RSA/Keys/PKCS8.php
@@ -70,20 +70,17 @@ abstract class PKCS8 extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $components = ['isPublicKey' => strpos($key, 'PUBLIC') !== false];
 
         $key = parent::load($key, $password);
-        if ($key === false) {
-            return false;
-        }
 
         $type = isset($key['privateKey']) ? 'private' : 'public';
 
diff --git a/phpseclib/Crypt/RSA/Keys/PuTTY.php b/phpseclib/Crypt/RSA/Keys/PuTTY.php
index af5653d0..ea8d61b5 100644
--- a/phpseclib/Crypt/RSA/Keys/PuTTY.php
+++ b/phpseclib/Crypt/RSA/Keys/PuTTY.php
@@ -39,10 +39,10 @@ abstract class PuTTY extends Progenitor
     /**
      * Algorithm Identifier
      *
-     * @var string
+     * @var array
      * @access private
      */
-    const TYPE = 'ssh-rsa';
+    protected static $types = ['ssh-rsa'];
 
     /**
      * Break a public or private key down into its constituent components
@@ -50,7 +50,7 @@ abstract class PuTTY extends Progenitor
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
@@ -60,21 +60,23 @@ abstract class PuTTY extends Progenitor
         }
 
         $components = parent::load($key, $password);
-        if ($components === false || !isset($components['private'])) {
+        if (!isset($components['private'])) {
             return $components;
         }
+        extract($components);
+        unset($components['public'], $components['private']);
 
         $isPublicKey = false;
 
-        $result = Strings::unpackSSH2('ii', $components['public']);
+        $result = Strings::unpackSSH2('ii', $public);
         if ($result === false) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
         list($publicExponent, $modulus) = $result;
 
-        $result = Strings::unpackSSH2('iiii', $components['private']);
+        $result = Strings::unpackSSH2('iiii', $private);
         if ($result === false) {
-            return false;
+            throw new \UnexpectedValueException('Key appears to be malformed');
         }
         $primes = $coefficients = [];
         list($privateExponent, $primes[1], $primes[2], $coefficients[2]) = $result;
@@ -84,10 +86,6 @@ abstract class PuTTY extends Progenitor
         $temp = $primes[2]->subtract($one);
         $exponents[] = $publicExponent->modInverse($temp);
 
-        if (isset($components['comment'])) {
-            $comment = $components['comment'];
-        }
-
         return compact('publicExponent', 'modulus', 'privateExponent', 'primes', 'coefficients', 'exponents', 'comment', 'isPublicKey');
     }
 
@@ -113,7 +111,7 @@ abstract class PuTTY extends Progenitor
         $public =  Strings::packSSH2('ii', $e, $n);
         $private = Strings::packSSH2('iiii', $d, $primes[1], $primes[2], $coefficients[2]);
 
-        return self::wrapPrivateKey($public, $private, $password);
+        return self::wrapPrivateKey($public, $private, 'ssh-rsa', $password);
     }
 
     /**
@@ -126,6 +124,6 @@ abstract class PuTTY extends Progenitor
      */
     public static function savePublicKey(BigInteger $n, BigInteger $e)
     {
-        return self::wrapPublicKey(Strings::packSSH2($e, $n));
+        return self::wrapPublicKey(Strings::packSSH2($e, $n), 'ssh-rsa');
     }
 }
diff --git a/phpseclib/Crypt/RSA/Keys/Raw.php b/phpseclib/Crypt/RSA/Keys/Raw.php
index fe3c4c62..28a58cb5 100644
--- a/phpseclib/Crypt/RSA/Keys/Raw.php
+++ b/phpseclib/Crypt/RSA/Keys/Raw.php
@@ -42,12 +42,12 @@ abstract class Raw
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_array($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a array - not a ' . gettype($key));
         }
         if (isset($key['isPublicKey']) && isset($key['modulus'])) {
             if (isset($key['privateExponent']) || isset($key['publicExponent'])) {
@@ -86,7 +86,11 @@ abstract class Raw
             case isset($key[1]):
                 $components['modulus'] = $key[1];
         }
-        return isset($components['modulus']) && isset($components['publicExponent']) ? $components : false;
+        if (isset($components['modulus']) && isset($components['publicExponent'])) {
+            return $components;
+        }
+
+        throw new \UnexpectedValueException('Modulus / exponent not present');
     }
 
     /**
diff --git a/phpseclib/Crypt/RSA/Keys/XML.php b/phpseclib/Crypt/RSA/Keys/XML.php
index 07549026..c8caf4b5 100644
--- a/phpseclib/Crypt/RSA/Keys/XML.php
+++ b/phpseclib/Crypt/RSA/Keys/XML.php
@@ -40,12 +40,12 @@ abstract class XML
      * @access public
      * @param string $key
      * @param string $password optional
-     * @return array|bool
+     * @return array
      */
     public static function load($key, $password = '')
     {
         if (!is_string($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
         }
 
         $components = [
@@ -62,7 +62,7 @@ abstract class XML
             $key = '<xml>' . $key . '</xml>';
         }
         if (!$dom->loadXML($key)) {
-            return false;
+            throw new \UnexpectedValueException('Key does not appear to contain XML');
         }
         $xpath = new \DOMXPath($dom);
         $keys = ['modulus', 'exponent', 'p', 'q', 'dp', 'dq', 'inverseq', 'd'];
@@ -102,7 +102,11 @@ abstract class XML
 
         libxml_use_internal_errors($use_errors);
 
-        return isset($components['modulus']) && isset($components['publicExponent']) ? $components : false;
+        if (isset($components['modulus']) && isset($components['publicExponent'])) {
+            return $components;
+        }
+
+        throw new \UnexpectedValueException('Modulus / exponent not present');
     }
 
     /**
diff --git a/phpseclib/Crypt/Twofish.php b/phpseclib/Crypt/Twofish.php
index ff77834b..b83818e4 100644
--- a/phpseclib/Crypt/Twofish.php
+++ b/phpseclib/Crypt/Twofish.php
@@ -73,7 +73,7 @@ class Twofish extends BlockCipher
      * @var array
      * @access private
      */
-    private $q0 = [
+    private static $q0 = [
         0xA9, 0x67, 0xB3, 0xE8, 0x04, 0xFD, 0xA3, 0x76,
         0x9A, 0x92, 0x80, 0x78, 0xE4, 0xDD, 0xD1, 0x38,
         0x0D, 0xC6, 0x35, 0x98, 0x18, 0xF7, 0xEC, 0x6C,
@@ -114,7 +114,7 @@ class Twofish extends BlockCipher
      * @var array
      * @access private
      */
-    private $q1 = [
+    private static $q1 = [
         0x75, 0xF3, 0xC6, 0xF4, 0xDB, 0x7B, 0xFB, 0xC8,
         0x4A, 0xD3, 0xE6, 0x6B, 0x45, 0x7D, 0xE8, 0x4B,
         0xD6, 0x32, 0xD8, 0xFD, 0x37, 0x71, 0xF1, 0xE1,
@@ -155,7 +155,7 @@ class Twofish extends BlockCipher
      * @var array
      * @access private
      */
-    private $m0 = [
+    private static $m0 = [
         0xBCBC3275, 0xECEC21F3, 0x202043C6, 0xB3B3C9F4, 0xDADA03DB, 0x02028B7B, 0xE2E22BFB, 0x9E9EFAC8,
         0xC9C9EC4A, 0xD4D409D3, 0x18186BE6, 0x1E1E9F6B, 0x98980E45, 0xB2B2387D, 0xA6A6D2E8, 0x2626B74B,
         0x3C3C57D6, 0x93938A32, 0x8282EED8, 0x525298FD, 0x7B7BD437, 0xBBBB3771, 0x5B5B97F1, 0x474783E1,
@@ -196,7 +196,7 @@ class Twofish extends BlockCipher
      * @var array
      * @access private
      */
-    private $m1 = [
+    private static $m1 = [
         0xA9D93939, 0x67901717, 0xB3719C9C, 0xE8D2A6A6, 0x04050707, 0xFD985252, 0xA3658080, 0x76DFE4E4,
         0x9A084545, 0x92024B4B, 0x80A0E0E0, 0x78665A5A, 0xE4DDAFAF, 0xDDB06A6A, 0xD1BF6363, 0x38362A2A,
         0x0D54E6E6, 0xC6432020, 0x3562CCCC, 0x98BEF2F2, 0x181E1212, 0xF724EBEB, 0xECD7A1A1, 0x6C774141,
@@ -237,7 +237,7 @@ class Twofish extends BlockCipher
      * @var array
      * @access private
      */
-    private $m2 = [
+    private static $m2 = [
         0xBC75BC32, 0xECF3EC21, 0x20C62043, 0xB3F4B3C9, 0xDADBDA03, 0x027B028B, 0xE2FBE22B, 0x9EC89EFA,
         0xC94AC9EC, 0xD4D3D409, 0x18E6186B, 0x1E6B1E9F, 0x9845980E, 0xB27DB238, 0xA6E8A6D2, 0x264B26B7,
         0x3CD63C57, 0x9332938A, 0x82D882EE, 0x52FD5298, 0x7B377BD4, 0xBB71BB37, 0x5BF15B97, 0x47E14783,
@@ -278,7 +278,7 @@ class Twofish extends BlockCipher
      * @var array
      * @access private
      */
-    private $m3 = [
+    private static $m3 = [
         0xD939A9D9, 0x90176790, 0x719CB371, 0xD2A6E8D2, 0x05070405, 0x9852FD98, 0x6580A365, 0xDFE476DF,
         0x08459A08, 0x024B9202, 0xA0E080A0, 0x665A7866, 0xDDAFE4DD, 0xB06ADDB0, 0xBF63D1BF, 0x362A3836,
         0x54E60D54, 0x4320C643, 0x62CC3562, 0xBEF298BE, 0x1E12181E, 0x24EBF724, 0xD7A1ECD7, 0x77416C77,
@@ -449,12 +449,12 @@ class Twofish extends BlockCipher
         /* Key expanding and generating the key-depended s-boxes */
         $le_longs = unpack('V*', $this->key);
         $key = unpack('C*', $this->key);
-        $m0 = $this->m0;
-        $m1 = $this->m1;
-        $m2 = $this->m2;
-        $m3 = $this->m3;
-        $q0 = $this->q0;
-        $q1 = $this->q1;
+        $m0 = self::$m0;
+        $m1 = self::$m1;
+        $m2 = self::$m2;
+        $m3 = self::$m3;
+        $q0 = self::$q0;
+        $q1 = self::$q1;
 
         $K = $S0 = $S1 = $S2 = $S3 = [];
 
diff --git a/phpseclib/Exception/UnsupportedCurveException.php b/phpseclib/Exception/UnsupportedCurveException.php
new file mode 100644
index 00000000..bd2c81b5
--- /dev/null
+++ b/phpseclib/Exception/UnsupportedCurveException.php
@@ -0,0 +1,26 @@
+<?php
+
+/**
+ * UnsupportedCurveException
+ *
+ * PHP version 5
+ *
+ * @category  Exception
+ * @package   UnsupportedCurveException
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\Exception;
+
+/**
+ * UnsupportedCurveException
+ *
+ * @package UnsupportedCurveException
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class UnsupportedCurveException extends \RuntimeException
+{
+}
diff --git a/phpseclib/File/ASN1.php b/phpseclib/File/ASN1.php
index fbc06063..2e3ec8e3 100644
--- a/phpseclib/File/ASN1.php
+++ b/phpseclib/File/ASN1.php
@@ -818,6 +818,27 @@ abstract class ASN1
         }
     }
 
+    /**
+     * DER-decode the length
+     *
+     * DER supports lengths up to (2**8)**127, however, we'll only support lengths up to (2**8)**4.  See
+     * {@link http://itu.int/ITU-T/studygroups/com17/languages/X.690-0207.pdf#p=13 X.690 paragraph 8.1.3} for more information.
+     *
+     * @access public
+     * @param string $string
+     * @return int
+     */
+    public static function decodeLength(&$string)
+    {
+        $length = ord(Strings::shift($string));
+        if ($length & 0x80) { // definite length, long form
+            $length&= 0x7F;
+            $temp = Strings::shift($string, $length);
+            list(, $length) = unpack('N', substr(str_pad($temp, 4, chr(0), STR_PAD_LEFT), -4));
+        }
+        return $length;
+    }
+
     /**
      * ASN.1 Encode
      *
@@ -1219,8 +1240,8 @@ abstract class ASN1
      */
     public static function loadOIDs($oids)
     {
-        self::$oids+= $oids;
-        self::$reverseOIDs = array_flip(self::$oids);
+        self::$reverseOIDs+= $oids;
+        self::$oids = array_flip(self::$reverseOIDs);
     }
 
     /**
diff --git a/phpseclib/File/ASN1/Maps/Characteristic_two.php b/phpseclib/File/ASN1/Maps/Characteristic_two.php
new file mode 100644
index 00000000..92817031
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/Characteristic_two.php
@@ -0,0 +1,40 @@
+<?php
+
+/**
+ * Characteristic_two
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * Characteristic_two
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Characteristic_two
+{
+    const MAP = [
+        'type' => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'm' => ['type' => ASN1::TYPE_INTEGER], // field size 2**m
+            'basis' => ['type' => ASN1::TYPE_OBJECT_IDENTIFIER],
+            'parameters' => [
+                'type' => ASN1::TYPE_ANY,
+                'optional' => true
+            ]
+        ]
+    ];
+}
\ No newline at end of file
diff --git a/phpseclib/File/ASN1/Maps/Curve.php b/phpseclib/File/ASN1/Maps/Curve.php
new file mode 100644
index 00000000..1a438028
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/Curve.php
@@ -0,0 +1,40 @@
+<?php
+
+/**
+ * Curve
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * Curve
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Curve
+{
+    const MAP = [
+        'type' => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'a' => FieldElement::MAP,
+            'b' => FieldElement::MAP,
+            'seed' => [
+                'type' => ASN1::TYPE_BIT_STRING,
+                'optional' => true
+            ]
+        ]
+    ];
+}
diff --git a/phpseclib/File/ASN1/Maps/ECParameters.php b/phpseclib/File/ASN1/Maps/ECParameters.php
new file mode 100644
index 00000000..21e096ea
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/ECParameters.php
@@ -0,0 +1,49 @@
+<?php
+
+/**
+ * ECParameters
+ *
+ * From: https://tools.ietf.org/html/rfc5915
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * ECParameters
+ *
+ *  ECParameters ::= CHOICE {
+ *    namedCurve         OBJECT IDENTIFIER
+ *    -- implicitCurve   NULL
+ *    -- specifiedCurve  SpecifiedECDomain
+ *  }
+ *    -- implicitCurve and specifiedCurve MUST NOT be used in PKIX.
+ *    -- Details for SpecifiedECDomain can be found in [X9.62].
+ *    -- Any future additions to this CHOICE should be coordinated
+ *    -- with ANSI X9.
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class ECParameters
+{
+    const MAP = [
+        'type'     => ASN1::TYPE_CHOICE,
+        'children' => [
+            'namedCurve' => ['type' => ASN1::TYPE_OBJECT_IDENTIFIER],
+            'implicitCurve' => ['type' => ASN1::TYPE_NULL],
+            'specifiedCurve' => SpecifiedECDomain::MAP
+        ]
+    ];
+}
diff --git a/phpseclib/File/ASN1/Maps/ECPoint.php b/phpseclib/File/ASN1/Maps/ECPoint.php
new file mode 100644
index 00000000..bd6ea09e
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/ECPoint.php
@@ -0,0 +1,30 @@
+<?php
+
+/**
+ * ECPoint
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * ECPoint
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class ECPoint
+{
+    const MAP = ['type' => ASN1::TYPE_OCTET_STRING];
+}
diff --git a/phpseclib/File/ASN1/Maps/ECPrivateKey.php b/phpseclib/File/ASN1/Maps/ECPrivateKey.php
new file mode 100644
index 00000000..fb17c412
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/ECPrivateKey.php
@@ -0,0 +1,52 @@
+<?php
+
+/**
+ * ECPrivateKey
+ *
+ * From: https://tools.ietf.org/html/rfc5915
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * ECPrivateKey
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class ECPrivateKey
+{
+    const MAP = [
+        'type' => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'version' => [
+                'type' => ASN1::TYPE_INTEGER,
+                'mapping' => [1 => 'ecPrivkeyVer1']
+            ],
+            'privateKey' => ['type' => ASN1::TYPE_OCTET_STRING],
+            'parameters' => [
+                'constant' => 0,
+                'optional' => true,
+                'explicit' => true
+            ] + ECParameters::MAP,
+            'publicKey' => [
+                'type' => ASN1::TYPE_BIT_STRING,
+                'constant' => 1,
+                'optional' => true,
+                'explicit' => true
+            ]
+        ]
+    ];
+}
diff --git a/phpseclib/File/ASN1/Maps/EcdsaSigValue.php b/phpseclib/File/ASN1/Maps/EcdsaSigValue.php
new file mode 100644
index 00000000..69f95bda
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/EcdsaSigValue.php
@@ -0,0 +1,36 @@
+<?php
+
+/**
+ * EcdsaSigValue
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * EcdsaSigValue
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class EcdsaSigValue
+{
+    const MAP = [
+        'type'     => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'r' => ['type' => ASN1::TYPE_INTEGER],
+            's' => ['type' => ASN1::TYPE_INTEGER]
+        ]
+    ];
+}
diff --git a/phpseclib/File/ASN1/Maps/FieldElement.php b/phpseclib/File/ASN1/Maps/FieldElement.php
new file mode 100644
index 00000000..5617607f
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/FieldElement.php
@@ -0,0 +1,30 @@
+<?php
+
+/**
+ * FieldElement
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * FieldElement
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class FieldElement
+{
+    const MAP = ['type' => ASN1::TYPE_OCTET_STRING];
+}
diff --git a/phpseclib/File/ASN1/Maps/FieldID.php b/phpseclib/File/ASN1/Maps/FieldID.php
new file mode 100644
index 00000000..b5642030
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/FieldID.php
@@ -0,0 +1,39 @@
+<?php
+
+/**
+ * FieldID
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * FieldID
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class FieldID
+{
+    const MAP = [
+        'type' => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'fieldType' => ['type' => ASN1::TYPE_OBJECT_IDENTIFIER],
+            'parameters' => [
+                'type' => ASN1::TYPE_ANY,
+                'optional' => true
+            ]
+        ]
+    ];
+}
\ No newline at end of file
diff --git a/phpseclib/File/ASN1/Maps/HashAlgorithm.php b/phpseclib/File/ASN1/Maps/HashAlgorithm.php
new file mode 100644
index 00000000..49e718ec
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/HashAlgorithm.php
@@ -0,0 +1,30 @@
+<?php
+
+/**
+ * HashAglorithm
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * HashAglorithm
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class HashAlgorithm
+{
+    const MAP = AlgorithmIdentifier::MAP;
+}
\ No newline at end of file
diff --git a/phpseclib/File/ASN1/Maps/OneAsymmetricKey.php b/phpseclib/File/ASN1/Maps/OneAsymmetricKey.php
new file mode 100644
index 00000000..73af0695
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/OneAsymmetricKey.php
@@ -0,0 +1,52 @@
+<?php
+
+/**
+ * OneAsymmetricKey
+ *
+ * See https://tools.ietf.org/html/rfc5958
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * OneAsymmetricKey
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class OneAsymmetricKey
+{
+    const MAP = [
+        'type'     => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'version' => [
+                'type' => ASN1::TYPE_INTEGER,
+                'mapping' => ['v1', 'v2']
+            ],
+            'privateKeyAlgorithm'=> AlgorithmIdentifier::MAP,
+            'privateKey' => PrivateKey::MAP,
+            'attributes' => [
+                'constant' => 0,
+                'optional' => true,
+                'implicit' => true
+            ] + Attributes::MAP,
+            'publicKey' => [
+                'constant' => 1,
+                'optional' => true,
+                'implicit' => true
+            ] + PublicKey::MAP
+        ]
+    ];
+}
diff --git a/phpseclib/File/ASN1/Maps/Pentanomial.php b/phpseclib/File/ASN1/Maps/Pentanomial.php
new file mode 100644
index 00000000..2474680e
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/Pentanomial.php
@@ -0,0 +1,37 @@
+<?php
+
+/**
+ * Pentanomial
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * Pentanomial
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Pentanomial
+{
+    const MAP = [
+        'type' => ASN1::TYPE_SEQUENCE,
+        'children' => [
+             'k1' => ['type' => ASN1::TYPE_INTEGER], // k1 > 0
+             'k2' => ['type' => ASN1::TYPE_INTEGER], // k2 > k1
+             'k3' => ['type' => ASN1::TYPE_INTEGER], // k3 > h2
+        ]
+    ];
+}
\ No newline at end of file
diff --git a/phpseclib/File/ASN1/Maps/Prime_p.php b/phpseclib/File/ASN1/Maps/Prime_p.php
new file mode 100644
index 00000000..fe107750
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/Prime_p.php
@@ -0,0 +1,30 @@
+<?php
+
+/**
+ * Prime_p
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * Prime_p
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Prime_p
+{
+    const MAP = ['type' => ASN1::TYPE_INTEGER];
+}
\ No newline at end of file
diff --git a/phpseclib/File/ASN1/Maps/PublicKey.php b/phpseclib/File/ASN1/Maps/PublicKey.php
new file mode 100644
index 00000000..1f269480
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/PublicKey.php
@@ -0,0 +1,30 @@
+<?php
+
+/**
+ * PublicKey
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * PublicKey
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class PublicKey
+{
+    const MAP = ['type' => ASN1::TYPE_BIT_STRING];
+}
diff --git a/phpseclib/File/ASN1/Maps/SpecifiedECDomain.php b/phpseclib/File/ASN1/Maps/SpecifiedECDomain.php
new file mode 100644
index 00000000..b44541e2
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/SpecifiedECDomain.php
@@ -0,0 +1,49 @@
+<?php
+
+/**
+ * SpecifiedECDomain
+ *
+ * From: http://www.secg.org/sec1-v2.pdf#page=109
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * SpecifiedECDomain
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class SpecifiedECDomain
+{
+    const MAP = [
+        'type'     => ASN1::TYPE_SEQUENCE,
+        'children' => [
+            'version' => [
+                'type' => ASN1::TYPE_INTEGER,
+                'mapping' => [1 => 'ecdpVer1', 'ecdpVer2', 'ecdpVer3']
+            ],
+            'fieldID' => FieldID::MAP,
+            'curve' => Curve::MAP,
+            'base' => ECPoint::MAP,
+            'order' => ['type' => ASN1::TYPE_INTEGER],
+            'cofactor' => [
+                'type' => ASN1::TYPE_INTEGER,
+                'optional' => true
+            ],
+            'hash' => ['optional' => true] + HashAlgorithm::MAP
+        ]
+    ];
+}
diff --git a/phpseclib/File/ASN1/Maps/Trinomial.php b/phpseclib/File/ASN1/Maps/Trinomial.php
new file mode 100644
index 00000000..3e0dac82
--- /dev/null
+++ b/phpseclib/File/ASN1/Maps/Trinomial.php
@@ -0,0 +1,30 @@
+<?php
+
+/**
+ * Trinomial
+ *
+ * PHP version 5
+ *
+ * @category  File
+ * @package   ASN1
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2016 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://phpseclib.sourceforge.net
+ */
+
+namespace phpseclib\File\ASN1\Maps;
+
+use phpseclib\File\ASN1;
+
+/**
+ * Trinomial
+ *
+ * @package ASN1
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Trinomial
+{
+    const MAP = ['type' => ASN1::TYPE_INTEGER];
+}
\ No newline at end of file
diff --git a/phpseclib/File/X509.php b/phpseclib/File/X509.php
index 7c3451f1..fe0e32a6 100644
--- a/phpseclib/File/X509.php
+++ b/phpseclib/File/X509.php
@@ -273,168 +273,168 @@ class X509
         if (!self::$oidsLoaded) {
             // OIDs from RFC5280 and those RFCs mentioned in RFC5280#section-4.1.1.2
             ASN1::loadOIDs([
-                '1.3.6.1.5.5.7' => 'id-pkix',
-                '1.3.6.1.5.5.7.1' => 'id-pe',
-                '1.3.6.1.5.5.7.2' => 'id-qt',
-                '1.3.6.1.5.5.7.3' => 'id-kp',
-                '1.3.6.1.5.5.7.48' => 'id-ad',
-                '1.3.6.1.5.5.7.2.1' => 'id-qt-cps',
-                '1.3.6.1.5.5.7.2.2' => 'id-qt-unotice',
-                '1.3.6.1.5.5.7.48.1' =>'id-ad-ocsp',
-                '1.3.6.1.5.5.7.48.2' => 'id-ad-caIssuers',
-                '1.3.6.1.5.5.7.48.3' => 'id-ad-timeStamping',
-                '1.3.6.1.5.5.7.48.5' => 'id-ad-caRepository',
-                '2.5.4' => 'id-at',
-                '2.5.4.41' => 'id-at-name',
-                '2.5.4.4' => 'id-at-surname',
-                '2.5.4.42' => 'id-at-givenName',
-                '2.5.4.43' => 'id-at-initials',
-                '2.5.4.44' => 'id-at-generationQualifier',
-                '2.5.4.3' => 'id-at-commonName',
-                '2.5.4.7' => 'id-at-localityName',
-                '2.5.4.8' => 'id-at-stateOrProvinceName',
-                '2.5.4.10' => 'id-at-organizationName',
-                '2.5.4.11' => 'id-at-organizationalUnitName',
-                '2.5.4.12' => 'id-at-title',
-                '2.5.4.13' => 'id-at-description',
-                '2.5.4.46' => 'id-at-dnQualifier',
-                '2.5.4.6' => 'id-at-countryName',
-                '2.5.4.5' => 'id-at-serialNumber',
-                '2.5.4.65' => 'id-at-pseudonym',
-                '2.5.4.17' => 'id-at-postalCode',
-                '2.5.4.9' => 'id-at-streetAddress',
-                '2.5.4.45' => 'id-at-uniqueIdentifier',
-                '2.5.4.72' => 'id-at-role',
-                '2.5.4.16' => 'id-at-postalAddress',
+                'id-pkix' => '1.3.6.1.5.5.7',
+                'id-pe' => '1.3.6.1.5.5.7.1',
+                'id-qt' => '1.3.6.1.5.5.7.2',
+                'id-kp' => '1.3.6.1.5.5.7.3',
+                'id-ad' => '1.3.6.1.5.5.7.48',
+                'id-qt-cps' => '1.3.6.1.5.5.7.2.1',
+                'id-qt-unotice' => '1.3.6.1.5.5.7.2.2',
+                'id-ad-ocsp' =>'1.3.6.1.5.5.7.48.1',
+                'id-ad-caIssuers' => '1.3.6.1.5.5.7.48.2',
+                'id-ad-timeStamping' => '1.3.6.1.5.5.7.48.3',
+                'id-ad-caRepository' => '1.3.6.1.5.5.7.48.5',
+                'id-at' => '2.5.4',
+                'id-at-name' => '2.5.4.41',
+                'id-at-surname' => '2.5.4.4',
+                'id-at-givenName' => '2.5.4.42',
+                'id-at-initials' => '2.5.4.43',
+                'id-at-generationQualifier' => '2.5.4.44',
+                'id-at-commonName' => '2.5.4.3',
+                'id-at-localityName' => '2.5.4.7',
+                'id-at-stateOrProvinceName' => '2.5.4.8',
+                'id-at-organizationName' => '2.5.4.10',
+                'id-at-organizationalUnitName' => '2.5.4.11',
+                'id-at-title' => '2.5.4.12',
+                'id-at-description' => '2.5.4.13',
+                'id-at-dnQualifier' => '2.5.4.46',
+                'id-at-countryName' => '2.5.4.6',
+                'id-at-serialNumber' => '2.5.4.5',
+                'id-at-pseudonym' => '2.5.4.65',
+                'id-at-postalCode' => '2.5.4.17',
+                'id-at-streetAddress' => '2.5.4.9',
+                'id-at-uniqueIdentifier' => '2.5.4.45',
+                'id-at-role' => '2.5.4.72',
+                'id-at-postalAddress' => '2.5.4.16',
 
