diff --git a/phpseclib/Net/SSH2.php b/phpseclib/Net/SSH2.php
index 2b881ac6..c82d4d81 100644
--- a/phpseclib/Net/SSH2.php
+++ b/phpseclib/Net/SSH2.php
@@ -1170,28 +1170,29 @@ class Net_SSH2 {
             // see http://tools.ietf.org/html/rfc2409#section-6.2 and 
             // http://tools.ietf.org/html/rfc2412, appendex E
             case 'diffie-hellman-group1-sha1':
-                $p = pack('H256', 'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74' . 
-                                  '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437' . 
-                                  '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED' . 
-                                  'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF');
-                $keyLength = $keyLength < 20 ? $keyLength : 20;
-                $hash = 'sha1';
+                $prime = 'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74' . 
+                         '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437' . 
+                         '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED' . 
+                         'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE65381FFFFFFFFFFFFFFFF';
                 break;
             // see http://tools.ietf.org/html/rfc3526#section-3
             case 'diffie-hellman-group14-sha1':
-                $p = pack('H512', 'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74' . 
-                                  '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437' . 
-                                  '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED' . 
-                                  'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3DC2007CB8A163BF05' . 
-                                  '98DA48361C55D39A69163FA8FD24CF5F83655D23DCA3AD961C62F356208552BB' . 
-                                  '9ED529077096966D670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B' . 
-                                  'E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718' . 
-                                  '3995497CEA956AE515D2261898FA051015728E5A8AACAA68FFFFFFFFFFFFFFFF');
-                $keyLength = $keyLength < 20 ? $keyLength : 20;
-                $hash = 'sha1';
+                $prime = 'FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD129024E088A67CC74' . 
+                         '020BBEA63B139B22514A08798E3404DDEF9519B3CD3A431B302B0A6DF25F1437' . 
+                         '4FE1356D6D51C245E485B576625E7EC6F44C42E9A637ED6B0BFF5CB6F406B7ED' . 
+                         'EE386BFB