-                '0.9.2342.19200300.100.1.25' => 'id-domainComponent',
-                '1.2.840.113549.1.9' => 'pkcs-9',
-                '1.2.840.113549.1.9.1' => 'pkcs-9-at-emailAddress',
-                '2.5.29' => 'id-ce',
-                '2.5.29.35' => 'id-ce-authorityKeyIdentifier',
-                '2.5.29.14' => 'id-ce-subjectKeyIdentifier',
-                '2.5.29.15' => 'id-ce-keyUsage',
-                '2.5.29.16' => 'id-ce-privateKeyUsagePeriod',
-                '2.5.29.32' => 'id-ce-certificatePolicies',
-                '2.5.29.32.0' => 'anyPolicy',
+                'id-domainComponent' => '0.9.2342.19200300.100.1.25',
+                'pkcs-9' => '1.2.840.113549.1.9',
+                'pkcs-9-at-emailAddress' => '1.2.840.113549.1.9.1',
+                'id-ce' => '2.5.29',
+                'id-ce-authorityKeyIdentifier' => '2.5.29.35',
+                'id-ce-subjectKeyIdentifier' => '2.5.29.14',
+                'id-ce-keyUsage' => '2.5.29.15',
+                'id-ce-privateKeyUsagePeriod' => '2.5.29.16',
+                'id-ce-certificatePolicies' => '2.5.29.32',
+                'anyPolicy' => '2.5.29.32.0',
 
-                '2.5.29.33' => 'id-ce-policyMappings',
-                '2.5.29.17' => 'id-ce-subjectAltName',
-                '2.5.29.18' => 'id-ce-issuerAltName',
-                '2.5.29.9' => 'id-ce-subjectDirectoryAttributes',
-                '2.5.29.19' => 'id-ce-basicConstraints',
-                '2.5.29.30' => 'id-ce-nameConstraints',
-                '2.5.29.36' => 'id-ce-policyConstraints',
-                '2.5.29.31' => 'id-ce-cRLDistributionPoints',
-                '2.5.29.37' => 'id-ce-extKeyUsage',
-                '2.5.29.37.0' => 'anyExtendedKeyUsage',
-                '1.3.6.1.5.5.7.3.1' => 'id-kp-serverAuth',
-                '1.3.6.1.5.5.7.3.2' => 'id-kp-clientAuth',
-                '1.3.6.1.5.5.7.3.3' => 'id-kp-codeSigning',
-                '1.3.6.1.5.5.7.3.4' => 'id-kp-emailProtection',
-                '1.3.6.1.5.5.7.3.8' => 'id-kp-timeStamping',
-                '1.3.6.1.5.5.7.3.9' => 'id-kp-OCSPSigning',
-                '2.5.29.54' => 'id-ce-inhibitAnyPolicy',
-                '2.5.29.46' => 'id-ce-freshestCRL',
-                '1.3.6.1.5.5.7.1.1' => 'id-pe-authorityInfoAccess',
-                '1.3.6.1.5.5.7.1.11' => 'id-pe-subjectInfoAccess',
-                '2.5.29.20' => 'id-ce-cRLNumber',
-                '2.5.29.28' => 'id-ce-issuingDistributionPoint',
-                '2.5.29.27' => 'id-ce-deltaCRLIndicator',
-                '2.5.29.21' => 'id-ce-cRLReasons',
-                '2.5.29.29' => 'id-ce-certificateIssuer',
-                '2.5.29.23' => 'id-ce-holdInstructionCode',
-                '1.2.840.10040.2' => 'holdInstruction',
-                '1.2.840.10040.2.1' => 'id-holdinstruction-none',
-                '1.2.840.10040.2.2' => 'id-holdinstruction-callissuer',
-                '1.2.840.10040.2.3' => 'id-holdinstruction-reject',
-                '2.5.29.24' => 'id-ce-invalidityDate',
+                'id-ce-policyMappings' => '2.5.29.33',
+                'id-ce-subjectAltName' => '2.5.29.17',
+                'id-ce-issuerAltName' => '2.5.29.18',
+                'id-ce-subjectDirectoryAttributes' => '2.5.29.9',
+                'id-ce-basicConstraints' => '2.5.29.19',
+                'id-ce-nameConstraints' => '2.5.29.30',
+                'id-ce-policyConstraints' => '2.5.29.36',
+                'id-ce-cRLDistributionPoints' => '2.5.29.31',
+                'id-ce-extKeyUsage' => '2.5.29.37',
+                'anyExtendedKeyUsage' => '2.5.29.37.0',
+                'id-kp-serverAuth' => '1.3.6.1.5.5.7.3.1',
+                'id-kp-clientAuth' => '1.3.6.1.5.5.7.3.2',
+                'id-kp-codeSigning' => '1.3.6.1.5.5.7.3.3',
+                'id-kp-emailProtection' => '1.3.6.1.5.5.7.3.4',
+                'id-kp-timeStamping' => '1.3.6.1.5.5.7.3.8',
+                'id-kp-OCSPSigning' => '1.3.6.1.5.5.7.3.9',
+                'id-ce-inhibitAnyPolicy' => '2.5.29.54',
+                'id-ce-freshestCRL' => '2.5.29.46',
+                'id-pe-authorityInfoAccess' => '1.3.6.1.5.5.7.1.1',
+                'id-pe-subjectInfoAccess' => '1.3.6.1.5.5.7.1.11',
+                'id-ce-cRLNumber' => '2.5.29.20',
+                'id-ce-issuingDistributionPoint' => '2.5.29.28',
+                'id-ce-deltaCRLIndicator' => '2.5.29.27',
+                'id-ce-cRLReasons' => '2.5.29.21',
+                'id-ce-certificateIssuer' => '2.5.29.29',
+                'id-ce-holdInstructionCode' => '2.5.29.23',
+                'holdInstruction' => '1.2.840.10040.2',
+                'id-holdinstruction-none' => '1.2.840.10040.2.1',
+                'id-holdinstruction-callissuer' => '1.2.840.10040.2.2',
+                'id-holdinstruction-reject' => '1.2.840.10040.2.3',
+                'id-ce-invalidityDate' => '2.5.29.24',
 
-                '1.2.840.113549.2.2' => 'md2',
-                '1.2.840.113549.2.5' => 'md5',
-                '1.3.14.3.2.26' => 'id-sha1',
-                '1.2.840.10040.4.1' => 'id-dsa',
-                '1.2.840.10040.4.3' => 'id-dsa-with-sha1',
-                '1.2.840.113549.1.1' => 'pkcs-1',
-                '1.2.840.113549.1.1.1' => 'rsaEncryption',
-                '1.2.840.113549.1.1.2' => 'md2WithRSAEncryption',
-                '1.2.840.113549.1.1.4' => 'md5WithRSAEncryption',
-                '1.2.840.113549.1.1.5' => 'sha1WithRSAEncryption',
-                '1.2.840.10046.2.1' => 'dhpublicnumber',
-                '2.16.840.1.101.2.1.1.22' => 'id-keyExchangeAlgorithm',
-                '1.2.840.10045' => 'ansi-X9-62',
-                '1.2.840.10045.4' => 'id-ecSigType',
-                '1.2.840.10045.4.1' => 'ecdsa-with-SHA1',
-                '1.2.840.10045.1' => 'id-fieldType',
-                '1.2.840.10045.1.1' => 'prime-field',
-                '1.2.840.10045.1.2' => 'characteristic-two-field',
-                '1.2.840.10045.1.2.3' => 'id-characteristic-two-basis',
-                '1.2.840.10045.1.2.3.1' => 'gnBasis',
-                '1.2.840.10045.1.2.3.2' => 'tpBasis',
-                '1.2.840.10045.1.2.3.3' => 'ppBasis',
-                '1.2.840.10045.2' => 'id-publicKeyType',
-                '1.2.840.10045.2.1' => 'id-ecPublicKey',
-                '1.2.840.10045.3' => 'ellipticCurve',
-                '1.2.840.10045.3.0' => 'c-TwoCurve',
-                '1.2.840.10045.3.0.1' => 'c2pnb163v1',
-                '1.2.840.10045.3.0.2' => 'c2pnb163v2',
-                '1.2.840.10045.3.0.3' => 'c2pnb163v3',
-                '1.2.840.10045.3.0.4' => 'c2pnb176w1',
-                '1.2.840.10045.3.0.5' => 'c2pnb191v1',
-                '1.2.840.10045.3.0.6' => 'c2pnb191v2',
-                '1.2.840.10045.3.0.7' => 'c2pnb191v3',
-                '1.2.840.10045.3.0.8' => 'c2pnb191v4',
-                '1.2.840.10045.3.0.9' => 'c2pnb191v5',
-                '1.2.840.10045.3.0.10' => 'c2pnb208w1',
-                '1.2.840.10045.3.0.11' => 'c2pnb239v1',
-                '1.2.840.10045.3.0.12' => 'c2pnb239v2',
-                '1.2.840.10045.3.0.13' => 'c2pnb239v3',
-                '1.2.840.10045.3.0.14' => 'c2pnb239v4',
-                '1.2.840.10045.3.0.15' => 'c2pnb239v5',
-                '1.2.840.10045.3.0.16' => 'c2pnb272w1',
-                '1.2.840.10045.3.0.17' => 'c2pnb304w1',
-                '1.2.840.10045.3.0.18' => 'c2pnb359v1',
-                '1.2.840.10045.3.0.19' => 'c2pnb368w1',
-                '1.2.840.10045.3.0.20' => 'c2pnb431r1',
-                '1.2.840.10045.3.1' => 'primeCurve',
-                '1.2.840.10045.3.1.1' => 'prime192v1',
-                '1.2.840.10045.3.1.2' => 'prime192v2',
-                '1.2.840.10045.3.1.3' => 'prime192v3',
-                '1.2.840.10045.3.1.4' => 'prime239v1',
-                '1.2.840.10045.3.1.5' => 'prime239v2',
-                '1.2.840.10045.3.1.6' => 'prime239v3',
-                '1.2.840.10045.3.1.7' => 'prime256v1',
-                '1.2.840.113549.1.1.7' => 'id-RSAES-OAEP',
-                '1.2.840.113549.1.1.9' => 'id-pSpecified',
-                '1.2.840.113549.1.1.10' => 'id-RSASSA-PSS',
-                '1.2.840.113549.1.1.8' => 'id-mgf1',
-                '1.2.840.113549.1.1.14' => 'sha224WithRSAEncryption',
-                '1.2.840.113549.1.1.11' => 'sha256WithRSAEncryption',
-                '1.2.840.113549.1.1.12' => 'sha384WithRSAEncryption',
-                '1.2.840.113549.1.1.13' => 'sha512WithRSAEncryption',
-                '2.16.840.1.101.3.4.2.4' => 'id-sha224',
-                '2.16.840.1.101.3.4.2.1' => 'id-sha256',
-                '2.16.840.1.101.3.4.2.2' => 'id-sha384',
-                '2.16.840.1.101.3.4.2.3' => 'id-sha512',
-                '1.2.643.2.2.4' => 'id-GostR3411-94-with-GostR3410-94',
-                '1.2.643.2.2.3' => 'id-GostR3411-94-with-GostR3410-2001',
-                '1.2.643.2.2.20' => 'id-GostR3410-2001',
-                '1.2.643.2.2.19' => 'id-GostR3410-94',
+                'md2' => '1.2.840.113549.2.2',
+                'md5' => '1.2.840.113549.2.5',
+                'id-sha1' => '1.3.14.3.2.26',
+                'id-dsa' => '1.2.840.10040.4.1',
+                'id-dsa-with-sha1' => '1.2.840.10040.4.3',
+                'pkcs-1' => '1.2.840.113549.1.1',
+                'rsaEncryption' => '1.2.840.113549.1.1.1',
+                'md2WithRSAEncryption' => '1.2.840.113549.1.1.2',
+                'md5WithRSAEncryption' => '1.2.840.113549.1.1.4',
+                'sha1WithRSAEncryption' => '1.2.840.113549.1.1.5',
+                'dhpublicnumber' => '1.2.840.10046.2.1',
+                'id-keyExchangeAlgorithm' => '2.16.840.1.101.2.1.1.22',
+                'ansi-X9-62' => '1.2.840.10045',
+                'id-ecSigType' => '1.2.840.10045.4',
+                'ecdsa-with-SHA1' => '1.2.840.10045.4.1',
+                'id-fieldType' => '1.2.840.10045.1',
+                'prime-field' => '1.2.840.10045.1.1',
+                'characteristic-two-field' => '1.2.840.10045.1.2',
+                'id-characteristic-two-basis' => '1.2.840.10045.1.2.3',
+                'gnBasis' => '1.2.840.10045.1.2.3.1',
+                'tpBasis' => '1.2.840.10045.1.2.3.2',
+                'ppBasis' => '1.2.840.10045.1.2.3.3',
+                'id-publicKeyType' => '1.2.840.10045.2',
+                'id-ecPublicKey' => '1.2.840.10045.2.1',
+                'ellipticCurve' => '1.2.840.10045.3',
+                'c-TwoCurve' => '1.2.840.10045.3.0',
+                'c2pnb163v1' => '1.2.840.10045.3.0.1',
+                'c2pnb163v2' => '1.2.840.10045.3.0.2',
+                'c2pnb163v3' => '1.2.840.10045.3.0.3',
+                'c2pnb176w1' => '1.2.840.10045.3.0.4',
+                'c2pnb191v1' => '1.2.840.10045.3.0.5',
+                'c2pnb191v2' => '1.2.840.10045.3.0.6',
+                'c2pnb191v3' => '1.2.840.10045.3.0.7',
+                'c2pnb191v4' => '1.2.840.10045.3.0.8',
+                'c2pnb191v5' => '1.2.840.10045.3.0.9',
+                'c2pnb208w1' => '1.2.840.10045.3.0.10',
+                'c2pnb239v1' => '1.2.840.10045.3.0.11',
+                'c2pnb239v2' => '1.2.840.10045.3.0.12',
+                'c2pnb239v3' => '1.2.840.10045.3.0.13',
+                'c2pnb239v4' => '1.2.840.10045.3.0.14',
+                'c2pnb239v5' => '1.2.840.10045.3.0.15',
+                'c2pnb272w1' => '1.2.840.10045.3.0.16',
+                'c2pnb304w1' => '1.2.840.10045.3.0.17',
+                'c2pnb359v1' => '1.2.840.10045.3.0.18',
+                'c2pnb368w1' => '1.2.840.10045.3.0.19',
+                'c2pnb431r1' => '1.2.840.10045.3.0.20',
+                'primeCurve' => '1.2.840.10045.3.1',
+                'prime192v1' => '1.2.840.10045.3.1.1',
+                'prime192v2' => '1.2.840.10045.3.1.2',
+                'prime192v3' => '1.2.840.10045.3.1.3',
+                'prime239v1' => '1.2.840.10045.3.1.4',
+                'prime239v2' => '1.2.840.10045.3.1.5',
+                'prime239v3' => '1.2.840.10045.3.1.6',
+                'prime256v1' => '1.2.840.10045.3.1.7',
+                'id-RSAES-OAEP' => '1.2.840.113549.1.1.7',
+                'id-pSpecified' => '1.2.840.113549.1.1.9',
+                'id-RSASSA-PSS' => '1.2.840.113549.1.1.10',
+                'id-mgf1' => '1.2.840.113549.1.1.8',
+                'sha224WithRSAEncryption' => '1.2.840.113549.1.1.14',
+                'sha256WithRSAEncryption' => '1.2.840.113549.1.1.11',
+                'sha384WithRSAEncryption' => '1.2.840.113549.1.1.12',
+                'sha512WithRSAEncryption' => '1.2.840.113549.1.1.13',
+                'id-sha224' => '2.16.840.1.101.3.4.2.4',
+                'id-sha256' => '2.16.840.1.101.3.4.2.1',
+                'id-sha384' => '2.16.840.1.101.3.4.2.2',
+                'id-sha512' => '2.16.840.1.101.3.4.2.3',
+                'id-GostR3411-94-with-GostR3410-94' => '1.2.643.2.2.4',
+                'id-GostR3411-94-with-GostR3410-2001' => '1.2.643.2.2.3',
+                'id-GostR3410-2001' => '1.2.643.2.2.20',
+                'id-GostR3410-94' => '1.2.643.2.2.19',
                 // Netscape Object Identifiers from "Netscape Certificate Extensions"
-                '2.16.840.1.113730' => 'netscape',
-                '2.16.840.1.113730.1' => 'netscape-cert-extension',
-                '2.16.840.1.113730.1.1' => 'netscape-cert-type',
-                '2.16.840.1.113730.1.13' => 'netscape-comment',
-                '2.16.840.1.113730.1.8' => 'netscape-ca-policy-url',
+                'netscape' => '2.16.840.1.113730',
+                'netscape-cert-extension' => '2.16.840.1.113730.1',
+                'netscape-cert-type' => '2.16.840.1.113730.1.1',
+                'netscape-comment' => '2.16.840.1.113730.1.13',
+                'netscape-ca-policy-url' => '2.16.840.1.113730.1.8',
                 // the following are X.509 extensions not supported by phpseclib
-                '1.3.6.1.5.5.7.1.12' => 'id-pe-logotype',
-                '1.2.840.113533.7.65.0' => 'entrustVersInfo',
-                '2.16.840.1.113733.1.6.9' => 'verisignPrivate',
+                'id-pe-logotype' => '1.3.6.1.5.5.7.1.12',
+                'entrustVersInfo' => '1.2.840.113533.7.65.0',
+                'verisignPrivate' => '2.16.840.1.113733.1.6.9',
                 // for Certificate Signing Requests
                 // see http://tools.ietf.org/html/rfc2985
-                '1.2.840.113549.1.9.2' => 'pkcs-9-at-unstructuredName', // PKCS #9 unstructured name
-                '1.2.840.113549.1.9.7' => 'pkcs-9-at-challengePassword', // Challenge password for certificate revocations
-                '1.2.840.113549.1.9.14' => 'pkcs-9-at-extensionRequest' // Certificate extension request
+                'pkcs-9-at-unstructuredName' => '1.2.840.113549.1.9.2', // PKCS #9 unstructured name
+                'pkcs-9-at-challengePassword' => '1.2.840.113549.1.9.7', // Challenge password for certificate revocations
+                'pkcs-9-at-extensionRequest' => '1.2.840.113549.1.9.14' // Certificate extension request
             ]);
         }
     }
diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php
index 0ba13dad..1ca135aa 100644
--- a/phpseclib/Math/BigInteger.php
+++ b/phpseclib/Math/BigInteger.php
@@ -114,16 +114,21 @@ class BigInteger implements \Serializable
     }
 
     /**
-     * Converts base-2, base-10, base-16, and binary strings (base-256) to BigIntegers.
+     * Returns the engine type
      *
-     * If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using
-     * two's compliment.  The sole exception to this is -10, which is treated the same as 10 is.
-     *
-     * @param $x integer|BigInteger\Engines\Engine Base-10 number or base-$base number if $base set.
-     * @param int $base
-     * @return BigInteger
+     * @return string[]
      */
-    public function __construct($x = 0, $base = 10)
+    public static function getEngine()
+    {
+        self::initialize_static_variables();
+
+        return self::$engines;
+    }
+
+    /**
+     * Initialize static variables
+     */
+    private static function initialize_static_variables()
     {
         if (!isset(self::$mainEngine)) {
             $engines = [
@@ -140,6 +145,21 @@ class BigInteger implements \Serializable
                 }
             }
         }
+    }
+
+    /**
+     * Converts base-2, base-10, base-16, and binary strings (base-256) to BigIntegers.
+     *
+     * If the second parameter - $base - is negative, then it will be assumed that the number's are encoded using
+     * two's compliment.  The sole exception to this is -10, which is treated the same as 10 is.
+     *
+     * @param $x integer|BigInteger\Engines\Engine Base-10 number or base-$base number if $base set.
+     * @param int $base
+     * @return BigInteger
+     */
+    public function __construct($x = 0, $base = 10)
+    {
+        self::initialize_static_variables();
 
         if ($x instanceof self::$mainEngine) {
             $this->value = clone $x;
@@ -569,6 +589,8 @@ class BigInteger implements \Serializable
      */
     public static function minMaxBits($bits)
     {
+        self::initialize_static_variables();
+
         $class = self::$mainEngine;
         extract($class::minMaxBits($bits));
         /** @var BigInteger $min
@@ -610,6 +632,8 @@ class BigInteger implements \Serializable
      */
     public static function random($size)
     {
+        self::initialize_static_variables();
+
         $class = self::$mainEngine;
         return new static($class::random($size));
     }
@@ -624,6 +648,8 @@ class BigInteger implements \Serializable
      */
     public static function randomPrime($size)
     {
+        self::initialize_static_variables();
+
         $class = self::$mainEngine;
         return new static($class::randomPrime($size));
     }
@@ -746,4 +772,92 @@ class BigInteger implements \Serializable
     {
         $this->value = clone $this->value;
     }
+
+    /**
+     * Is Odd?
+     *
+     * @return boolean
+     */
+    public function isOdd()
+    {
+        return $this->value->isOdd();
+    }
+
+    /**
+     * Tests if a bit is set
+     *
+     * @param int $x
+     * @return boolean
+     */
+    public function testBit($x)
+    {
+        return $this->value->testBit($x);
+    }
+
+    /**
+     * Is Negative?
+     *
+     * @return boolean
+     */
+    public function isNegative()
+    {
+        return $this->value->isNegative();
+    }
+
+    /**
+     * Negate
+     *
+     * Given $k, returns -$k
+     *
+     * @return BigInteger
+     */
+    public function negate()
+    {
+        return new static($this->value->negate());
+    }
+
+    /**
+     * Scan for 1 and right shift by that amount
+     *
+     * ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));
+     *
+     * @param BigInteger $r
+     * @return int
+     */
+    public static function scan1divide(BigInteger $r)
+    {
+        $class = self::$mainEngine;
+        return $class::scan1divide($r->value);
+    }
+
+    /**
+     * Create Recurring Modulo Function
+     *
+     * Sometimes it may be desirable to do repeated modulos with the same number outside of
+     * modular exponentiation
+     *
+     * @return callable
+     */
+    public function createRecurringModuloFunction()
+    {
+        $func = $this->value->createRecurringModuloFunction();
+        return function(BigInteger $x) use ($func) {
+            return new static($func($x->value));
+        };
+    }
+
+    /**
+     * Bitwise Split
+     *
+     * Splits BigInteger's into chunks of $split bits
+     *
+     * @param int $split
+     * @return \phpseclib\Math\BigInteger[]
+     */
+    public function bitwise_split($split)
+    {
+        return array_map(function($val) {
+            return new static($val);
+        }, $this->value->bitwise_split($split));
+    }
 }
\ No newline at end of file
diff --git a/phpseclib/Math/BigInteger/Engines/BCMath.php b/phpseclib/Math/BigInteger/Engines/BCMath.php
index d4f2e824..4ed6b05c 100644
--- a/phpseclib/Math/BigInteger/Engines/BCMath.php
+++ b/phpseclib/Math/BigInteger/Engines/BCMath.php
@@ -353,7 +353,7 @@ class BCMath extends Engine
     public function abs()
     {
         $temp = new static();
-        $temp->value = bccomp($this->value, '0', 0) < 0 ?
+        $temp->value = strlen($this->value) && $this->value[0] == '-' ?
             substr($this->value, 1) :
             $this->value;
 
@@ -537,6 +537,8 @@ class BCMath extends Engine
      */
     protected function normalize(BCMath $result)
     {
+        unset($result->reduce);
+
         $result->precision = $this->precision;
         $result->bitmask = $this->bitmask;
 
@@ -588,7 +590,7 @@ class BCMath extends Engine
      */
     protected function make_odd()
     {
-        if ($this->value[strlen($this->value) - 1] % 2 == 0) {
+        if (!$this->isOdd()) {
             $this->value = bcadd($this->value, '1');
         }
     }
@@ -631,7 +633,7 @@ class BCMath extends Engine
      * @param BCMath $r
      * @return int
      */
-    protected static function scan1divide(BCMath $r)
+    public static function scan1divide(BCMath $r)
     {
         $r_value = &$r->value;
         $s = 0;
@@ -704,4 +706,60 @@ class BCMath extends Engine
         $temp = parent::setBitmask($bits);
         return $temp->add(static::$one);
     }
+
+    /**
+     * Is Odd?
+     *
+     * @return boolean
+     */
+    public function isOdd()
+    {
+        return $this->value[strlen($this->value) - 1] % 2 == 1;
+    }
+
+    /**
+     * Tests if a bit is set
+     *
+     * @return boolean
+     */
+    public function testBit($x)
+    {
+        return bccomp(
+            bcmod($this->value, bcpow('2', $x + 1, 0), 0),
+            bcpow('2', $x, 0),
+            0
+        ) >= 0;
+    }
+
+    /**
+     * Is Negative?
+     *
+     * @return boolean
+     */
+    public function isNegative()
+    {
+        return strlen($this->value) && $this->value[0] == '-';
+    }
+
+    /**
+     * Negate
+     *
+     * Given $k, returns -$k
+     *
+     * @return BCMath
+     */
+    public function negate()
+    {
+        $temp = clone $this;
+
+        if (!strlen($temp->value)) {
+            return $temp;
+        }
+
+        $temp->value = $temp->value[0] == '-' ?
+            substr($this->value, 1) :
+            '-' . $this->value;
+
+        return $temp;
+    }
 }
\ No newline at end of file
diff --git a/phpseclib/Math/BigInteger/Engines/BCMath/Base.php b/phpseclib/Math/BigInteger/Engines/BCMath/Base.php
index 09c002f0..d2c1314d 100644
--- a/phpseclib/Math/BigInteger/Engines/BCMath/Base.php
+++ b/phpseclib/Math/BigInteger/Engines/BCMath/Base.php
@@ -68,11 +68,6 @@ abstract class Base extends BCMath
             return $x->normalize($temp);
         }
 
-        if ($e->value == '1') {
-            $temp = bcdiv($x, $n);
-            return $x->normalize($temp);
-        }
-
         return $x->normalize(static::slidingWindow($x, $e, $n, $class));
     }
 
diff --git a/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/EvalBarrett.php b/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/EvalBarrett.php
index ae1e896a..2b5a387f 100644
--- a/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/EvalBarrett.php
+++ b/phpseclib/Math/BigInteger/Engines/BCMath/Reductions/EvalBarrett.php
@@ -59,6 +59,11 @@ abstract class EvalBarrett extends Base
      */
     protected static function generateCustomReduction(BCMath $m, $class)
     {
+        if (isset($n->reduce)) {
+            self::$custom_reduction = $n->reduce;
+            return $n->reduce;
+        }
+
         $m_length = strlen($m);
 
         if ($m_length < 5) {
@@ -106,5 +111,7 @@ abstract class EvalBarrett extends Base
         eval('$func = function ($n) { ' . $code . '};');
 
         self::$custom_reduction = $func;
+
+        return $func;
     }
 }
\ No newline at end of file
diff --git a/phpseclib/Math/BigInteger/Engines/Engine.php b/phpseclib/Math/BigInteger/Engines/Engine.php
index aa0c793d..f19281d4 100644
--- a/phpseclib/Math/BigInteger/Engines/Engine.php
+++ b/phpseclib/Math/BigInteger/Engines/Engine.php
@@ -19,6 +19,7 @@ use ParagonIE\ConstantTime\Hex;
 use phpseclib\Exception\BadConfigurationException;
 use phpseclib\Crypt\Random;
 use phpseclib\Math\BigInteger;
+use phpseclib\Common\Functions\Strings;
 
 /**
  * Base Engine.
@@ -57,6 +58,13 @@ abstract class Engine implements \Serializable
      */
     protected $bitmask = false;
 
+    /**
+     * Recurring Modulo Function
+     *
+     * @var callable
+     */
+    protected $reduce;
+
     /**
      * Default constructor
      *
@@ -137,6 +145,9 @@ abstract class Engine implements \Serializable
                 // (?<=^|-)0*: find any 0's that are preceded by the start of the string or by a - (ie. octals)
                 // [^-0-9].*: find any non-numeric characters and then any characters that follow that
                 $this->value = preg_replace('#(?<!^)(?:-).*|(?<=^|-)0*|[^-0-9].*#', '', $x);
+                if (!strlen($this->value)) {
+                    $this->value = '0';
+                }
                 static::initialize($base);
                 break;
             case -2:
@@ -147,22 +158,12 @@ abstract class Engine implements \Serializable
                 }
 
                 $x = preg_replace('#^([01]*).*#', '$1', $x);
-                $x = str_pad($x, strlen($x) + (3 * strlen($x)) % 4, 0, STR_PAD_LEFT);
 
-                $str = '0x';
-                while (strlen($x)) {
-                    $part = substr($x, 0, 4);
-                    $str.= dechex(bindec($part));
-                    $x = substr($x, 4);
-                }
-
-                if ($this->is_negative) {
-                    $str = '-' . $str;
-                }
-
-                $temp = new static($str, 8 * $base); // ie. either -16 or +16
+                $temp = new static(Strings::bits2bin($x), 128 * $base); // ie. either -16 or +16
                 $this->value = $temp->value;
-                $this->is_negative = $temp->is_negative;
+                if ($temp->is_negative) {
+                    $this->is_negative = true;
+                }
 
                 break;
             default:
@@ -239,14 +240,9 @@ abstract class Engine implements \Serializable
      */
     public function toBits($twos_compliment = false)
     {
-        $hex = $this->toHex($twos_compliment);
-        $bits = '';
-        for ($i = strlen($hex) - 8, $start = strlen($hex) & 7; $i >= $start; $i-=8) {
-            $bits = str_pad(decbin(hexdec(substr($hex, $i, 8))), 32, '0', STR_PAD_LEFT) . $bits;
-        }
-        if ($start) { // hexdec('') == 0
-            $bits = str_pad(decbin(hexdec(substr($hex, 0, $start))), 8, '0', STR_PAD_LEFT) . $bits;
-        }
+        $hex = $this->toBytes($twos_compliment);
+        $bits = Strings::bin2bits($hex);
+
         $result = $this->precision > 0 ? substr($bits, -$this->precision) : ltrim($bits, '0');
 
         if ($twos_compliment && $this->compare(new static()) > 0 && $this->precision <= 0) {
@@ -1058,4 +1054,106 @@ abstract class Engine implements \Serializable
         }
         return $max;
     }
+
+    /**
+     * Create Recurring Modulo Function
+     *
+     * Sometimes it may be desirable to do repeated modulos with the same number outside of
+     * modular exponentiation
+     *
+     * @return callable
+     */
+    public function createRecurringModuloFunction()
+    {
+        $class = static::class;
+
+        $fqengine = !method_exists(static::$modexpEngine, 'reduce') ?
+            '\\phpseclib\\Math\\BigInteger\\Engines\\' . static::ENGINE_DIR . '\\DefaultEngine' :
+            static::$modexpEngine;
+        if (method_exists($fqengine, 'generateCustomReduction')) {
+            $func = $fqengine::generateCustomReduction($this, static::class);
+            $this->reduce = eval('return function(' . static::class . ' $x) use ($func, $class) {
+                $r = new $class();
+                $r->value = $func($x->value);
+                return $r;
+            };');
+            return clone $this->reduce;
+        }
+        $n = $this->value;
+        $this->reduce = eval('return function(' . static::class . ' $x) use ($n, $fqengine, $class) {
+            $r = new $class();
+            $r->value = $fqengine::reduce($x->value, $n, $class);
+            return $r;
+        };');
+        return clone $this->reduce;
+    }
+
+    /**
+     * Calculates the greatest common divisor and Bezout's identity.
+     *
+     * @param Engine $n
+     * @return Engine
+     */
+    protected function extendedGCDHelper(Engine $n, Engine $stop = null)
+    {
+        $u = clone $this;
+        $v = clone $n;
+
+        $one = new static(1);
+        $zero = new static();
+
+        $a = clone $one;
+        $b = clone $zero;
+        $c = clone $zero;
+        $d = clone $one;
+
+        while (!$v->equals($zero)) {
+            list($q) = $u->divide($v);
+
+            $temp = $u;
+            $u = $v;
+            $v = $temp->subtract($v->multiply($q));
+
+            $temp = $a;
+            $a = $c;
+            $c = $temp->subtract($a->multiply($q));
+
+            $temp = $b;
+            $b = $d;
+            $d = $temp->subtract($b->multiply($q));
+        }
+
+        return [
+            'gcd'=> $u,
+            'x' => $a,
+            'y' => $b
+        ];
+    }
+
+    /**
+     * Bitwise Split
+     *
+     * Splits BigInteger's into chunks of $split bits
+     *
+     * @param int $split
+     * @return \phpseclib\Math\BigInteger\Engine[]
+     */
+    public function bitwise_split($split)
+    {
+        if ($split < 1) {
+            throw new \RuntimeException('Offset must be greater than 1');
+        }
+
+        $mask = static::$one->bitwise_leftShift($split)->subtract(static::$one);
+
+        $num = clone $this;
+
+        $vals = [];
+        while (!$num->equals(static::$zero)) {
+            $vals[] = $num->bitwise_and($mask);
+            $num = $num->bitwise_rightShift($split);
+        }
+
+        return array_reverse($vals);
+    }
 }
\ No newline at end of file
diff --git a/phpseclib/Math/BigInteger/Engines/GMP.php b/phpseclib/Math/BigInteger/Engines/GMP.php
index 17696c17..148492de 100644
--- a/phpseclib/Math/BigInteger/Engines/GMP.php
+++ b/phpseclib/Math/BigInteger/Engines/GMP.php
@@ -158,6 +158,32 @@ class GMP extends Engine
         return (string) $this->value;
     }
 
+    /**
+     * Converts a BigInteger to a bit string (eg. base-2).
+     *
+     * Negative numbers are saved as positive numbers, unless $twos_compliment is set to true, at which point, they're
+     * saved as two's compliment.
+     *
+     * @param bool $twos_compliment
+     * @return string
+     */
+    public function toBits($twos_compliment = false)
+    {
+        $hex = $this->toHex($twos_compliment);
+
+        $bits = gmp_strval(gmp_init($hex, 16), 2);
+
+        if ($this->precision > 0) {
+            $bits = substr($bits, -$this->precision);
+        }
+
+        if ($twos_compliment && $this->compare(new static()) > 0 && $this->precision <= 0) {
+            return '0' . $bits;
+        }
+
+        return $bits;
+    }
+
     /**
      * Converts a BigInteger to a byte string (eg. base-256).
      *
@@ -476,6 +502,8 @@ class GMP extends Engine
      */
     protected function normalize(GMP $result)
     {
+        unset($result->reduce);
+
         $result->precision = $this->precision;
         $result->bitmask = $this->bitmask;
 
@@ -626,4 +654,81 @@ class GMP extends Engine
     {
         return $this->compare($min) >= 0 && $this->compare($max) <= 0;
     }
+
+    /**
+     * Create Recurring Modulo Function
+     *
+     * Sometimes it may be desirable to do repeated modulos with the same number outside of
+     * modular exponentiation
+     *
+     * @return callable
+     */
+    public function createRecurringModuloFunction()
+    {
+        $temp = $this->value;
+        $this->reduce = function(GMP $x) use ($temp) {
+            return new GMP($x->value % $temp);
+        };
+        return $this->reduce;
+    }
+
+    /**
+     * Scan for 1 and right shift by that amount
+     *
+     * ie. $s = gmp_scan1($n, 0) and $r = gmp_div_q($n, gmp_pow(gmp_init('2'), $s));
+     *
+     * @param GMP $r
+     * @return int
+     */
+    public static function scan1divide(GMP $r)
+    {
+        $s = gmp_scan1($r->value, 0);
+        $r->value >>= $s;
+        return $s;
+    }
+
+    /**
+     * Is Odd?
+     *
+     * @return boolean
+     */
+    public function isOdd()
+    {
+        return gmp_testbit($this->value, 0);
+    }
+
+    /**
+     * Tests if a bit is set
+     *
+     * @return boolean
+     */
+    public function testBit($x)
+    {
+        return gmp_testbit($this->value, $x);
+    }
+
+    /**
+     * Is Negative?
+     *
+     * @return boolean
+     */
+    public function isNegative()
+    {
+        return gmp_sign($this->value) == -1;
+    }
+
+    /**
+     * Negate
+     *
+     * Given $k, returns -$k
+     *
+     * @return GMP
+     */
+    public function negate()
+    {
+        $temp = clone $this;
+        $temp->value = -$this->value;
+
+        return $temp;
+    }
 }
\ No newline at end of file
diff --git a/phpseclib/Math/BigInteger/Engines/PHP.php b/phpseclib/Math/BigInteger/Engines/PHP.php
index b0df2a36..2b20c906 100644
--- a/phpseclib/Math/BigInteger/Engines/PHP.php
+++ b/phpseclib/Math/BigInteger/Engines/PHP.php
@@ -19,7 +19,7 @@ use ParagonIE\ConstantTime\Hex;
 use phpseclib\Exception\BadConfigurationException;
 
 /**
- * pure-PHP Engine.
+ * Pure-PHP Engine.
  *
  * @package PHP
  * @author  Jim Wigginton <terrafrost@php.net>
@@ -101,18 +101,6 @@ abstract class PHP extends Engine
     protected function initialize($base)
     {
         switch (abs($base)) {
-            case 256:
-                $x = $this->value;
-                $this->value = [];
-
-                while (strlen($x)) {
-                    $this->value[] = self::bytes2int(self::base256_rshift($x, static::BASE));
-                }
-
-                if ($this->value == [0]) {
-                    $this->value = [];
-                }
-                break;
             case 16:
                 $x = (strlen($this->value) & 1) ? '0' . $this->value : $this->value;
                 $temp = new static(Hex::decode($x), 256);
@@ -205,12 +193,9 @@ abstract class PHP extends Engine
         if (!count($this->value)) {
             return $this->precision > 0 ? str_repeat(chr(0), ($this->precision + 1) >> 3) : '';
         }
-        $result = self::int2bytes($this->value[count($this->value) - 1]);
 
-        for ($i = count($this->value) - 2; $i >= 0; --$i) {
-            self::base256_lshift($result, static::BASE);
-            $result = $result | str_pad(self::int2bytes($this->value[$i]), strlen($result), chr(0), STR_PAD_LEFT);
-        }
+        $result = $this->bitwise_small_split(8);
+        $result = implode('', array_map('chr', $result));
 
         return $this->precision > 0 ?
             str_pad(substr($result, -(($this->precision + 7) >> 3)), ($this->precision + 7) >> 3, chr(0), STR_PAD_LEFT) :
@@ -405,7 +390,7 @@ abstract class PHP extends Engine
     {
         //if ( $x_value == $y_value ) {
         //    return [
-        //        self::VALUE => $this->_square($x_value),
+        //        self::VALUE => self::square($x_value),
         //        self::SIGN => $x_sign != $y_value
         //    ];
         //}
@@ -743,6 +728,8 @@ abstract class PHP extends Engine
      */
     protected function normalize(PHP $result)
     {
+        unset($result->reduce);
+
         $result->precision = $this->precision;
         $result->bitmask = $this->bitmask;
 
@@ -752,7 +739,7 @@ abstract class PHP extends Engine
             return $result;
         }
 
-        $value = $this->trim($value);
+        $value = static::trim($value);
 
         if (!empty($result->bitmask->value)) {
             $length = min(count($value), count($result->bitmask->value));
@@ -801,83 +788,6 @@ abstract class PHP extends Engine
         return 0;
     }
 
-    /**
-     * Calculates the greatest common divisor and Bezout's identity.
-     *
-     * Say you have 693 and 609.  The GCD is 21.  Bezout's identity states that there exist integers x and y such that
-     * 693*x + 609*y == 21.  In point of fact, there are actually an infinite number of x and y combinations and which
-     * combination is returned is dependent upon which mode is in use.  See
-     * {@link http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity Bezout's identity - Wikipedia} for more information.
-     *
-     * @param PHP $n
-     * @return PHP[]
-     * @internal Calculates the GCD using the binary xGCD algorithim described in
-     *    {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap14.pdf#page=19 HAC 14.61}.  As the text above 14.61 notes,
-     *    the more traditional algorithim requires "relatively costly multiple-precision divisions".
-     */
-    protected function extendedGCDHelper(PHP $n)
-    {
-        $y = clone $n;
-        $x = clone $this;
-        $g = new static();
-        $g->value = [1];
-
-        while (!(($x->value[0] & 1)|| ($y->value[0] & 1))) {
-            $x->rshift(1);
-            $y->rshift(1);
-            $g->lshift(1);
-        }
-
-        $u = clone $x;
-        $v = clone $y;
-
-        $a = new static();
-        $b = new static();
-        $c = new static();
-        $d = new static();
-
-        $a->value = $d->value = $g->value = [1];
-        $b->value = $c->value = [];
-
-        while (!empty($u->value)) {
-            while (!($u->value[0] & 1)) {
-                $u->rshift(1);
-                if ((!empty($a->value) && ($a->value[0] & 1)) || (!empty($b->value) && ($b->value[0] & 1))) {
-                    $a = $a->add($y);
-                    $b = $b->subtract($x);
-                }
-                $a->rshift(1);
-                $b->rshift(1);
-            }
-
-            while (!($v->value[0] & 1)) {
-                $v->rshift(1);
-                if ((!empty($d->value) && ($d->value[0] & 1)) || (!empty($c->value) && ($c->value[0] & 1))) {
-                    $c = $c->add($y);
-                    $d = $d->subtract($x);
-                }
-                $c->rshift(1);
-                $d->rshift(1);
-            }
-
-            if ($u->compare($v) >= 0) {
-                $u = $u->subtract($v);
-                $a = $a->subtract($c);
-                $b = $b->subtract($d);
-            } else {
-                $v = $v->subtract($u);
-                $c = $c->subtract($a);
-                $d = $d->subtract($b);
-            }
-        }
-
-        return [
-            'gcd' => $this->normalize($g->multiply($v)),
-            'x'   => $this->normalize($c),
-            'y'   => $this->normalize($d)
-        ];
-    }
-
     /**
      * Absolute value.
      *
@@ -973,46 +883,6 @@ abstract class PHP extends Engine
         return $value;
     }
 
-    /**
-     * Logical Right Shift
-     *
-     * Shifts binary strings $shift bits, essentially dividing by 2**$shift and returning the remainder.
-     *
-     * @param $x String
-     * @param $shift Integer
-     * @return string
-     */
-    private static function base256_rshift(&$x, $shift)
-    {
-        if ($shift == 0) {
-            $x = ltrim($x, chr(0));
-            return '';
-        }
-
-        $num_bytes = $shift >> 3; // eg. floor($shift/8)
-        $shift &= 7; // eg. $shift % 8
-
-        $remainder = '';
-        if ($num_bytes) {
-            $start = $num_bytes > strlen($x) ? -strlen($x) : -$num_bytes;
-            $remainder = substr($x, $start);
-            $x = substr($x, 0, -$num_bytes);
-        }
-
-        $carry = 0;
-        $carry_shift = 8 - $shift;
-        for ($i = 0; $i < strlen($x); ++$i) {
-            $temp = (ord($x[$i]) >> $shift) | $carry;
-            $carry = (ord($x[$i]) << $carry_shift) & 0xFF;
-            $x[$i] = chr($temp);
-        }
-        $x = ltrim($x, chr(0));
-
-        $remainder = chr($carry >> $carry_shift) . $remainder;
-
-        return ltrim($remainder, chr(0));
-    }
-
     /**
      * Logical Right Shift
      *
@@ -1063,18 +933,6 @@ abstract class PHP extends Engine
         return ltrim(pack('N', $x), chr(0));
     }
 
-    /**
-     * Converts bytes to 32-bit integers
-     *
-     * @param string $x
-     * @return int
-     */
-    private static function bytes2int($x)
-    {
-        $temp = unpack('Nint', str_pad($x, 4, chr(0), STR_PAD_LEFT));
-        return $temp['int'];
-    }
-
     /**
      * Array Repeat
      *
@@ -1151,7 +1009,7 @@ abstract class PHP extends Engine
             $this->value[$i] = $temp;
         }
 
-        $this->value = $this->trim($this->value);
+        $this->value = static::trim($this->value);
     }
 
     /**
@@ -1309,7 +1167,7 @@ abstract class PHP extends Engine
      * @param PHP $r
      * @return int
      */
-    protected static function scan1divide(PHP $r)
+    public static function scan1divide(PHP $r)
     {
         $r_value = &$r->value;
         for ($i = 0, $r_length = count($r_value); $i < $r_length; ++$i) {
@@ -1337,7 +1195,6 @@ abstract class PHP extends Engine
             return new static(1);
         } // n^0 = 1
 
-
         $temp = clone $this;
         while (!$n->equals(static::$one)) {
             $temp = $temp->multiply($this);
@@ -1346,4 +1203,172 @@ abstract class PHP extends Engine
 
         return $temp;
     }
+
+    /**
+     * Is Odd?
+     *
+     * @return boolean
+     */
+    public function isOdd()
+    {
+        return (bool) ($this->value[0] & 1);
+    }
+
+    /**
+     * Tests if a bit is set
+     *
+     * @return boolean
+     */
+    public function testBit($x)
+    {
+        $digit = floor($x / static::BASE);
+        $bit = $x % static::BASE;
+
+        if (!isset($this->value[$digit])) {
+            return false;
+        }
+
+        return (bool) ($this->value[$digit] & (1 << $bit));
+    }
+
+    /**
+     * Is Negative?
+     *
+     * @return boolean
+     */
+    public function isNegative()
+    {
+        return $this->is_negative;
+    }
+
+    /**
+     * Negate
+     *
+     * Given $k, returns -$k
+     *
+     * @return BigInteger
+     */
+    public function negate()
+    {
+        $temp = clone $this;
+        $temp->is_negative = !$temp->is_negative;
+
+        return $temp;
+    }
+
+    /**
+     * Bitwise Split
+     *
+     * Splits BigInteger's into chunks of $split bits
+     *
+     * @param int $split
+     * @return \phpseclib\Math\BigInteger\Engines\PHP[]
+     */
+    public function bitwise_split($split)
+    {
+        if ($split < 1) {
+            throw new \RuntimeException('Offset must be greater than 1');
+        }
+
+        $width = (int) ($split / static::BASE);
+        if (!$width) {
+            $arr = $this->bitwise_small_split($split);
+            return array_map(function ($digit) {
+                $temp = new static();
+                $temp->value = $digit != 0 ? [$digit] : [];
+                return $temp;
+            }, $arr);
+        }
+
+        $vals = [];
+        $val = $this->value;
+
+        $i = $overflow = 0;
+        $len = count($val);
+        while ($i < $len) {
+            $digit = [];
+            if (!$overflow) {
+                $digit = array_slice($val, $i, $width);
+                $i+= $width;
+                $overflow = $split % static::BASE;
+                if ($overflow) {
+                    $mask = (1 << $overflow) - 1;
+                    $temp = isset($val[$i]) ? $val[$i] : 0;
+                    $digit[] = $temp & $mask;
+                }
+            } else {
+                $remaining = static::BASE - $overflow;
+                $tempsplit = $split - $remaining;
+                $tempwidth = (int) ($tempsplit / static::BASE + 1);
+                $digit = array_slice($val, $i, $tempwidth);
+                $i+= $tempwidth;
+                $tempoverflow = $tempsplit % static::BASE;
+                if ($tempoverflow) {
+                    $tempmask = (1 << $tempoverflow) - 1;
+                    $temp = isset($val[$i]) ? $val[$i] : 0;
+                    $digit[] = $temp & $tempmask;
+                }
+                $newbits = 0;
+                for ($j = count($digit) - 1; $j >= 0; $j--) {
+                    $temp = $digit[$j] & $mask;
+                    $digit[$j] = ($digit[$j] >> $overflow) | ($newbits << $remaining);
+                    $newbits = $temp;
+                }
+                $overflow = $tempoverflow;
+                $mask = $tempmask;
+            }
+            $temp = new static();
+            $temp->value = static::trim($digit);
+            $vals[] = $temp;
+        }
+
+        return array_reverse($vals);
+    }
+
+    /**
+     * Bitwise Split where $split < static::BASE
+     *
+     * @param int $split
+     * @return \phpseclib\Math\BigInteger\Engines\PHP[]
+     */
+    private function bitwise_small_split($split)
+    {
+        $vals = [];
+        $val = $this->value;
+
+        $mask = (1 << $split) - 1;
+
+        $i = $overflow = 0;
+        $len = count($val);
+        $val[] = 0;
+        $remaining = static::BASE;
+        while ($i != $len) {
+            $digit = $val[$i] & $mask;
+            $val[$i]>>= $split;
+            if (!$overflow) {
+                $remaining-= $split;
+                $overflow = $split <= $remaining ? 0 : $split - $remaining;
+
+                if (!$remaining) {
+                    $i++;
+                    $remaining = static::BASE;
+                    $overflow = 0;
+                }
+            } else if (++$i != $len) {
+                $tempmask = (1 << $overflow) - 1;
+                $digit|= ($val[$i] & $tempmask) << $remaining;
+                $val[$i]>>= $overflow;
+                $remaining = static::BASE - $overflow;
+                $overflow = $split <= $remaining ? 0 : $split - $remaining;
+            }
+
+            $vals[] = $digit;
+        }
+
+        while ($vals[count($vals) - 1] == 0) {
+            unset($vals[count($vals) - 1]);
+        }
+
+        return array_reverse($vals);
+    }
 }
\ No newline at end of file
diff --git a/phpseclib/Math/BigInteger/Engines/PHP/Reductions/EvalBarrett.php b/phpseclib/Math/BigInteger/Engines/PHP/Reductions/EvalBarrett.php
index ec130b69..479ac385 100644
--- a/phpseclib/Math/BigInteger/Engines/PHP/Reductions/EvalBarrett.php
+++ b/phpseclib/Math/BigInteger/Engines/PHP/Reductions/EvalBarrett.php
@@ -60,6 +60,11 @@ abstract class EvalBarrett extends Base
      */
     protected static function generateCustomReduction(PHP $m, $class)
     {
+        if (isset($n->reduce)) {
+            self::$custom_reduction = $n->reduce;
+            return $n->reduce;
+        }
+
         $m_length = count($m->value);
 
         if ($m_length < 5) {
@@ -75,7 +80,7 @@ abstract class EvalBarrett extends Base
             eval('$func = function ($x) { ' . $code . '};');
             self::$custom_reduction = $func;
             //self::$custom_reduction = \Closure::bind($func, $m, $class);
-            return;
+            return $func;
         }
 
         $lhs = new $class();
@@ -151,6 +156,8 @@ abstract class EvalBarrett extends Base
 
         self::$custom_reduction = $func;
 
+        return $func;
+
         //self::$custom_reduction = \Closure::bind($func, $m, $class);
     }
 
diff --git a/phpseclib/Math/BigInteger/Engines/PHP32.php b/phpseclib/Math/BigInteger/Engines/PHP32.php
index bf071e7b..6f0a1ec7 100644
--- a/phpseclib/Math/BigInteger/Engines/PHP32.php
+++ b/phpseclib/Math/BigInteger/Engines/PHP32.php
@@ -92,6 +92,56 @@ class PHP32 extends PHP
      */
     protected static $two;
 
+    /**
+     * Initialize a PHP32 BigInteger Engine instance
+     *
+     * @param int $base
+     * @see parent::initialize()
+     */
+    protected function initialize($base)
+    {
+        if ($base != 256 && $base != -256) {
+            return parent::initialize($base);
+        }
+
+        $val = $this->value;
+        $this->value = [];
+        $vals = &$this->value;
+        $i = strlen($val);
+        if (!$i) {
+            return;
+        }
+
+        while (true) {
+            $i-= 4;
+            if ($i < 0) {
+                if ($i == -4) {
+                    break;
+                }
+                $val = substr($val, 0, 4 + $i);
+                $val = str_pad($val, 4, "\0", STR_PAD_LEFT);
+                if ($val == "\0\0\0\0") {
+                    break;
+                }
+                $i = 0;
+            }
+            list(, $digit) = unpack('N', substr($val, $i, 4));
+            $step = count($vals) & 3;
+            if ($step) {
+                $digit>>= 2 * $step;
+            }
+            if ($step != 3) {
+                $digit&= static::MAX_DIGIT;
+                $i++;
+            }
+            $vals[] = $digit;
+        }
+        while (end($vals) === 0) {
+            array_pop($vals);
+        }
+        reset($vals);
+    }
+
     /**
      * Test for engine validity
      *
diff --git a/phpseclib/Math/BigInteger/Engines/PHP64.php b/phpseclib/Math/BigInteger/Engines/PHP64.php
index 5ebcc599..5966782a 100644
--- a/phpseclib/Math/BigInteger/Engines/PHP64.php
+++ b/phpseclib/Math/BigInteger/Engines/PHP64.php
@@ -92,6 +92,60 @@ class PHP64 extends PHP
      */
     protected static $two;
 
+    /**
+     * Initialize a PHP64 BigInteger Engine instance
+     *
+     * @param int $base
+     * @see parent::initialize()
+     */
+    protected function initialize($base)
+    {
+        if ($base != 256 && $base != -256) {
+            return parent::initialize($base);
+        }
+
+        $val = $this->value;
+        $this->value = [];
+        $vals = &$this->value;
+        $i = strlen($val);
+        if (!$i) {
+            return;
+        }
+
+        while (true) {
+            $i-= 4;
+            if ($i < 0) {
+                if ($i == -4) {
+                    break;
+                }
+                $val = substr($val, 0, 4 + $i);
+                $val = str_pad($val, 4, "\0", STR_PAD_LEFT);
+                if ($val == "\0\0\0\0") {
+                    break;
+                }
+                $i = 0;
+            }
+            list(, $digit) = unpack('N', substr($val, $i, 4));
+            $step = count($vals) & 7;
+            if (!$step) {
+                $digit&= static::MAX_DIGIT;
+                $i++;
+            } else {
+                $shift = 8 - $step;
+                $digit>>= $shift;
+                $shift = 32 - $shift;
+                $digit&= (1 << $shift) - 1;
+                $temp = $i > 0 ? ord($val[$i - 1]) : 0;
+                $digit|= ($temp << $shift) & 0x7F000000;
+            }
+            $vals[] = $digit;
+        }
+        while (end($vals) === 0) {
+            array_pop($vals);
+        }
+        reset($vals);
+    }
+
     /**
      * Test for engine validity
      *
diff --git a/phpseclib/Math/BinaryField.php b/phpseclib/Math/BinaryField.php
new file mode 100644
index 00000000..ac7fa2df
--- /dev/null
+++ b/phpseclib/Math/BinaryField.php
@@ -0,0 +1,193 @@
+<?php
+
+/**
+ * Binary Finite Fields
+ *
+ * Utilizes the factory design pattern
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Math
+ * @package   BigInteger
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Math;
+
+use ParagonIE\ConstantTime\Hex;
+use phpseclib\Math\Common\FiniteField;
+use phpseclib\Math\BinaryField\Integer;
+use phpseclib\Common\Functions\Strings;
+
+/**
+ * Binary Finite Fields
+ *
+ * @package Math
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class BinaryField extends FiniteField
+{
+    /**
+     * Instance Counter
+     *
+     * @var int
+     */
+    private static $instanceCounter = 0;
+
+    /**
+     * Keeps track of current instance
+     *
+     * @var int
+     */
+    protected $instanceID;
+
+    /**
+     * Default constructor
+     */
+    public function __construct(...$indices)
+    {
+        $m = array_shift($indices);
+        $val = str_repeat('0', $m) . '1';
+        foreach ($indices as $index) {
+            $val[$index] = '1';
+        }
+        $modulo = static::base2ToBase256(strrev($val));
+
+        $mStart = 2 * $m - 2;
+        $t = ceil($m / 8);
+        $finalMask = chr((1 << ($m % 8)) - 1);
+        $bitLen = $mStart + 1;
+        $pad = ceil($bitLen / 8);
+        $h = $bitLen & 7;
+        $h = $h ? 8 - $h : 0;
+
+        $r = rtrim(substr($val, 0, -1), '0');
+        $u = [static::base2ToBase256(strrev($r))];
+        for ($i = 1; $i < 8; $i++) {
+            $u[] = static::base2ToBase256(strrev(str_repeat('0', $i) . $r));
+        }
+
+        // implements algorithm 2.40 (in section 2.3.5) in "Guide to Elliptic Curve Cryptography"
+        // with W = 8
+        $reduce = function($c) use ($u, $mStart, $m, $t, $finalMask, $pad, $h) {
+            $c = str_pad($c, $pad, "\0", STR_PAD_LEFT);
+            for ($i = $mStart; $i >= $m;) {
+                $g = $h >> 3;
+                $mask = $h & 7;
+                $mask = $mask ? 1 << (7 - $mask) : 0x80;
+                for (; $mask > 0; $mask >>= 1, $i--, $h++) {
+                    if (ord($c[$g]) & $mask) {
+                        $temp = $i - $m;
+                        $j = $temp >> 3;
+                        $k = $temp & 7;
+                        $t1 = $j ? substr($c, 0, -$j) : $c;
+                        $length = strlen($t1);
+                        if ($length) {
+                            $t2 = str_pad($u[$k], $length, "\0", STR_PAD_LEFT);
+                            $temp = $t1 ^ $t2;
+                            $c = $j ? substr_replace($c, $temp, 0, $length) : $temp;
+                        }
+                    }
+                }
+            }
+            $c = substr($c, -$t);
+            if (strlen($c) == $t) {
+                $c[0] = $c[0] & $finalMask;
+            }
+            return ltrim($c, "\0");
+        };
+
+        $this->instanceID = self::$instanceCounter++;
+        Integer::setModulo($this->instanceID, $modulo);
+        Integer::setRecurringModuloFunction($this->instanceID, $reduce);
+
+        $this->randomMax = new BigInteger($modulo, 2);
+    }
+
+    /**
+     * Returns an instance of a dynamically generated PrimeFieldInteger class
+     *
+     * @param string $num
+     * @return object
+     */
+    public function newInteger($num)
+    {
+        return new Integer($this->instanceID, $num instanceof BigInteger ? $num->toBytes() : $num);
+    }
+
+    /**
+     * Returns an integer on the finite field between one and the prime modulo
+     *
+     * @return object
+     */
+    public function randomInteger()
+    {
+        static $one;
+        if (!isset($one)) {
+            $one = new BigInteger(1);
+        }
+
+        return new Integer($this->instanceID, BigInteger::randomRange($one, $this->randomMax)->toBytes());
+    }
+
+    /**
+     * Returns the length of the modulo in bytes
+     *
+     * @return integer
+     */
+    public function getLengthInBytes()
+    {
+        return strlen(Integer::getModulo($this->instanceID));
+    }
+
+    /**
+     * Returns the length of the modulo in bits
+     *
+     * @return integer
+     */
+    public function getLength()
+    {
+        return strlen(Integer::getModulo($this->instanceID)) << 3;
+    }
+
+    /**
+     * Converts a base-2 string to a base-256 string
+     *
+     * @param string $x
+     * @param integer $size 
+     * @return string
+     */
+    public static function base2ToBase256($x, $size = null)
+    {
+        $str = Strings::bits2bin($x);
+
+        $pad = strlen($x) >> 3;
+        if (strlen($x) & 3) {
+            $pad++;
+        }
+        $str = str_pad($str, $pad, "\0", STR_PAD_LEFT);
+        if (isset($size)) {
+            $str = str_pad($str, $size, "\0", STR_PAD_LEFT);
+        }
+
+        return $str;
+    }
+
+    /**
+     * Converts a base-256 string to a base-2 string
+     *
+     * @param string $x
+     * @return string
+     */
+    public static function base256ToBase2($x)
+    {
+        if (function_exists('gmp_import')) {
+            return gmp_strval(gmp_import($x), 2);
+        }
+
+        return Strings::bin2bits($x);
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Math/BinaryField/Integer.php b/phpseclib/Math/BinaryField/Integer.php
new file mode 100644
index 00000000..0bde2b07
--- /dev/null
+++ b/phpseclib/Math/BinaryField/Integer.php
@@ -0,0 +1,400 @@
+<?php
+
+/**
+ * Binary Finite Fields
+ *
+ * In a binary finite field numbers are actually polynomial equations. If you
+ * represent the number as a sequence of bits you get a sequence of 1's or 0's.
+ * These 1's or 0's represent the coefficients of the x**n, where n is the
+ * location of the given bit. When you add numbers over a binary finite field
+ * the result should have a coefficient of 1 or 0 as well. Hence addition
+ * and subtraction become the same operation as XOR, etc.
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Math
+ * @package   BigInteger
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Math\BinaryField;
+
+use phpseclib\Math\Common\FiniteField\Integer as Base;
+use phpseclib\Math\BigInteger;
+use phpseclib\Math\BinaryField;
+use ParagonIE\ConstantTime\Hex;
+
+/**
+ * Binary Finite Fields
+ *
+ * @package Math
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class Integer extends Base
+{
+    /**
+     * Holds the BinaryField's value
+     *
+     * @var string
+     */
+    protected $value;
+
+    /**
+     * Keeps track of current instance
+     *
+     * @var int
+     */
+    protected $instanceID;
+
+    /**
+     * Holds the PrimeField's modulo
+     *
+     * @var string[]
+     */
+    protected static $modulo;
+
+    /**
+     * Holds a pre-generated function to perform modulo reductions
+     *
+     * @var callable[]
+     */
+    protected static $reduce;
+
+    /**
+     * Default constructor
+     */
+    public function __construct($instanceID, $num = '')
+    {
+        $this->instanceID = $instanceID;
+        if (!strlen($num)) {
+            $this->value = '';
+        } else {
+            $reduce = static::$reduce[$instanceID];
+            $this->value = $reduce($num);
+        }
+    }
+
+    /**
+     * Set the modulo for a given instance
+     */
+    public static function setModulo($instanceID, $modulo)
+    {
+        static::$modulo[$instanceID] = $modulo;
+    }
+
+    /**
+     * Set the modulo for a given instance
+     */
+    public static function setRecurringModuloFunction($instanceID, callable $function)
+    {
+        static::$reduce[$instanceID] = $function;
+    }
+
+    /**
+     * Tests a parameter to see if it's of the right instance
+     *
+     * Throws an exception if the incorrect class is being utilized
+     */
+    private static function checkInstance(self $x, self $y)
+    {
+        if ($x->instanceID != $y->instanceID) {
+            throw new \UnexpectedValueException('The instances of the two BinaryField\Integer objects do not match');
+        }
+    }
+
+    /**
+     * Tests the equality of two numbers.
+     *
+     * @return bool
+     */
+    public function equals(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        return $this->value == $x->value;
+    }
+
+    /**
+     * Compares two numbers.
+     *
+     * @return int
+     */
+    public function compare(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        $a = $this->value;
+        $b = $x->value;
+
+        $length = max(strlen($a), strlen($b));
+
+        $a = str_pad($a, $length, "\0", STR_PAD_LEFT);
+        $b = str_pad($b, $length, "\0", STR_PAD_LEFT);
+
+        return strcmp($a, $b);
+    }
+
+    /**
+     * Returns the degree of the polynomial
+     *
+     * @param string $x
+     * @return int
+     */
+    private static function deg($x)
+    {
+        $x = ltrim($x, "\0");
+        $xbit = decbin(ord($x[0]));
+        $xlen = $xbit == '0' ? 0 : strlen($xbit);
+        $len = strlen($x);
+        if (!$len) {
+            return -1;
+        }
+        return 8 * strlen($x) - 9 + $xlen;
+    }
+
+    /**
+     * Perform polynomial division
+     *
+     * @return string[]
+     * @link https://en.wikipedia.org/wiki/Polynomial_greatest_common_divisor#Euclidean_division
+     */
+    private static function polynomialDivide($x, $y)
+    {
+        if (strcmp($x, str_pad($y, strlen($x), "\0", STR_PAD_LEFT)) < 0) {
+            return ['', ltrim($x, "\0")];
+        }
+
+        // in wikipedia's description of the algorithm, lc() is the leading coefficient. over a binary field that's
+        // always going to be 1.
+
+        $q = chr(0);
+        $d = static::deg($y);
+        $r = $x;
+        while (($degr = static::deg($r)) >= $d) {
+            $s = '1' . str_repeat('0', $degr - $d);
+            $s = BinaryField::base2ToBase256($s);
+            $length = max(strlen($s), strlen($q));
+            $q = !isset($q) ? $s :
+                str_pad($q, $length, "\0", STR_PAD_LEFT) ^
+                str_pad($s, $length, "\0", STR_PAD_LEFT);
+            $s = static::polynomialMultiply($s, $y);
+            $length = max(strlen($r), strlen($s));
+            $r = str_pad($r, $length, "\0", STR_PAD_LEFT) ^
+                 str_pad($s, $length, "\0", STR_PAD_LEFT);
+        }
+
+        return [ltrim($q, "\0"), ltrim($r, "\0")];
+    }
+
+    /**
+     * Perform polynomial multiplation
+     *
+     * @return string[]
+     * @link https://en.wikipedia.org/wiki/Finite_field_arithmetic#Multiplication
+     */
+    private static function polynomialMultiply($x, $y)
+    {
+        $precomputed = [ltrim($x, "\0")];
+        $x = strrev(BinaryField::base256ToBase2($x));
+        $y = strrev(BinaryField::base256ToBase2($y));
+        if (strlen($x) == strlen($y)) {
+            $length = strlen($x);
+        } else {
+            $length = max(strlen($x), strlen($y));
+            $x = str_pad($x, $length, '0');
+            $y = str_pad($y, $length, '0');
+        }
+        $result = str_repeat('0', 2 * $length - 1);
+        $result = BinaryField::base2ToBase256($result);
+        $size = strlen($result);
+        $x = strrev($x);
+
+        // precompute left shift 1 through 7
+        for ($i = 1; $i < 8; $i++) {
+            $precomputed[$i] = BinaryField::base2ToBase256($x . str_repeat('0', $i));
+        }
+        for ($i = 0; $i < strlen($y); $i++) {
+            if ($y[$i] == '1') {
+                $temp = $precomputed[$i & 7] . str_repeat("\0", $i >> 3);
+                $result^= str_pad($temp, $size, "\0", STR_PAD_LEFT);
+            }
+        }
+
+        return $result;
+    }
+
+    /**
+     * Adds two BinaryFieldIntegers.
+     *
+     * @return static
+     */
+    public function add(self $y)
+    {
+        static::checkInstance($this, $y);
+
+        $length = strlen(static::$modulo[$this->instanceID]);
+
+        $x = str_pad($this->value, $length, "\0", STR_PAD_LEFT);
+        $y = str_pad($y->value, $length, "\0", STR_PAD_LEFT);
+
+        return new static($this->instanceID, $x ^ $y);
+    }
+
+    /**
+     * Subtracts two BinaryFieldIntegers.
+     *
+     * @return static
+     */
+    public function subtract(self $x)
+    {
+        return $this->add($x);
+    }
+
+    /**
+     * Multiplies two BinaryFieldIntegers.
+     *
+     * @return static
+     */
+    public function multiply(self $y)
+    {
+        static::checkInstance($this, $y);
+
+        return new static($this->instanceID, static::polynomialMultiply($this->value, $y->value));
+    }
+
+    /**
+     * Returns the modular inverse of a BinaryFieldInteger
+     *
+     * @return static
+     */
+    public function modInverse()
+    {
+        $remainder0 = static::$modulo[$this->instanceID];
+        $remainder1 = $this->value;
+
+        if ($remainder1 == '') {
+            return new static($this->instanceID);
+        }
+
+        $aux0 = "\0";
+        $aux1 = "\1";
+        while ($remainder1 != "\1") {
+            list($q, $r) = static::polynomialDivide($remainder0, $remainder1);
+            $remainder0 = $remainder1;
+            $remainder1 = $r;
+            // the auxiliary in row n is given by the sum of the auxiliary in
+            // row n-2 and the product of the quotient and the auxiliary in row
+            // n-1
+            $temp = static::polynomialMultiply($aux1, $q);
+            $aux = str_pad($aux0, strlen($temp), "\0", STR_PAD_LEFT) ^ $temp;
+            $aux0 = $aux1;
+            $aux1 = $aux;
+        }
+
+        $temp = new static($this->instanceID);
+        $temp->value = $aux1;
+        return $temp;
+    }
+
+    /**
+     * Divides two PrimeFieldIntegers.
+     *
+     * @return static
+     */
+    public function divide(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        $x = $x->modInverse();
+        return $this->multiply($x);
+    }
+
+    /**
+     * Negate
+     *
+     * A negative number can be written as 0-12. With modulos, 0 is the same thing as the modulo
+     * so 0-12 is the same thing as modulo-12
+     *
+     * @return object
+     */
+    public function negate()
+    {
+        $x = str_pad($this->value, strlen(static::$modulo[$this->instanceID]), "\0", STR_PAD_LEFT);
+
+        return new static($x ^ static::$modulo[$this->instanceID]);
+    }
+
+    /**
+     * Returns the modulo
+     *
+     * @return integer
+     */
+    public static function getModulo($instanceID)
+    {
+        return static::$modulo[$instanceID];
+    }
+
+    /**
+     * Converts an Integer to a byte string (eg. base-256).
+     *
+     * @return string
+     */
+    public function toBytes()
+    {
+        return str_pad($this->value, strlen(static::$modulo[$this->instanceID]), "\0", STR_PAD_LEFT);
+    }
+
+    /**
+     * Converts an Integer to a hex string (eg. base-16).
+     *
+     * @return string
+     */
+    public function toHex()
+    {
+        return Hex::encode($this->toBytes());
+    }
+
+    /**
+     * Converts an Integer to a bit string (eg. base-2).
+     *
+     * @return string
+     */
+    public function toBits()
+    {
+        //return str_pad(BinaryField::base256ToBase2($this->value), strlen(static::$modulo[$this->instanceID]), '0', STR_PAD_LEFT);
+        return BinaryField::base256ToBase2($this->value);
+    }
+
+    /**
+     * Converts an Integer to a BigInteger
+     *
+     * @return string
+     */
+    public function toBigInteger()
+    {
+        return new BigInteger($this->value, 256);
+    }
+
+    /**
+     *  __toString() magic method
+     *
+     * @access public
+     */
+    public function __toString()
+    {
+        return (string) $this->toBigInteger();
+    }
+
+    /**
+     *  __debugInfo() magic method
+     *
+     * @access public
+     */
+    public function __debugInfo()
+    {
+        return ['value' => $this->toHex()];
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Math/Common/FiniteField.php b/phpseclib/Math/Common/FiniteField.php
new file mode 100644
index 00000000..7777d88b
--- /dev/null
+++ b/phpseclib/Math/Common/FiniteField.php
@@ -0,0 +1,26 @@
+<?php
+
+/**
+ * Finite Fields Base Class
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Math
+ * @package   BigInteger
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Math\Common;
+
+/**
+ * Finite Fields
+ *
+ * @package Math
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class FiniteField
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Math/Common/FiniteField/Integer.php b/phpseclib/Math/Common/FiniteField/Integer.php
new file mode 100644
index 00000000..a4caafd8
--- /dev/null
+++ b/phpseclib/Math/Common/FiniteField/Integer.php
@@ -0,0 +1,26 @@
+<?php
+
+/**
+ * Finite Field Integer Base Class
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Math
+ * @package   BigInteger
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Math\Common\FiniteField;
+
+/**
+ * Finite Field Integer
+ *
+ * @package Math
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+abstract class Integer
+{
+}
\ No newline at end of file
diff --git a/phpseclib/Math/PrimeField.php b/phpseclib/Math/PrimeField.php
new file mode 100644
index 00000000..199c6a35
--- /dev/null
+++ b/phpseclib/Math/PrimeField.php
@@ -0,0 +1,116 @@
+<?php
+
+/**
+ * Prime Finite Fields
+ *
+ * Utilizes the factory design pattern
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Math
+ * @package   BigInteger
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Math;
+
+use phpseclib\Math\Common\FiniteField;
+use phpseclib\Math\PrimeField\Integer;
+
+/**
+ * Prime Finite Fields
+ *
+ * @package Math
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class PrimeField extends FiniteField
+{
+    /**
+     * Instance Counter
+     *
+     * @var int
+     */
+    private static $instanceCounter = 0;
+
+    /**
+     * Keeps track of current instance
+     *
+     * @var int
+     */
+    protected $instanceID;
+
+    /**
+     * Default constructor
+     */
+    public function __construct(BigInteger $modulo)
+    {
+        //if (!$modulo->isPrime()) {
+        //    throw new \UnexpectedValueException('PrimeField requires a prime number be passed to the constructor');
+        //}
+
+        $this->modulo = $modulo;
+
+        $this->instanceID = self::$instanceCounter++;
+        Integer::setModulo($this->instanceID, $modulo);
+        Integer::setRecurringModuloFunction($this->instanceID, $modulo->createRecurringModuloFunction());
+    }
+
+    /**
+     * Use a custom defined modular reduction function
+     *
+     * @return object
+     */
+    public function setReduction(callable $func)
+    {
+        $this->reduce = $func->bindTo($this, $this);
+    }
+
+    /**
+     * Returns an instance of a dynamically generated PrimeFieldInteger class
+     *
+     * @return object
+     */
+    public function newInteger(BigInteger $num)
+    {
+        return new Integer($this->instanceID, $num);
+    }
+
+    /**
+     * Returns an integer on the finite field between one and the prime modulo
+     *
+     * @return object
+     */
+    public function randomInteger()
+    {
+        static $one;
+        if (!isset($one)) {
+            $one = new BigInteger(1);
+        }
+
+        return new Integer($this->instanceID, BigInteger::randomRange($one, Integer::getModulo($this->instanceID)));
+    }
+
+    /**
+     * Returns the length of the modulo in bytes
+     *
+     * @return integer
+     */
+    public function getLengthInBytes()
+    {
+        return Integer::getModulo($this->instanceID)->getLengthInBytes();
+    }
+
+    /**
+     * Returns the length of the modulo in bits
+     *
+     * @return integer
+     */
+    public function getLength()
+    {
+        return Integer::getModulo($this->instanceID)->getLength();
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Math/PrimeField/Integer.php b/phpseclib/Math/PrimeField/Integer.php
new file mode 100644
index 00000000..160ca92b
--- /dev/null
+++ b/phpseclib/Math/PrimeField/Integer.php
@@ -0,0 +1,399 @@
+<?php
+
+/**
+ * Prime Finite Fields
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Math
+ * @package   BigInteger
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib\Math\PrimeField;
+
+use phpseclib\Math\Common\FiniteField\Integer as Base;
+use phpseclib\Math\BigInteger;
+use ParagonIE\ConstantTime\Hex;
+
+/**
+ * Prime Finite Fields
+ *
+ * @package Math
+ * @author  Jim Wigginton <terrafrost@php.net>
+ * @access  public
+ */
+class Integer extends Base
+{
+    /**
+     * Holds the PrimeField's value
+     *
+     * @var \phpseclib\Math\BigInteger
+     */
+    protected $value;
+
+    /**
+     * Keeps track of current instance
+     *
+     * @var int
+     */
+    protected $instanceID;
+
+    /**
+     * Holds the PrimeField's modulo
+     *
+     * @var \phpseclib\Math\BigInteger
+     */
+    protected static $modulo;
+
+    /**
+     * Holds a pre-generated function to perform modulo reductions
+     *
+     * @var Callable
+     */
+    protected static $reduce;
+
+    /**
+     * Zero
+     *
+     * @var \phpseclib\Math\BigInteger
+     */
+    protected static $zero;
+
+    /**
+     * Default constructor
+     */
+    public function __construct($instanceID, BigInteger $num = null)
+    {
+        $this->instanceID = $instanceID;
+        if (!isset($num)) {
+            $this->value = clone static::$zero;
+        } else {
+            $reduce = static::$reduce[$instanceID];
+            $this->value = $reduce($num);
+        }
+    }
+
+    /**
+     * Set the modulo for a given instance
+     */
+    public static function setModulo($instanceID, BigInteger $modulo)
+    {
+        static::$modulo[$instanceID] = $modulo;
+    }
+
+    /**
+     * Set the modulo for a given instance
+     */
+    public static function setRecurringModuloFunction($instanceID, callable $function)
+    {
+        static::$reduce[$instanceID] = $function;
+        if (!isset(static::$zero)) {
+            static::$zero = new BigInteger();
+        }
+    }
+
+    /**
+     * Returns the modulo
+     *
+     * @return integer
+     */
+    public static function getModulo($instanceID)
+    {
+        return static::$modulo[$instanceID];
+    }
+
+    /**
+     * Tests a parameter to see if it's of the right instance
+     *
+     * Throws an exception if the incorrect class is being utilized
+     */
+    public static function checkInstance(self $x, self $y)
+    {
+        if ($x->instanceID != $y->instanceID) {
+            throw new \UnexpectedValueException('The instances of the two PrimeField\Integer objects do not match');
+        }
+    }
+
+    /**
+     * Tests the equality of two numbers.
+     *
+     * @return bool
+     */
+    public function equals(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        return $this->value->equals($x->value);
+    }
+
+    /**
+     * Compares two numbers.
+     *
+     * @return int
+     */
+    public function compare(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        return $this->value->compare($x->value);
+    }
+
+    /**
+     * Adds two PrimeFieldIntegers.
+     *
+     * @return static
+     */
+    public function add(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        $temp = new static($this->instanceID);
+        $temp->value = $this->value->add($x->value);
+        if ($temp->value->compare(static::$modulo[$this->instanceID]) >= 0) {
+            $temp->value = $temp->value->subtract(static::$modulo[$this->instanceID]);
+        }
+
+        return $temp;
+    }
+
+    /**
+     * Subtracts two PrimeFieldIntegers.
+     *
+     * @return static
+     */
+    public function subtract(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        $temp = new static($this->instanceID);
+        $temp->value = $this->value->subtract($x->value);
+        if ($temp->value->isNegative()) {
+            $temp->value = $temp->value->add(static::$modulo[$this->instanceID]);
+        }
+
+        return $temp;
+    }
+
+    /**
+     * Multiplies two PrimeFieldIntegers.
+     *
+     * @return static
+     */
+    public function multiply(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        return new static($this->instanceID, $this->value->multiply($x->value));
+    }
+
+    /**
+     * Divides two PrimeFieldIntegers.
+     *
+     * @return static
+     */
+    public function divide(self $x)
+    {
+        static::checkInstance($this, $x);
+
+        $denominator = $x->value->modInverse(static::$modulo[$this->instanceID]);
+        return new static($this->instanceID, $this->value->multiply($denominator));
+    }
+
+    /**
+     * Performs power operation on a PrimeFieldInteger.
+     *
+     * @return static
+     */
+    public function pow(BigInteger $x)
+    {
+        $temp = new static($this->instanceID);
+        $temp->value = $this->value->powMod($x, static::$modulo[$this->instanceID]);
+
+        return $temp;
+    }
+
+    /**
+     * Calculates the square root
+     *
+     * @link https://en.wikipedia.org/wiki/Tonelli%E2%80%93Shanks_algorithm
+     * @return static|false
+     */
+    public function squareRoot()
+    {
+        static $one, $two;
+        if (!isset($one)) {
+            $one = new BigInteger(1);
+            $two = new BigInteger(2);
+        }
+        $reduce = static::$reduce[$this->instanceID];
+        $p_1 = static::$modulo[$this->instanceID]->subtract($one);
+        $q = clone $p_1;
+        $s = BigInteger::scan1divide($q);
+        list($pow) = $p_1->divide($two);
+        for ($z = $one; !$z->equals(static::$modulo[$this->instanceID]); $z = $z->add($one)) {
+            $temp = $z->powMod($pow, static::$modulo[$this->instanceID]);
+            if ($temp->equals($p_1)) {
+                break;
+            }
+        }
+
+        $m = new BigInteger($s);
+        $c = $z->powMod($q, static::$modulo[$this->instanceID]);
+        $t = $this->value->powMod($q, static::$modulo[$this->instanceID]);
+        list($temp) = $q->add($one)->divide($two);
+        $r = $this->value->powMod($temp, static::$modulo[$this->instanceID]);
+
+        while (!$t->equals($one)) {
+            $i = clone $one;
+
+            while (!$t->powMod($two->pow($i), static::$modulo[$this->instanceID])->equals($one)) {
+                $i = $i->add($one);
+            }
+
+            if ($i->compare($m) >= 0) {
+                return false;
+            }
+            $b = $c->powMod($two->pow($m->subtract($i)->subtract($one)), static::$modulo[$this->instanceID]);
+            $m = $i;
+            $c = $reduce($b->multiply($b));
+            $t = $reduce($t->multiply($c));
+            $r = $reduce($r->multiply($b));
+        }
+
+        return new static($this->instanceID, $r);
+    }
+
+    /**
+     * Is Odd?
+     *
+     * @return boolean
+     */
+    public function isOdd()
+    {
+        return $this->value->isOdd();
+    }
+
+    /**
+     * Negate
+     *
+     * A negative number can be written as 0-12. With modulos, 0 is the same thing as the modulo
+     * so 0-12 is the same thing as modulo-12
+     *
+     * @return object
+     */
+    public function negate()
+    {
+        return new static($this->instanceID, static::$modulo[$this->instanceID]->subtract($this->value));
+    }
+
+    /**
+     * Converts an Integer to a byte string (eg. base-256).
+     *
+     * @return string
+     */
+    public function toBytes()
+    {
+        $length = static::$modulo[$this->instanceID]->getLengthInBytes();
+        return str_pad($this->value->toBytes(), $length, "\0", STR_PAD_LEFT);
+    }
+
+    /**
+     * Converts an Integer to a hex string (eg. base-16).
+     *
+     * @return string
+     */
+    public function toHex()
+    {
+        return Hex::encode($this->toBytes());
+    }
+
+    /**
+     * Converts an Integer to a bit string (eg. base-2).
+     *
+     * @return string
+     */
+    public function toBits()
+    {
+        // return $this->value->toBits();
+        static $length;
+        if (!isset($length)) {
+            $length = static::$modulo[$this->instanceID]->getLength();
+        }
+
+        return str_pad($this->value->toBits(), $length, '0', STR_PAD_LEFT);
+    }
+
+    /**
+     * Returns the w-ary non-adjacent form (wNAF)
+     *
+     * @param int $w optional
+     * @return int[]
+     */
+    public function getNAF($w = 1)
+    {
+        $w++;
+
+        $mask = new BigInteger((1 << $w) - 1);
+        $sub = new BigInteger(1 << $w);
+        //$sub = new BigInteger(1 << ($w - 1));
+        $d = $this->toBigInteger();
+        $d_i = [];
+
+        $i = 0;
+        while ($d->compare(static::$zero) > 0) {
+            if ($d->isOdd()) {
+                // start mods
+                $d_i[$i] = $d->testBit($w - 1) ?
+                    $d->bitwise_and($mask)->subtract($sub) :
+                    //$sub->subtract($d->bitwise_and($mask)) :
+                    $d->bitwise_and($mask);
+                // end mods
+                $d = $d->subtract($d_i[$i]);
+                $d_i[$i] = (int) $d_i[$i]->toString();
+            } else {
+                $d_i[$i] = 0;
+            }
+            $shift = !$d->equals(static::$zero) && $d->bitwise_and($mask)->equals(static::$zero) ? $w : 1; // $w or $w + 1?
+            $d = $d->bitwise_rightShift($shift);
+            while (--$shift > 0) {
+                $d_i[++$i] = 0;
+            }
+            $i++;
+        }
+
+        return $d_i;
+    }
+
+    /**
+     * Converts an Integer to a BigInteger
+     *
+     * @return string
+     */
+    public function toBigInteger()
+    {
+        return clone $this->value;
+    }
+
+    /**
+     *  __toString() magic method
+     *
+     * @access public
+     */
+    public function __toString()
+    {
+        return (string) $this->value;
+    }
+
+    /**
+     *  __debugInfo() magic method
+     *
+     * @access public
+     */
+    public function __debugInfo()
+    {
+        return ['value' => $this->toHex()];
+    }
+}
\ No newline at end of file
diff --git a/tests/Unit/Crypt/AES/TestCase.php b/tests/Unit/Crypt/AES/TestCase.php
index 643123a6..523a45f3 100644
--- a/tests/Unit/Crypt/AES/TestCase.php
+++ b/tests/Unit/Crypt/AES/TestCase.php
@@ -407,4 +407,16 @@ abstract class Unit_Crypt_AES_TestCase extends PhpseclibTestCase
 
         $this->assertEquals($plaintext, $actual);
     }
+
+    /**
+     * @expectedException \UnexpectedValueException
+     */
+    public function testNoKey()
+    {
+        $aes = new AES('cbc');
+        $aes->setPreferredEngine($this->engine);
+        $aes->setIV(str_repeat('x', 16));
+
+        $aes->encrypt(str_repeat('a', 16));
+    }
 }
diff --git a/tests/Unit/Crypt/DSA/LoadKeyTest.php b/tests/Unit/Crypt/DSA/LoadKeyTest.php
index d7277a9a..996b00f5 100644
--- a/tests/Unit/Crypt/DSA/LoadKeyTest.php
+++ b/tests/Unit/Crypt/DSA/LoadKeyTest.php
@@ -158,7 +158,7 @@ Syea3pSvWdBpVhWzOX4A7qbxs+bhWAQWAhQiF7sFfCtZ7oOgCb2aJ9ySC9sTug==
         $this->assertTrue($dsa->load($key));
         $this->assertInternalType('string', "$dsa");
         $this->assertSame("$dsa", $dsa->getPrivateKey());
-        $this->assertInternalType('string', $dsa->getPublicKey());
+        $this->assertInstanceOf(DSA::class, $dsa->getPublicKey());
         $this->assertInternalType('string', $dsa->getParameters());
     }
 
diff --git a/tests/Unit/Crypt/DSA/SignatureTest.php b/tests/Unit/Crypt/DSA/SignatureTest.php
index 8ba19de5..8e59a786 100644
--- a/tests/Unit/Crypt/DSA/SignatureTest.php
+++ b/tests/Unit/Crypt/DSA/SignatureTest.php
@@ -28,7 +28,7 @@ pQFV8eVJfk91ERQ4Dn6ePLUv2dRIt4a0S0qHqadgzyoFyqkmmUi1kNLyixtRqh+m
 2gXx0t63HEpZDbEPppdpnlppZquVQh7TyrKSXW9MTzUkQjFI9UY7kZeKAhQXiJgI
 kBniZHdFBAZBTE14YJUBkw==
 -----END DSA PRIVATE KEY-----');
-        $signature = $dsa->sign($message, 'PKCS');
+        $signature = $dsa->sign($message, 'ASN1');
 
         $dsa->load('-----BEGIN PUBLIC KEY-----
 MIIBuDCCASwGByqGSM44BAEwggEfAoGBAOwYAcAzXpuw+XCXuNp5zhAzKdhrRguI
@@ -43,8 +43,8 @@ zyoFyqkmmUi1kNLyixtRqh+m2gXx0t63HEpZDbEPppdpnlppZquVQh7TyrKSXW9M
 TzUkQjFI9UY7kZeK
 -----END PUBLIC KEY-----');
 
-        $this->assertTrue($dsa->verify($message, $signature, 'PKCS'));
-        $this->assertFalse($dsa->verify('foozbar', $signature, 'PKCS'));
+        $this->assertTrue($dsa->verify($message, $signature, 'ASN1'));
+        $this->assertFalse($dsa->verify('foozbar', $signature, 'ASN1'));
 
         // openssl dgst -dss1 -sign dsa_priv.pem foo.txt > sigfile.bin
         $signature = '302c021456d7e7da10d1538a6cd45dcb2b0ce15c28bac03402147e973a4de1e92e8a87ed5218c797952a3f854df5';
@@ -52,8 +52,8 @@ TzUkQjFI9UY7kZeK
 
         $dsa->setHash('sha1');
 
-        $this->assertTrue($dsa->verify("foobar\n", $signature, 'PKCS'));
-        $this->assertFalse($dsa->verify('foozbar', $signature, 'PKCS'));
+        $this->assertTrue($dsa->verify("foobar\n", $signature, 'ASN1'));
+        $this->assertFalse($dsa->verify('foozbar', $signature, 'ASN1'));
 
         // openssl dgst -sha256 -sign dsa_priv.pem foo.txt > sigfile.bin
         $signature = '302e021500b131ec2682c4c0be13e6558ba3d64929ebc0ac420215009946300a03561cef50c0a51d0cd0a2c835e798fc';
@@ -61,8 +61,8 @@ TzUkQjFI9UY7kZeK
 
         $dsa->setHash('sha256');
 
-        $this->assertTrue($dsa->verify('abcdefghijklmnopqrstuvwxyz', $signature, 'PKCS'));
-        $this->assertFalse($dsa->verify('zzzz', $signature, 'PKCS'));
+        $this->assertTrue($dsa->verify('abcdefghijklmnopqrstuvwxyz', $signature, 'ASN1'));
+        $this->assertFalse($dsa->verify('zzzz', $signature, 'ASN1'));
     }
 
     public function testRandomSignature()
@@ -83,8 +83,8 @@ pQFV8eVJfk91ERQ4Dn6ePLUv2dRIt4a0S0qHqadgzyoFyqkmmUi1kNLyixtRqh+m
 2gXx0t63HEpZDbEPppdpnlppZquVQh7TyrKSXW9MTzUkQjFI9UY7kZeKAhQXiJgI
 kBniZHdFBAZBTE14YJUBkw==
 -----END DSA PRIVATE KEY-----');
-        $signature1 = $dsa->sign($message, 'PKCS');
-        $signature2 = $dsa->sign($message, 'PKCS');
+        $signature1 = $dsa->sign($message, 'ASN1');
+        $signature2 = $dsa->sign($message, 'ASN1');
 
         // phpseclib's DSA implementation uses a CSPRNG to generate the k parameter.
         // used correctly this should result in different signatures every time.
@@ -93,8 +93,8 @@ kBniZHdFBAZBTE14YJUBkw==
         // unit test would need to be updated
         $this->assertNotEquals($signature1, $signature2);
 
-        $this->assertTrue($dsa->verify($message, $signature1, 'PKCS'));
-        $this->assertTrue($dsa->verify($message, $signature2, 'PKCS'));
+        $this->assertTrue($dsa->verify($message, $signature1, 'ASN1'));
+        $this->assertTrue($dsa->verify($message, $signature2, 'ASN1'));
 
         $signature = $dsa->sign($message, 'SSH2');
 
diff --git a/tests/Unit/Crypt/ECDSA/CurveTest.php b/tests/Unit/Crypt/ECDSA/CurveTest.php
new file mode 100644
index 00000000..fb252d72
--- /dev/null
+++ b/tests/Unit/Crypt/ECDSA/CurveTest.php
@@ -0,0 +1,549 @@
+<?php
+
+/**
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2015 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+use phpseclib\Crypt\ECDSA;
+use phpseclib\File\ASN1;
+use phpseclib\Crypt\ECDSA\Curves\Ed448;
+use phpseclib\Math\BigInteger;
+
+class Ed448PublicKey
+{
+    use phpseclib\Crypt\ECDSA\Keys\Common;
+
+    public static function load($key, $password = '')
+    {
+        $components = ['curve' => new Ed448()];
+        $components['QA'] = self::extractPoint($key, $components['curve']);
+
+        return $components;
+    }
+}
+
+class Ed448PrivateKey
+{
+    public static function load($key, $password = '')
+    {
+        $components = ['curve' => new Ed448()];
+        $components['dA'] = $components['curve']->extractSecret($key);
+        $components['QA'] = $components['curve']->multiplyPoint($components['curve']->getBasePoint(), $components['dA']);
+
+        return $components;
+    }
+}
+
+class Unit_Crypt_ECDSA_CurveTest extends PhpseclibTestCase
+{
+    public function curves()
+    {
+        $curves = [];
+        foreach (new \DirectoryIterator(__DIR__ . '/../../../../phpseclib/Crypt/ECDSA/Curves/') as $file) {
+            if ($file->getExtension() != 'php') {
+                continue;
+            }
+            $testName = $file->getBasename('.php');
+            $class = 'phpseclib\Crypt\ECDSA\Curves\\' . $testName;
+            $reflect = new \ReflectionClass($class);
+            if ($reflect->isFinal()) {
+                continue;
+            }
+            $curves[] = [$testName];
+        }
+
+        return $curves;
+    }
+
+    public function allCurves()
+    {
+        $curves = [];
+        foreach (new \DirectoryIterator(__DIR__ . '/../../../../phpseclib/Crypt/ECDSA/Curves/') as $file) {
+            if ($file->getExtension() != 'php') {
+                continue;
+            }
+            $testName = $file->getBasename('.php');
+            $curves[] = [$testName];
+        }
+
+        return $curves;
+    }
+
+    public function curvesWithOIDs()
+    {
+        $class = new ReflectionClass('phpseclib\Crypt\ECDSA\Keys\PKCS8');
+
+        $initialize = $class->getMethod('initialize_static_variables');
+        $initialize->setAccessible(true);
+        $initialize->invoke(null);
+
+        $property = $class->getProperty('curveOIDs');
+        $property->setAccessible(true);
+
+        $curves = [];
+
+        foreach ($property->getValue() as $curve => $oid) {
+            $curves[] = [$curve];
+        }
+
+        return $curves;
+    }
+
+    /**
+     * Verify that the base points are correct and verify the finite field math
+     *
+     * @dataProvider curves
+     */
+    public function testBasePoint($name)
+    {
+        $class = 'phpseclib\Crypt\ECDSA\Curves\\' . $name;
+        $curve = new $class;
+        $this->assertTrue($curve->verifyPoint($curve->getBasePoint()), "Failed to verify basepoint of curve $name");
+    }
+
+    /**
+     * Verify the correctness of the point addition / doubling / multiplication algorithms
+     *
+     * @dataProvider curves
+     * @requires PHP 7.0
+     */
+    public function testKeyGeneration($name)
+    {
+        $class = 'phpseclib\Crypt\ECDSA\Curves\\' . $name;
+        $curve = new $class;
+        $dA = $curve->createRandomMultiplier();
+        $QA = $curve->multiplyPoint($curve->getBasePoint(), $dA);
+        $this->assertTrue($curve->verifyPoint($QA), "Failed to verify point multiplication on curve $name with $dA");
+    }
+
+    /**
+     * Verify that OIDs have corresponding curve class
+     *
+     * @dataProvider curvesWithOIDs
+     */
+    public function testCurveExistance($name)
+    {
+        $this->assertFileExists(__DIR__ . "/../../../../phpseclib/Crypt/ECDSA/Curves/$name.php");
+    }
+
+    /**
+     * Verify that all named curves have a corresponding OID
+     *
+     * @dataProvider allCurves
+     */
+    public function testOIDExistance($name)
+    {
+        switch ($name) {
+            case 'Ed25519':
+            case 'Ed448':
+                self::markTestSkipped('Ed25519 / Ed448 OIDs are treated a little differently');
+        }
+        $this->assertNotSame(ASN1::getOID($name), $name);
+    }
+
+    /**
+     * Sign with internal engine, verify with best engine
+     *
+     * @dataProvider curves
+     * @requires PHP 7.0
+     */
+    public function testInternalSign($name)
+    {
+        // tests utilizing dataProvider only seem to output when all the dataProvider input
+        // has been exhausted. ie. when this test has been ran on every curve. on my local
+        // system it takes about 2.5m for this test to run, with the most time consuming curves
+        // being sect571r1 and sect571k1, which take about 30s each. on Travis CI, however,
+        // these curves seem to take about 2m each to run:
+        // https://travis-ci.org/terrafrost/phpseclib/jobs/450262081
+        // because of the 10m timeout that Travis CI has this means that there's a very
+        // good chance the binary curves (sect*) will timeout before the test is able to
+        // output anything
+        if (substr($name, 0, 4) == 'sect') {
+            self::markTestSkipped('Binary field curves are being skipped');
+        }
+
+        $plaintext = 'zzz';
+
+        ECDSA::useInternalEngine();
+        extract(ECDSA::createKey($name));
+        $sig = $privatekey->sign($plaintext);
+
+        ECDSA::useBestEngine();
+        $this->assertTrue($publickey->verify($plaintext, $sig));
+    }
+
+    /**
+     * Sign with best engine, verify with internal engine
+     *
+     * @dataProvider curves
+     * @requires PHP 7.0
+     */
+    public function testInternalVerify($name)
+    {
+        if (substr($name, 0, 4) == 'sect') {
+            self::markTestSkipped('Binary field curves are being skipped');
+        }
+
+        $plaintext = 'zzz';
+
+        ECDSA::useBestEngine();
+        extract(ECDSA::createKey($name));
+        $sig = $privatekey->sign($plaintext);
+
+        ECDSA::useInternalEngine();
+        $this->assertTrue($publickey->verify($plaintext, $sig));
+    }
+
+    /**
+     * Ed448 test vectors from https://tools.ietf.org/html/rfc8032#section-7.4
+     */
+    public function testEd448TestVectors()
+    {
+        ECDSA::addFileFormat('Ed448PublicKey');
+        ECDSA::addFileFormat('Ed448PrivateKey');
+
+        $private = pack('H*', '6c82a562cb808d10d632be89c8513ebf6c929f34ddfa8c9f63c9960ef6e348a3528c8a3fcc2f044e39a3fc5b94492f8f032e7549a20098f95b');
+        $public = pack('H*', '5fd7449b59b461fd2ce787ec616ad46a1da1342485a70e1f8a0ea75d80e96778edf124769b46c7061bd6783df1e50f6cd1fa1abeafe8256180');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $expected = '533a37f6bbe457251f023c0d88f976ae2dfb504a843e34d2074fd823d41a591f2b233f034f628281f2fd7a22ddd47d7828c59bd0a21bfd3980' .
+                    'ff0d2028d4b18a9df63e006c5d1c2d345b925d8dc00b4104852db99ac5c7cdda8530a113a0f4dbb61149f05a7363268c71d95808ff2e652600';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign('')));
+        $this->assertTrue($publicKey->verify('', $sig));
+
+        $private = pack('H*', 'c4eab05d357007c632f3dbb48489924d552b08fe0c353a0d4a1f00acda2c463afbea67c5e8d2877c5e3bc397a659949ef8021e954e0a12274e');
+        $public = pack('H*', '43ba28f430cdff456ae531545f7ecd0ac834a55d9358c0372bfa0c6c6798c0866aea01eb00742802b8438ea4cb82169c235160627b4c3a9480');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $expected = '26b8f91727bd62897af15e41eb43c377efb9c610d48f2335cb0bd0087810f4352541b143c4b981b7e18f62de8ccdf633fc1bf037ab7cd77980' .
+                    '5e0dbcc0aae1cbcee1afb2e027df36bc04dcecbf154336c19f0af7e0a6472905e799f1953d2a0ff3348ab21aa4adafd1d234441cf807c03a00';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign("\x03")));
+        $this->assertTrue($publicKey->verify("\x03", $sig));
+
+        $publicKey->setContext(pack('H*', '666f6f'));
+        $privateKey->setContext(pack('H*', '666f6f'));
+
+        $expected = 'd4f8f6131770dd46f40867d6fd5d5055de43541f8c5e35abbcd001b32a89f7d2151f7647f11d8ca2ae279fb842d607217fce6e042f6815ea00' .
+                    '0c85741de5c8da1144a6a1aba7f96de42505d7a7298524fda538fccbbb754f578c1cad10d54d0d5428407e85dcbc98a49155c13764e66c3c00';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign("\x03")));
+        $this->assertTrue($publicKey->verify("\x03", $sig));
+
+        $private = pack('H*', '258cdd4ada32ed9c9ff54e63756ae582fb8fab2ac721f2c8e676a72768513d939f63dddb55609133f29adf86ec9929dccb52c1c5fd2ff7e21b');
+        $public = pack('H*', '3ba16da0c6f2cc1f30187740756f5e798d6bc5fc015d7c63cc9510ee3fd44adc24d8e968b6e46e6f94d19b945361726bd75e149ef09817f580');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = pack('H*', '64a65f3cdedcdd66811e2915');
+
+        $expected = '7eeeab7c4e50fb799b418ee5e3197ff6bf15d43a14c34389b59dd1a7b1b85b4ae90438aca634bea45e3a2695f1270f07fdcdf7c62b8efeaf00' .
+                    'b45c2c96ba457eb1a8bf075a3db28e5c24f6b923ed4ad747c3c9e03c7079efb87cb110d3a99861e72003cbae6d6b8b827e4e6c143064ff3c00';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', '7ef4e84544236752fbb56b8f31a23a10e42814f5f55ca037cdcc11c64c9a3b2949c1bb60700314611732a6c2fea98eebc0266a11a93970100e');
+        $public = pack('H*', 'b3da079b0aa493a5772029f0467baebee5a8112d9d3a22532361da294f7bb3815c5dc59e176b4d9f381ca0938e13c6c07b174be65dfa578e80');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = pack('H*', '64a65f3cdedcdd66811e2915e7');
+
+        $expected = '6a12066f55331b6c22acd5d5bfc5d71228fbda80ae8dec26bdd306743c5027cb4890810c162c027468675ecf645a83176c0d7323a2ccde2d80' .
+                    'efe5a1268e8aca1d6fbc194d3f77c44986eb4ab4177919ad8bec33eb47bbb5fc6e28196fd1caf56b4e7e0ba5519234d047155ac727a1053100';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', 'd65df341ad13e008567688baedda8e9dcdc17dc024974ea5b4227b6530e339bff21f99e68ca6968f3cca6dfe0fb9f4fab4fa135d5542ea3f01');
+        $public = pack('H*', 'df9705f58edbab802c7f8363cfe5560ab1c6132c20a9f1dd163483a26f8ac53a39d6808bf4a1dfbd261b099bb03b3fb50906cb28bd8a081f00');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = 'bd0f6a3747cd561bdddf4640a332461a4a30a12a434cd0bf40d766d9c6d458e5512204a30c17d1f50b5079631f64eb3112182da3005835461113718d1a5ef944';
+        $message = pack('H*', $message);
+
+        $expected = '554bc2480860b49eab8532d2a533b7d578ef473eeb58c98bb2d0e1ce488a98b18dfde9b9b90775e67f47d4a1c3482058efc9f40d2ca033a080' .
+                    '1b63d45b3b722ef552bad3b4ccb667da350192b61c508cf7b6b5adadc2c8d9a446ef003fb05cba5f30e88e36ec2703b349ca229c2670833900';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', '2ec5fe3c17045abdb136a5e6a913e32ab75ae68b53d2fc149b77e504132d37569b7e766ba74a19bd6162343a21c8590aa9cebca9014c636df5');
+        $public = pack('H*', '79756f014dcfe2079f5dd9e718be4171e2ef2486a08f25186f6bff43a9936b9bfe12402b08ae65798a3d81e22e9ec80e7690862ef3d4ed3a00');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = '15777532b0bdd0d1389f636c5f6b9ba734c90af572877e2d272dd078aa1e567cfa80e12928bb542330e8409f3174504107ecd5efac61ae7504dabe2a602ede89e5cca6257a7c77e27a702b3ae39fc769fc54f2395ae6a1178cab4738e543072fc1c177fe71e92e25bf03e4ecb72f47b64d0465aaea4c7fad372536c8ba516a60' .
+                   '39c3c2a39f0e4d832be432dfa9a706a6e5c7e19f397964ca4258002f7c0541b590316dbc5622b6b2a6fe7a4abffd96105eca76ea7b98816af0748c10df048ce012d901015a51f189f3888145c03650aa23ce894c3bd889e030d565071c59f409a9981b51878fd6fc110624dcbcde0bf7a69ccce38fabdf86f3bef6044819de11';
+        $message = pack('H*', $message);
+
+        $expected = 'c650ddbb0601c19ca11439e1640dd931f43c518ea5bea70d3dcde5f4191fe53f00cf966546b72bcc7d58be2b9badef28743954e3a44a23f880' .
+                    'e8d4f1cfce2d7a61452d26da05896f0a50da66a239a8a188b6d825b3305ad77b73fbac0836ecc60987fd08527c1a8e80d5823e65cafe2a3d00';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', '872d093780f5d3730df7c212664b37b8a0f24f56810daa8382cd4fa3f77634ec44dc54f1c2ed9bea86fafb7632d8be199ea165f5ad55dd9ce8');
+        $public = pack('H*', 'a81b2e8a70a5ac94ffdbcc9badfc3feb0801f258578bb114ad44ece1ec0e799da08effb81c5d685c0c56f64eecaef8cdf11cc38737838cf400');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = '6ddf802e1aae4986935f7f981ba3f0351d6273c0a0c22c9c0e8339168e675412a3debfaf435ed651558007db4384b650fcc07e3b586a27a4f7a00ac8a6fec2cd86ae4bf1570c41e6a40c931db27b2faa15a8cedd52cff7362c4e6e23daec0fbc3a79b6806e316efcc7b68119bf46bc76a26067a53f296dafdbdc11c77f7777e9' .
+                   '72660cf4b6a9b369a6665f02e0cc9b6edfad136b4fabe723d2813db3136cfde9b6d044322fee2947952e031b73ab5c603349b307bdc27bc6cb8b8bbd7bd323219b8033a581b59eadebb09b3c4f3d2277d4f0343624acc817804728b25ab797172b4c5c21a22f9c7839d64300232eb66e53f31c723fa37fe387c7d3e50bdf9813' .
+                   'a30e5bb12cf4cd930c40cfb4e1fc622592a49588794494d56d24ea4b40c89fc0596cc9ebb961c8cb10adde976a5d602b1c3f85b9b9a001ed3c6a4d3b1437f52096cd1956d042a597d561a596ecd3d1735a8d570ea0ec27225a2c4aaff26306d1526c1af3ca6d9cf5a2c98f47e1c46db9a33234cfd4d81f2c98538a09ebe76998' .
+                   'd0d8fd25997c7d255c6d66ece6fa56f11144950f027795e653008f4bd7ca2dee85d8e90f3dc315130ce2a00375a318c7c3d97be2c8ce5b6db41a6254ff264fa6155baee3b0773c0f497c573f19bb4f4240281f0b1f4f7be857a4e59d416c06b4c50fa09e1810ddc6b1467baeac5a3668d11b6ecaa901440016f389f80acc4db9' .
+                   '77025e7f5924388c7e340a732e554440e76570f8dd71b7d640b3450d1fd5f0410a18f9a3494f707c717b79b4bf75c98400b096b21653b5d217cf3565c9597456f70703497a078763829bc01bb1cbc8fa04eadc9a6e3f6699587a9e75c94e5bab0036e0b2e711392cff0047d0d6b05bd2a588bc109718954259f1d86678a579a3' .
+                   '120f19cfb2963f177aeb70f2d4844826262e51b80271272068ef5b3856fa8535aa2a88b2d41f2a0e2fda7624c2850272ac4a2f561f8f2f7a318bfd5caf9696149e4ac824ad3460538fdc25421beec2cc6818162d06bbed0c40a387192349db67a118bada6cd5ab0140ee273204f628aad1c135f770279a651e24d8c14d75a605' .
+                   '9d76b96a6fd857def5e0b354b27ab937a5815d16b5fae407ff18222c6d1ed263be68c95f32d908bd895cd76207ae726487567f9a67dad79abec316f683b17f2d02bf07e0ac8b5bc6162cf94697b3c27cd1fea49b27f23ba2901871962506520c392da8b6ad0d99f7013fbc06c2c17a569500c8a7696481c1cd33e9b14e40b82e' .
+                   '79a5f5db82571ba97bae3ad3e0479515bb0e2b0f3bfcd1fd33034efc6245eddd7ee2086ddae2600d8ca73e214e8c2b0bdb2b047c6a464a562ed77b73d2d841c4b34973551257713b753632efba348169abc90a68f42611a40126d7cb21b58695568186f7e569d2ff0f9e745d0487dd2eb997cafc5abf9dd102e62ff66cba87';
+        $message = pack('H*', $message);
+
+        $expected = 'e301345a41a39a4d72fff8df69c98075a0cc082b802fc9b2b6bc503f926b65bddf7f4c8f1cb49f6396afc8a70abe6d8aef0db478d4c6b29700' .
+                    '76c6a0484fe76d76b3a97625d79f1ce240e7c576750d295528286f719b413de9ada3e8eb78ed573603ce30d8bb761785dc30dbc320869e1a00';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+    }
+
+    /**
+     * Ed25519 test vectors from https://tools.ietf.org/html/rfc8032#section-7.1 (and 7.2)
+     */
+    public function testEd25519TestVectors()
+    {
+        ECDSA::useBestEngine();
+
+        $private = pack('H*', '9d61b19deffd5a60ba844af492ec2cc44449c5697b326919703bac031cae7f60');
+        $public = pack('H*', 'd75a980182b10ab7d54bfed3c964073a0ee172f3daa62325af021a68f707511a');
+
+        $privateKey = new ECDSA();
+        // libsodium format
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $expected = 'e5564300c360ac729086e2cc806e828a84877f1eb8e5d974d873e06522490155' .
+                    '5fb8821590a33bacc61e39701cf9b46bd25bf5f0595bbe24655141438e7a100b';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign('')));
+        $this->assertTrue($publicKey->verify('', $sig));
+
+        $private = pack('H*', '4ccd089b28ff96da9db6c346ec114e0f5b8a319f35aba624da8cf6ed4fb8a6fb');
+        $public = pack('H*', '3d4017c3e843895a92b70aa74d1b7ebc9c982ccf2ec4968cc0cd55f12af4660c');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $expected = '92a009a9f0d4cab8720e820b5f642540a2b27b5416503f8fb3762223ebdb69da' .
+                    '085ac1e43e15996e458f3613d0f11d8c387b2eaeb4302aeeb00d291612bb0c00';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign("\x72")));
+        $this->assertTrue($publicKey->verify("\x72", $sig));
+
+        $private = pack('H*', 'c5aa8df43f9f837bedb7442f31dcb7b166d38535076f094b85ce3a2e0b4458f7');
+        $public = pack('H*', 'fc51cd8e6218a1a38da47ed00230f0580816ed13ba3303ac5deb911548908025');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $expected = '6291d657deec24024827e69c3abe01a30ce548a284743a445e3680d7db5ac3ac' .
+                    '18ff9b538d16f290ae67f760984dc6594a7c15e9716ed28dc027beceea1ec40a';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign("\xaf\x82")));
+        $this->assertTrue($publicKey->verify("\xaf\x82", $sig));
+
+        $private = pack('H*', 'f5e5767cf153319517630f226876b86c8160cc583bc013744c6bf255f5cc0ee5');
+        $public = pack('H*', '278117fc144c72340f67d0f2316e8386ceffbf2b2428c9c51fef7c597f1d426e');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = '08b8b2b733424243760fe426a4b54908632110a66c2f6591eabd3345e3e4eb98' .
+                   'fa6e264bf09efe12ee50f8f54e9f77b1e355f6c50544e23fb1433ddf73be84d8' .
+                   '79de7c0046dc4996d9e773f4bc9efe5738829adb26c81b37c93a1b270b20329d' .
+                   '658675fc6ea534e0810a4432826bf58c941efb65d57a338bbd2e26640f89ffbc' .
+                   '1a858efcb8550ee3a5e1998bd177e93a7363c344fe6b199ee5d02e82d522c4fe' .
+                   'ba15452f80288a821a579116ec6dad2b3b310da903401aa62100ab5d1a36553e' .
+                   '06203b33890cc9b832f79ef80560ccb9a39ce767967ed628c6ad573cb116dbef' .
+                   'efd75499da96bd68a8a97b928a8bbc103b6621fcde2beca1231d206be6cd9ec7' .
+                   'aff6f6c94fcd7204ed3455c68c83f4a41da4af2b74ef5c53f1d8ac70bdcb7ed1' .
+                   '85ce81bd84359d44254d95629e9855a94a7c1958d1f8ada5d0532ed8a5aa3fb2' .
+                   'd17ba70eb6248e594e1a2297acbbb39d502f1a8c6eb6f1ce22b3de1a1f40cc24' .
+                   '554119a831a9aad6079cad88425de6bde1a9187ebb6092cf67bf2b13fd65f270' .
+                   '88d78b7e883c8759d2c4f5c65adb7553878ad575f9fad878e80a0c9ba63bcbcc' .
+                   '2732e69485bbc9c90bfbd62481d9089beccf80cfe2df16a2cf65bd92dd597b07' .
+                   '07e0917af48bbb75fed413d238f5555a7a569d80c3414a8d0859dc65a46128ba' .
+                   'b27af87a71314f318c782b23ebfe808b82b0ce26401d2e22f04d83d1255dc51a' .
+                   'ddd3b75a2b1ae0784504df543af8969be3ea7082ff7fc9888c144da2af58429e' .
+                   'c96031dbcad3dad9af0dcbaaaf268cb8fcffead94f3c7ca495e056a9b47acdb7' .
+                   '51fb73e666c6c655ade8297297d07ad1ba5e43f1bca32301651339e22904cc8c' .
+                   '42f58c30c04aafdb038dda0847dd988dcda6f3bfd15c4b4c4525004aa06eeff8' .
+                   'ca61783aacec57fb3d1f92b0fe2fd1a85f6724517b65e614ad6808d6f6ee34df' .
+                   'f7310fdc82aebfd904b01e1dc54b2927094b2db68d6f903b68401adebf5a7e08' .
+                   'd78ff4ef5d63653a65040cf9bfd4aca7984a74d37145986780fc0b16ac451649' .
+                   'de6188a7dbdf191f64b5fc5e2ab47b57f7f7276cd419c17a3ca8e1b939ae49e4' .
+                   '88acba6b965610b5480109c8b17b80e1b7b750dfc7598d5d5011fd2dcc5600a3' .
+                   '2ef5b52a1ecc820e308aa342721aac0943bf6686b64b2579376504ccc493d97e' .
+                   '6aed3fb0f9cd71a43dd497f01f17c0e2cb3797aa2a2f256656168e6c496afc5f' .
+                   'b93246f6b1116398a346f1a641f3b041e989f7914f90cc2c7fff357876e506b5' .
+                   '0d334ba77c225bc307ba537152f3f1610e4eafe595f6d9d90d11faa933a15ef1' .
+                   '369546868a7f3a45a96768d40fd9d03412c091c6315cf4fde7cb68606937380d' .
+                   'b2eaaa707b4c4185c32eddcdd306705e4dc1ffc872eeee475a64dfac86aba41c' .
+                   '0618983f8741c5ef68d3a101e8a3b8cac60c905c15fc910840b94c00a0b9d0';
+        $message = pack('H*', $message);
+
+        $expected = '0aab4c900501b3e24d7cdf4663326a3a87df5e4843b2cbdb67cbf6e460fec350' .
+                    'aa5371b1508f9f4528ecea23c436d94b5e8fcd4f681e30a6ac00a9704a188a03';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', '833fe62409237b9d62ec77587520911e9a759cec1d19755b7da901b96dca3d42');
+        $public = pack('H*', 'ec172b93ad5e563bf4932c70e1245034c35467ef2efd4d64ebf819683467e2bf');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $message = 'ddaf35a193617abacc417349ae20413112e6fa4e89a97ea20a9eeee64b55d39a' .
+                   '2192992a274fc1a836ba3c23a3feebbd454d4423643ce80e2a9ac94fa54ca49f';
+        $message = pack('H*', $message); // hash('sha512', 'abc')
+
+        $expected = 'dc2a4459e7369633a52b1bf277839a00201009a3efbf3ecb69bea2186c26b589' .
+                    '09351fc9ac90b3ecfdfbc7c66431e0303dca179c138ac17ad9bef1177331a704';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', '0305334e381af78f141cb666f6199f57bc3495335a256a95bd2a55bf546663f6');
+        $public = pack('H*', 'dfc9425e4f968f7f0c29f0259cf5f9aed6851c2bb4ad8bfb860cfee0ab248292');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $privateKey->setContext("\x62\x61\x72");
+        $publicKey->setContext("\x62\x61\x72");
+
+        $message = 'f726936d19c800494e3fdaff20b276a8';
+        $message = pack('H*', $message);
+
+        $expected = 'fc60d5872fc46b3aa69f8b5b4351d5808f92bcc044606db097abab6dbcb1aee3' .
+                    '216c48e8b3b66431b5b186d1d28f8ee15a5ca2df6668346291c2043d4eb3e90d';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', '0305334e381af78f141cb666f6199f57bc3495335a256a95bd2a55bf546663f6');
+        $public = pack('H*', 'dfc9425e4f968f7f0c29f0259cf5f9aed6851c2bb4ad8bfb860cfee0ab248292');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $privateKey->setContext("\x66\x6f\x6f");
+        $publicKey->setContext("\x66\x6f\x6f");
+
+        $message = '508e9e6882b979fea900f62adceaca35';
+        $message = pack('H*', $message);
+
+        $expected = '8b70c1cc8310e1de20ac53ce28ae6e7207f33c3295e03bb5c0732a1d20dc6490' .
+                    '8922a8b052cf99b7c4fe107a5abb5b2c4085ae75890d02df26269d8945f84b0b';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+
+        $private = pack('H*', 'ab9c2853ce297ddab85c993b3ae14bcad39b2c682beabc27d6d4eb20711d6560');
+        $public = pack('H*', '0f1d1274943b91415889152e893d80e93275a1fc0b65fd71b4b0dda10ad7d772');
+
+        $privateKey = new ECDSA();
+        $privateKey->load($private . $public);
+
+        $publicKey = new ECDSA();
+        $publicKey->load($public);
+
+        $privateKey->setContext("\x66\x6f\x6f");
+        $publicKey->setContext("\x66\x6f\x6f");
+
+        $message = 'f726936d19c800494e3fdaff20b276a8';
+        $message = pack('H*', $message);
+
+        $expected = '21655b5f1aa965996b3f97b3c849eafba922a0a62992f73b3d1b73106a84ad85' .
+                    'e9b86a7b6005ea868337ff2d20a7f5fbd4cd10b0be49a68da2b2e0dc0ad8960f';
+        $this->assertSame($expected, bin2hex($sig = $privateKey->sign($message)));
+        $this->assertTrue($publicKey->verify($message, $sig));
+    }
+
+    public function testRandomSignature()
+    {
+        $message = 'hello, world!';
+        $private = new ECDSA();
+        $private->load('PuTTY-User-Key-File-2: ecdsa-sha2-nistp256
+Encryption: none
+Comment: ecdsa-key-20181105
+Public-Lines: 3
+AAAAE2VjZHNhLXNoYTItbmlzdHAyNTYAAAAIbmlzdHAyNTYAAABBBJEXCsWA8s18
+m25MJlVE1urbXPYFi4q8oMbb2H0kE2f5WPxizsKXRmb1J68paXQizryL9fC4FTqI
+CJ1+UnaPfk0=
+Private-Lines: 1
+AAAAIQDwaPlajbXY1SxhuwsUqN1CEZ5g4adsbmJsKm+ZbUVm4g==
+Private-MAC: b85ca0eb7c612df5d18af85128821bd53faaa3ef');
+        $public = $private->getPublicKey();
+
+        $signature1 = $private->sign($message, 'ASN1');
+        $signature2 = $private->sign($message, 'ASN1');
+        // phpseclib's ECDSA implementation uses a CSPRNG to generate the k parameter.
+        // used correctly this should result in different signatures every time.
+        // RFC6979 describes a deterministic ECDSA scheme wherein two signatures for the same
+        // plaintext would yield the same value so if that were to be switched to then this
+        // unit test would need to be updated
+        $this->assertNotEquals($signature1, $signature2);
+
+        $this->assertTrue($public->verify($message, $signature1, 'ASN1'));
+        $this->assertTrue($public->verify($message, $signature2, 'ASN1'));
+
+        $signature1 = $private->sign($message, 'SSH2');
+        $signature2 = $private->sign($message, 'SSH2');
+        $this->assertNotEquals($signature1, $signature2);
+        $this->assertTrue($public->verify($message, $signature1, 'SSH2'));
+        $this->assertTrue($public->verify($message, $signature2, 'SSH2'));
+
+        $signature = $private->sign($message, 'Raw');
+        $this->assertTrue($public->verify($message, $signature, 'Raw'));
+    }
+}
diff --git a/tests/Unit/Crypt/ECDSA/KeyTest.php b/tests/Unit/Crypt/ECDSA/KeyTest.php
new file mode 100644
index 00000000..a47117a4
--- /dev/null
+++ b/tests/Unit/Crypt/ECDSA/KeyTest.php
@@ -0,0 +1,468 @@
+<?php
+/**
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2013 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+use phpseclib\Crypt\ECDSA;
+use phpseclib\Crypt\ECDSA\Keys\PKCS1;
+use phpseclib\Crypt\ECDSA\Keys\PKCS8;
+use phpseclib\Crypt\ECDSA\Keys\PuTTY;
+use phpseclib\Crypt\ECDSA\Keys\OpenSSH;
+use phpseclib\Crypt\ECDSA\Keys\XML;
+
+class Unit_Crypt_ECDSA_LoadKeyTest extends PhpseclibTestCase
+{
+    // openssl ecparam -name secp256k1 -genkey -noout -out secp256k1.pem
+    public function testPKCS1PrivateKey()
+    {
+        $key = new ECDSA;
+        $key->load($expected = '-----BEGIN EC PRIVATE KEY-----
+MHQCAQEEIEzUawcXqUsQhaEQ51JLeOIY0ddzlO2nNgwDk32ETqwkoAcGBSuBBAAK
+oUQDQgAEFuVcVb9iCUhg2cknHPE+BouHGhQ39ORjMaMI3T4RfRxr6dj5HAXdEqVZ
+1W94KMe30ndmTndcJ8BPeT1Dd15FdQ==
+-----END EC PRIVATE KEY-----');
+        $this->assertSame('secp256k1', $key->getCurve());
+        //PKCS1::useNamedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS1'));
+    }
+
+    // openssl ecparam -name secp256k1 -genkey -noout -out secp256k1.pem -param_enc explicit
+    public function testPKCS1PrivateKeySpecifiedCurve()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN EC PRIVATE KEY-----
+MIIBEwIBAQQgFr6TF5meGfgCXDqVxoSEltGI+T94G42PPbA6/ibq+ouggaUwgaIC
+AQEwLAYHKoZIzj0BAQIhAP////////////////////////////////////7///wv
+MAYEAQAEAQcEQQR5vmZ++dy7rFWgYpXOhwsHApv82y3OKNlZ8oFbFvgXmEg62ncm
+o8RlXaT7/A4RCKj9F7RIpoVUGZxH0I/7ENS4AiEA/////////////////////rqu
+3OavSKA7v9JejNA2QUECAQGhRANCAASCTRhjXqmdbqphSdxNkfTNAOmDW5cZ5fnZ
+ys0Tk4pUv/XdiMZtVCGTNsotGeFbT5X64JkP/BFi3PVqjwy2VhOc
+-----END EC PRIVATE KEY-----');
+        $this->assertSame('secp256k1', $key->getCurve());
+
+        // this key and the above key have a few small differences.
+        // in both keys the coefficient's are 0 and 7. in the above
+        // key both coefficients are encoded using a single byte.
+        // in the following key the coefficient's are encoded
+        // as 32 bytes (ie. the length of the reduction prime).
+        // eg. one byte null padded to 32 bytes.
+        // also, in the above key the cofactor (1; optional) is
+        // included whereas in the following key it is not
+        $expected = '-----BEGIN EC PRIVATE KEY-----
+MIIBTgIBAQQgFr6TF5meGfgCXDqVxoSEltGI+T94G42PPbA6/ibq+ouggeAwgd0C
+AQEwLAYHKoZIzj0BAQIhAP////////////////////////////////////7///wv
+MEQEIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABCAAAAAAAAAAAAAA
+AAAAAAAAAAAAAAAAAAAAAAAAAAAABwRBBHm+Zn753LusVaBilc6HCwcCm/zbLc4o
+2VnygVsW+BeYSDradyajxGVdpPv8DhEIqP0XtEimhVQZnEfQj/sQ1LgCIQD/////
+///////////////+uq7c5q9IoDu/0l6M0DZBQaFEA0IABIJNGGNeqZ1uqmFJ3E2R
+9M0A6YNblxnl+dnKzROTilS/9d2Ixm1UIZM2yi0Z4VtPlfrgmQ/8EWLc9WqPDLZW
+E5w=
+-----END EC PRIVATE KEY-----';
+        PKCS1::useSpecifiedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS1'));
+    }
+
+    // openssl ecparam -name secp256k1 -genkey -noout -out secp256k1.pem
+    // openssl pkcs8 -topk8 -nocrypt -in secp256k1.pem -out secp256k1-2.pem
+    public function testPKCS8PrivateKey()
+    {
+        $key = new ECDSA;
+        $key->load($expected = '-----BEGIN PRIVATE KEY-----
+MIGEAgEAMBAGByqGSM49AgEGBSuBBAAKBG0wawIBAQQgAYCXwnhqMT6fCIKIkQ0w
+cac7QqHrn4TCQMF9a+im74WhRANCAATwCjyGuP8xQbvVjznqazL36oeAnD32I+X2
++wscW3OmyTDpk41HaWYPh+j+BoufsSkCwf8dBRGEQbCieZbbZogy
+-----END PRIVATE KEY-----');
+        $this->assertSame('secp256k1', $key->getCurve());
+        $this->assertSame($expected, $key->getPrivateKey('PKCS8'));
+    }
+
+    // openssl ecparam -name secp256k1 -genkey -noout -out secp256k1.pem -param_enc explicit
+    // openssl pkcs8 -topk8 -nocrypt -in secp256k1.pem -out secp256k1-2.pem
+    public function testPKCS8PrivateKeySpecifiedCurve()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN PRIVATE KEY-----
+MIIBIwIBADCBrgYHKoZIzj0CATCBogIBATAsBgcqhkjOPQEBAiEA////////////
+/////////////////////////v///C8wBgQBAAQBBwRBBHm+Zn753LusVaBilc6H
+CwcCm/zbLc4o2VnygVsW+BeYSDradyajxGVdpPv8DhEIqP0XtEimhVQZnEfQj/sQ
+1LgCIQD////////////////////+uq7c5q9IoDu/0l6M0DZBQQIBAQRtMGsCAQEE
+IKFfw3vfd5pqA5SZOTFtpr7hdJoKP/rmTPMCggkAOA35oUQDQgAEnX66+UCzUW3T
+/fkLGIIfZjJm5bIMwAV85LpDom2hI441JRx+/W4WqtGuW+B/LABS6ZHp+qzepThC
+HsjS3Q9Pew==
+-----END PRIVATE KEY-----');
+        $this->assertSame('secp256k1', $key->getCurve());
+
+        // see testPKCS1PrivateKeySpecifiedCurve for an explanation
+        // of how this key and the above key differ
+        $expected = '-----BEGIN PRIVATE KEY-----
+MIIBXgIBADCB6QYHKoZIzj0CATCB3QIBATAsBgcqhkjOPQEBAiEA////////////
+/////////////////////////v///C8wRAQgAAAAAAAAAAAAAAAAAAAAAAAAAAAA
+AAAAAAAAAAAAAAAEIAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHBEEE
+eb5mfvncu6xVoGKVzocLBwKb/NstzijZWfKBWxb4F5hIOtp3JqPEZV2k+/wOEQio
+/Re0SKaFVBmcR9CP+xDUuAIhAP////////////////////66rtzmr0igO7/SXozQ
+NkFBBG0wawIBAQQgoV/De993mmoDlJk5MW2mvuF0mgo/+uZM8wKCCQA4DfmhRANC
+AASdfrr5QLNRbdP9+QsYgh9mMmblsgzABXzkukOibaEjjjUlHH79bhaq0a5b4H8s
+AFLpken6rN6lOEIeyNLdD097
+-----END PRIVATE KEY-----';
+        PKCS8::useSpecifiedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS8'));
+    }
+
+    // openssl ecparam -name sect113r1 -genkey -noout -out sect113r1.pem
+    public function testBinaryPKCS1PrivateKey()
+    {
+        $key = new ECDSA;
+        $key->load($expected = '-----BEGIN EC PRIVATE KEY-----
+MEECAQEEDwBZdP4eSzKk/uQa6jdtfKAHBgUrgQQABKEiAyAABAHqCoNb++mK5qvE
+c4rCzQEuI19czqvXpEPcAWSXew==
+-----END EC PRIVATE KEY-----');
+        $this->assertSame('sect113r1', $key->getCurve());
+
+        PKCS1::useNamedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS1'));
+    }
+
+    // openssl ecparam -name sect113r1 -genkey -noout -out sect113r1.pem -param_enc explicit
+    public function testBinaryPKCS1PrivateKeySpecifiedCurve()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN EC PRIVATE KEY-----
+MIHNAgEBBA8AuSc4BeeyYTq9rbSDuL2ggZIwgY8CAQEwHAYHKoZIzj0BAjARAgFx
+BgkqhkjOPQECAwICAQkwNwQOMIglDKbnx/5knOhYIPcEDui+5NPiJgdEGIvg6ccj
+AxUAEOcjqxTWluZ2h1YVF1b+v4/LSakEHwQAnXNhbzX0qxQH1zViwQ8ApSgwJ3lY
+7oTRMV7TGIYCDwEAAAAAAAAA2czsijnlbwIBAqEiAyAABAFC7c50y7uw+iuHeMCt
+WwCpKNBUcVeiHme609Dv/g==
+-----END EC PRIVATE KEY-----');
+        $this->assertSame('sect113r1', $key->getCurve());
+
+        // this key and the above key have a few small differences.
+        // the above key has the (optional) seed for the verifiably
+        // random function whereas the following key does not.
+        // also, in the above key the cofactor (1; optional) is
+        // included whereas in the following key it is not
+        $expected = '-----BEGIN EC PRIVATE KEY-----
+MIGxAgEBBA8AuSc4BeeyYTq9rbSDuL2gdzB1AgEBMBwGByqGSM49AQIwEQIBcQYJ
+KoZIzj0BAgMCAgEJMCAEDjCIJQym58f+ZJzoWCD3BA7ovuTT4iYHRBiL4OnHIwQf
+BACdc2FvNfSrFAfXNWLBDwClKDAneVjuhNExXtMYhgIPAQAAAAAAAADZzOyKOeVv
+oSIDIAAEAULtznTLu7D6K4d4wK1bAKko0FRxV6IeZ7rT0O/+
+-----END EC PRIVATE KEY-----';
+        PKCS1::useSpecifiedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS1'));
+    }
+
+    // openssl ecparam -name sect113r1 -genkey -noout -out sect113r1.pem
+    // openssl pkcs8 -topk8 -nocrypt -in sect113r1.pem -out sect113r1-2.pem
+    // sect113r1's reduction polynomial is a trinomial
+    public function testBinaryPKCS8PrivateKey()
+    {
+        $key = new ECDSA;
+        $key->load($expected = '-----BEGIN PRIVATE KEY-----
+MFECAQAwEAYHKoZIzj0CAQYFK4EEAAQEOjA4AgEBBA8A5OuqAY8HYoFOaz9mE6mh
+IgMgAAQASF3rOTPXvH0QdRBvsrMBdLMf27yd8AWABrZTxvI=
+-----END PRIVATE KEY-----');
+        $this->assertSame('sect113r1', $key->getCurve());
+
+        PKCS8::useNamedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS8'));
+    }
+
+    // openssl ecparam -name sect113r1 -genkey -noout -out sect113r1.pem -param_enc explicit
+    // openssl pkcs8 -topk8 -nocrypt -in sect113r1.pem -out sect113r1-2.pem
+    public function testBinaryPKCS8PrivateKeySpecifiedCurve()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN PRIVATE KEY-----
+MIHdAgEAMIGbBgcqhkjOPQIBMIGPAgEBMBwGByqGSM49AQIwEQIBcQYJKoZIzj0B
+AgMCAgEJMDcEDjCIJQym58f+ZJzoWCD3BA7ovuTT4iYHRBiL4OnHIwMVABDnI6sU
+1pbmdodWFRdW/r+Py0mpBB8EAJ1zYW819KsUB9c1YsEPAKUoMCd5WO6E0TFe0xiG
+Ag8BAAAAAAAAANnM7Io55W8CAQIEOjA4AgEBBA8AXtfDMRsRTx8snPbWHquhIgMg
+AAQA9xdWGJ6vV23+vkdq0C8BLJVg5E3amMyf/5keGa4=
+-----END PRIVATE KEY-----');
+        $this->assertSame('sect113r1', $key->getCurve());
+
+        // see testBinaryPKCS1PrivateKeySpecifiedCurve() for an
+        // explanation of the differences between the above key
+        // and the following key
+        $expected = '-----BEGIN PRIVATE KEY-----
+MIHCAgEAMIGABgcqhkjOPQIBMHUCAQEwHAYHKoZIzj0BAjARAgFxBgkqhkjOPQEC
+AwICAQkwIAQOMIglDKbnx/5knOhYIPcEDui+5NPiJgdEGIvg6ccjBB8EAJ1zYW81
+9KsUB9c1YsEPAKUoMCd5WO6E0TFe0xiGAg8BAAAAAAAAANnM7Io55W8EOjA4AgEB
+BA8AXtfDMRsRTx8snPbWHquhIgMgAAQA9xdWGJ6vV23+vkdq0C8BLJVg5E3amMyf
+/5keGa4=
+-----END PRIVATE KEY-----';
+        PKCS8::useSpecifiedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS8'));
+    }
+
+    // openssl ecparam -name sect131r1 -genkey -noout -out sect131r1.pem -param_enc explicit
+    // sect131r1's reduction polynomial is a pentanomial
+    public function testBinaryPentanomialPKCS1PrivateKey()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN EC PRIVATE KEY-----
+MIHoAgEBBBECPEK9NCISWf2riBsORoTM+6CBpzCBpAIBATAlBgcqhkjOPQECMBoC
+AgCDBgkqhkjOPQECAwMwCQIBAgIBAwIBCDA9BBEHoRsJp2tWIURBj/P/jCVwuAQR
+AhfAVhCIS2O5xscpFnj500EDFQBNaW5naHVhUXWYW9OtutohtDqX4gQjBACBuvkf
+35gzxA+cGBNDY4OZB4xufqOMAB9zyBNLG0754VACEQQAAAAAAAAAAjEjlTqUZLVN
+AgECoSYDJAAEBEIolGjo5lnsYqNagqYPOaEGOglkllDO2aWPtB6n+x/WXw==
+-----END EC PRIVATE KEY-----');
+        $this->assertSame('sect131r1', $key->getCurve());
+
+        // see testBinaryPKCS1PrivateKeySpecifiedCurve() for an
+        // explanation of the differences between the above key
+        // and the following key
+        $expected = '-----BEGIN EC PRIVATE KEY-----
+MIHOAgEBBBECPEK9NCISWf2riBsORoTM+6CBjTCBigIBATAlBgcqhkjOPQECMBoC
+AgCDBgkqhkjOPQECAwMwCQIBAgIBAwIBCDAmBBEHoRsJp2tWIURBj/P/jCVwuAQR
+AhfAVhCIS2O5xscpFnj500EEIwQAgbr5H9+YM8QPnBgTQ2ODmQeMbn6jjAAfc8gT
+SxtO+eFQAhEEAAAAAAAAAAIxI5U6lGS1TaEmAyQABARCKJRo6OZZ7GKjWoKmDzmh
+BjoJZJZQztmlj7Qep/sf1l8=
+-----END EC PRIVATE KEY-----';
+        PKCS1::useSpecifiedCurve();
+        $this->assertSame($expected, $key->getPrivateKey('PKCS1'));
+    }
+
+    // from https://tools.ietf.org/html/draft-ietf-curdle-pkix-07#section-10.1
+    public function testEd25519PublicKey()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN PUBLIC KEY-----
+MCowBQYDK2VwAyEAGb9ECWmEzf6FQbrBZ9w7lshQhqowtrbLDFw4rXAxZuE=
+-----END PUBLIC KEY-----');
+        $this->assertSame('Ed25519', $key->getCurve());
+
+        // in the above key AlgorithmIdentifier has a single "child". in the
+        // following key it has two. The second one is ("optional") NULL.
+        // https://security.stackexchange.com/q/110330/15922 elaborates on
+        // why phpseclib is encoding the NULL as opposed to omitting it.
+        $expected = '-----BEGIN PUBLIC KEY-----
+MCwwBwYDK2VwBQADIQC/RAlphM3+hUG6wWfcO5bIUIaqMLa2ywxcOK1wMWZhgA==
+-----END PUBLIC KEY-----';
+        $this->assertSame($expected, $key->getPublicKey('PKCS8'));
+    }
+
+    // from https://tools.ietf.org/html/draft-ietf-curdle-pkix-07#section-10.3
+    public function testEd25519PrivateKey()
+    {
+        // without public key (public key should be derived)
+        $key = new ECDSA;
+        $key->load('-----BEGIN PRIVATE KEY-----
+MC4CAQAwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC
+-----END PRIVATE KEY-----');
+        $this->assertSame('Ed25519', $key->getCurve());
+        $this->assertSame('Ed25519', $key->getPublicKey()->getCurve());
+
+        // with public key
+        $key = new ECDSA;
+        $key->load('-----BEGIN PRIVATE KEY-----
+MHICAQEwBQYDK2VwBCIEINTuctv5E1hK1bbY8fdp+K06/nwoy/HU++CXqI9EdVhC
+oB8wHQYKKoZIhvcNAQkJFDEPDA1DdXJkbGUgQ2hhaXJzgSEAGb9ECWmEzf6FQbrB
+Z9w7lshQhqowtrbLDFw4rXAxZuE=
+-----END PRIVATE KEY-----');
+        $this->assertSame('Ed25519', $key->getCurve());
+        $this->assertSame('Ed25519', $key->getPublicKey()->getCurve());
+
+        // the above key not only omits NULL - it also includes a
+        // unstructuredName attribute with a value of "Curdle Chairs"
+        // that the following key does not have
+        $expected = '-----BEGIN PRIVATE KEY-----
+MFICAQEwBwYDK2VwBQAEIgQg1O5y2/kTWErVttjx92n4rTr+fCjL8dT74Jeoj0R1
+WEKBIBm/RAlphM3+hUG6wWfcO5bIUIaqMLa2ywxcOK1wMWbh
+-----END PRIVATE KEY-----';
+        $this->assertSame($expected, $key->getPrivateKey('PKCS8'));
+    }
+
+    public function testPuTTYnistp256()
+    {
+        $key = new ECDSA;
+        $key->load($expected = 'PuTTY-User-Key-File-2: ecdsa-sha2-nistp256
+Encryption: none
+Comment: ecdsa-key-20181105
+Public-Lines: 3
+AAAAE2VjZHNhLXNoYTItbmlzdHAyNTYAAAAIbmlzdHAyNTYAAABBBJEXCsWA8s18
+m25MJlVE1urbXPYFi4q8oMbb2H0kE2f5WPxizsKXRmb1J68paXQizryL9fC4FTqI
+CJ1+UnaPfk0=
+Private-Lines: 1
+AAAAIQDwaPlajbXY1SxhuwsUqN1CEZ5g4adsbmJsKm+ZbUVm4g==
+Private-MAC: b85ca0eb7c612df5d18af85128821bd53faaa3ef
+');
+        $this->assertSame('nistp256', $key->getCurve());
+
+        PuTTY::setComment('ecdsa-key-20181105');
+        $this->assertSame($expected, $key->getPrivateKey('PuTTY'));
+
+        $key = new ECDSA;
+        $key->load($expected = 'ecdsa-sha2-nistp256 AAAAE2VjZHNhLXNoYTItbmlzdHAyNTYAAAAIbmlzdHAyNTYAAABBBJEXCsWA8s18m25MJlVE1urbXPYFi4q8oMbb2H0kE2f5WPxizsKXRmb1J68paXQizryL9fC4FTqICJ1+UnaPfk0= ecdsa-key-20181105');
+        $this->assertSame('nistp256', $key->getCurve());
+
+        OpenSSH::setComment('ecdsa-key-20181105');
+        $this->assertSame($expected, $key->getPublicKey('OpenSSH'));
+    }
+
+    public function testPuTTYnistp384()
+    {
+        $key = new ECDSA;
+        $key->load($expected = 'PuTTY-User-Key-File-2: ecdsa-sha2-nistp384
+Encryption: none
+Comment: ecdsa-key-20181105
+Public-Lines: 3
+AAAAE2VjZHNhLXNoYTItbmlzdHAzODQAAAAIbmlzdHAzODQAAABhBOI53wHG3Cdc
+AJZq5PXWZAEAxxsNVFQlQgOX9toWEOgqQF5LbK2nWLKRvaHMzocUXaTYZDccSS0A
+TZFPT3j1Er1LU9cu4PHpyS07v262jdzkxIvKCPcAeISuV80MC7rHog==
+Private-Lines: 2
+AAAAMQCEMkGMDg6N7bUqdvLXe0YmY4qBSi8hmAuMvU38RDoVFVmV+R4RYmMueyrX
+be9Oyus=
+Private-MAC: 97a990a3d5f6b8f268d4be9c4ab9ebfd8fa79849
+');
+        $this->assertSame('nistp384', $key->getCurve());
+
+        PuTTY::setComment('ecdsa-key-20181105');
+        $this->assertSame($expected, $key->getPrivateKey('PuTTY'));
+
+        $key = new ECDSA;
+        $key->load($expected = 'ecdsa-sha2-nistp384 AAAAE2VjZHNhLXNoYTItbmlzdHAzODQAAAAIbmlzdHAzODQAAABhBOI53wHG3CdcAJZq5PXWZAEAxxsNVFQlQgOX9toWEOgqQF5LbK2nWLKRvaHMzocUXaTYZDccSS0ATZFPT3j1Er1LU9cu4PHpyS07v262jdzkxIvKCPcAeISuV80MC7rHog== ecdsa-key-20181105');
+        $this->assertSame('nistp384', $key->getCurve());
+
+        OpenSSH::setComment('ecdsa-key-20181105');
+        $this->assertSame($expected, $key->getPublicKey('OpenSSH'));
+
+    }
+
+    public function testPuTTYnistp521()
+    {
+        $key = new ECDSA;
+        $key->load($expected = 'PuTTY-User-Key-File-2: ecdsa-sha2-nistp521
+Encryption: none
+Comment: ecdsa-key-20181105
+Public-Lines: 4
+AAAAE2VjZHNhLXNoYTItbmlzdHA1MjEAAAAIbmlzdHA1MjEAAACFBAF1Eg0MjaJw
+ooFj6HCNh4RWbvmQRY+sdczJyBdT3EaTc/6IUcCfW7w7rAeRp2CDdE9RlAVD8IuL
+qW7DJH06Xeov8wBO5G6jUqXu0rlHsOSiC6VcCxBJuWVNB1IorHnS7PX0f6HdLlIE
+me73P77drqpn5YY0XLtP6hFrF7H5XfCxpNyaJA==
+Private-Lines: 2
+AAAAQgHJl8/dIArolFymdzhagXCfd2l8UF3CQXWGVGDQ0R04nnntlyztYiVdRXXK
+r84NnzS7dJcAsR9YaUOZ69NRKNiUAQ==
+Private-MAC: 6d49ce289b85549a43d74422dd8bb3ba8798c72c
+');
+        $this->assertSame('nistp521', $key->getCurve());
+
+        PuTTY::setComment('ecdsa-key-20181105');
+        $this->assertSame($expected, $key->getPrivateKey('PuTTY'));
+
+        $key = new ECDSA;
+        $key->load($expected = 'ecdsa-sha2-nistp521 AAAAE2VjZHNhLXNoYTItbmlzdHA1MjEAAAAIbmlzdHA1MjEAAACFBAF1Eg0MjaJwooFj6HCNh4RWbvmQRY+sdczJyBdT3EaTc/6IUcCfW7w7rAeRp2CDdE9RlAVD8IuLqW7DJH06Xeov8wBO5G6jUqXu0rlHsOSiC6VcCxBJuWVNB1IorHnS7PX0f6HdLlIEme73P77drqpn5YY0XLtP6hFrF7H5XfCxpNyaJA== ecdsa-key-20181105');
+        $this->assertSame('nistp521', $key->getCurve());
+
+        OpenSSH::setComment('ecdsa-key-20181105');
+        $this->assertSame($expected, $key->getPublicKey('OpenSSH'));
+    }
+
+    public function testPuTTYed25519()
+    {
+        $key = new ECDSA;
+        $key->load($expected = 'PuTTY-User-Key-File-2: ssh-ed25519
+Encryption: none
+Comment: ed25519-key-20181105
+Public-Lines: 2
+AAAAC3NzaC1lZDI1NTE5AAAAIC6I6RyYAqtBcWXws9EDqGbhFtc5rKG4NMn/G7te
+mQtu
+Private-Lines: 1
+AAAAIAHu1uI7dxFzo/SleEI2CekXKmgqlXwOgvfaRWxiX4Jd
+Private-MAC: 8a06821a1c8b8b40fc40f876e543c4ea3fb81bb9
+');
+        $this->assertSame('Ed25519', $key->getCurve());
+
+        PuTTY::setComment('ed25519-key-20181105');
+        $this->assertSame($expected, $key->getPrivateKey('PuTTY'));
+
+        $key = new ECDSA;
+        $key->load($expected = 'ssh-ed25519 AAAAC3NzaC1lZDI1NTE5AAAAIC6I6RyYAqtBcWXws9EDqGbhFtc5rKG4NMn/G7temQtu ed25519-key-20181105');
+        $this->assertSame('Ed25519', $key->getCurve());
+
+        OpenSSH::setComment('ed25519-key-20181105');
+        $this->assertSame($expected, $key->getPublicKey('OpenSSH'));
+    }
+
+    public function testlibsodium()
+    {
+        if (!function_exists('sodium_crypto_sign_keypair')) {
+            self::markTestSkipped('libsodium extension is not available.');
+        }
+
+        $kp = sodium_crypto_sign_keypair();
+
+        $key = new ECDSA;
+        $key->load($expected = sodium_crypto_sign_secretkey($kp));
+        $this->assertSame('Ed25519', $key->getCurve());
+        $this->assertSame($expected, $key->getPrivateKey('libsodium'));
+
+        $key = new ECDSA;
+        $key->load($expected = sodium_crypto_sign_publickey($kp));
+        $this->assertSame('Ed25519', $key->getCurve());
+        $this->assertSame($expected, $key->getPublicKey('libsodium'));
+    }
+
+    // ssh-keygen -t ed25519
+    public function testOpenSSHPrivateKey()
+    {
+        $key = new ECDSA;
+        $key->load('-----BEGIN OPENSSH PRIVATE KEY-----
+b3BlbnNzaC1rZXktdjEAAAAABG5vbmUAAAAEbm9uZQAAAAAAAAABAAAAMwAAAAtzc2gtZW
+QyNTUxOQAAACCpm7dS1/WDTW+uuhp2+aFLPKaJle6+oJqDGLXhlQAX4AAAAJg8TmN5PE5j
+eQAAAAtzc2gtZWQyNTUxOQAAACCpm7dS1/WDTW+uuhp2+aFLPKaJle6+oJqDGLXhlQAX4A
+AAAEDltCTSbrr42IS4hhkS6ly0W2XItRQwxjLT+03bIyA+V6mbt1LX9YNNb666Gnb5oUs8
+pomV7r6gmoMYteGVABfgAAAAD3ZhZ3JhbnRAdmFncmFudAECAwQFBg==
+-----END OPENSSH PRIVATE KEY-----');
+        $this->assertSame('Ed25519', $key->getCurve());
+
+        // testing this key is a little difficult because of this format's
+        // two back to back checkint fields. both fields correspond to the
+        // same randomly generated number. ostensibly this let's you verify
+        // successful decryption of encrypted keys but phpseclib doesn't
+        // support encrypted keys
+        // none-the-less, because of the randomized component we can't easily
+        // see if the key string is equal to another known string
+        $key2 = new ECDSA;
+        $key2->load($key->getPrivateKey('OpenSSH'));
+        $this->assertSame('Ed25519', $key2->getCurve());
+    }
+
+    // from https://www.w3.org/TR/xmldsig-core/#sec-RFC4050Compat
+    public function testXMLKey()
+    {
+        $key = new ECDSA;
+        $key->load($orig = '<ECDSAKeyValue xmlns="http://www.w3.org/2001/04/xmldsig-more#">
+<DomainParameters>
+  <NamedCurve URN="urn:oid:1.2.840.10045.3.1.7" />
+</DomainParameters>
+<PublicKey>
+  <X Value="58511060653801744393249179046482833320204931884267326155134056258624064349885" />
+  <Y Value="102403352136827775240910267217779508359028642524881540878079119895764161434936" />
+</PublicKey>
+</ECDSAKeyValue>');
+        $this->assertSame('nistp256', $key->getCurve());
+
+        XML::enableRFC4050Syntax();
+
+        $dom = new DOMDocument();
+        $dom->preserveWhiteSpace = false;
+        $dom->loadXML($orig);
+        $expected = $dom->C14N();
+
+        //$dom = new DOMDocument();
+        //$dom->preserveWhiteSpace = false;
+        $dom->loadXML($key->getPublicKey('XML'));
+        $actual = $dom->C14N();
+
+        $this->assertSame($expected, $actual);
+    }
+
+    public static function assertSame($expected, $actual, $message = '')
+    {
+        $expected = str_replace("\r\n", "\n", $expected);
+        $actual = str_replace("\r\n", "\n", $actual);
+        return parent::assertSame($expected, $actual, $message);
+    }
+}
diff --git a/tests/Unit/Crypt/RSA/CreateKeyTest.php b/tests/Unit/Crypt/RSA/CreateKeyTest.php
index 20107991..761ed4e5 100644
--- a/tests/Unit/Crypt/RSA/CreateKeyTest.php
+++ b/tests/Unit/Crypt/RSA/CreateKeyTest.php
@@ -38,7 +38,7 @@ class Unit_Crypt_RSA_CreateKeyTest extends PhpseclibTestCase
 
     public function testMultiPrime()
     {
-        RSA::setPreferredEngine(RSA::ENGINE_INTERNAL);
+        RSA::useInternalEngine();
         RSA::setSmallestPrime(256);
         extract(RSA::createKey(1024));
         $this->assertInstanceOf('\phpseclib\Crypt\RSA', $privatekey);
@@ -62,6 +62,6 @@ class Unit_Crypt_RSA_CreateKeyTest extends PhpseclibTestCase
         $rsa->load($rsa->getPublicKey());
         $this->assertTrue($rsa->verify('zzz', $signature));
 
-        RSA::setPreferredEngine(RSA::ENGINE_OPENSSL);
+        RSA::useBestEngine();
     }
 }
diff --git a/tests/Unit/Crypt/RSA/LoadKeyTest.php b/tests/Unit/Crypt/RSA/LoadKeyTest.php
index c4ea67c4..200145c7 100644
--- a/tests/Unit/Crypt/RSA/LoadKeyTest.php
+++ b/tests/Unit/Crypt/RSA/LoadKeyTest.php
@@ -9,10 +9,17 @@ use phpseclib\Crypt\RSA;
 use phpseclib\Crypt\RSA\Keys\PKCS1;
 use phpseclib\Crypt\RSA\Keys\PKCS8;
 use phpseclib\Crypt\RSA\Keys\PuTTY;
+use phpseclib\Crypt\RSA\Keys\OpenSSH;
 use phpseclib\Math\BigInteger;
 
 class Unit_Crypt_RSA_LoadKeyTest extends PhpseclibTestCase
 {
+    public static function setUpBeforeClass()
+    {
+        PuTTY::setComment('phpseclib-generated-key');
+        OpenSSH::setComment('phpseclib-generated-key');
+    }
+
     public function testBadKey()
     {
         $rsa = new RSA();
@@ -208,7 +215,7 @@ Ao8eayMp6FcvNucIpUndo1X8dKMv3Y26ZQIDAQAB
 -----END RSA PUBLIC KEY-----';
 
         $this->assertTrue($rsa->load($key));
-        $this->assertInternalType('string', $rsa->getPublicKey());
+        $this->assertInstanceOf(RSA::class, $rsa->getPublicKey());
         $this->assertFalse($rsa->getPrivateKey());
     }
 
@@ -227,7 +234,7 @@ ZQIDAQAB
 -----END PUBLIC KEY-----';
 
         $this->assertTrue($rsa->load($key));
-        $this->assertInternalType('string', $rsa->getPublicKey());
+        $this->assertInstanceOf(RSA::class, $rsa->getPublicKey());
         $this->assertFalse($rsa->getPrivateKey());
     }
 
@@ -241,7 +248,7 @@ ZQIDAQAB
                'phpseclib-generated-key';
 
         $this->assertTrue($rsa->load($key));
-        $this->assertInternalType('string', $rsa->getPublicKey());
+        $this->assertInstanceOf(RSA::class, $rsa->getPublicKey());
         $this->assertFalse($rsa->getPrivateKey());
     }
 
@@ -393,6 +400,7 @@ Private-MAC: 03e2cb74e1d67652fbad063d2ed0478f31bdf256
         $rsa->setPrivateKeyFormat('PuTTY');
         $key2 = (string) $rsa;
 
+        OpenSSH::setComment('ecdsa-key-20181105');
         $this->assertSame($key, $key2);
     }
 
@@ -936,7 +944,7 @@ Ao8eayMp6FcvNucIpUndo1X8dKMv3Y26ZQIDAQAB
 -----END RSA PUBLIC KEY-----';
 
         $this->assertTrue($rsa->load($key));
-        $this->assertInternalType('string', $rsa->getPublicKey());
+        $this->assertInstanceOf(RSA::class, $rsa->getPublicKey());
         $this->assertFalse($rsa->load('zzz'));
         $this->assertFalse($rsa->getPublicKey());
     }
@@ -958,6 +966,6 @@ Ao8eayMp6FcvNucIpUndo1X8dKMv3Y26ZQIDAQAB
 </RSAKeyValue>';
 
         $this->assertTrue($rsa->load($key));
-        $this->assertInternalType('string', $rsa->getPublicKey());
+        $this->assertInstanceOf(RSA::class, $rsa->getPublicKey());
     }
 }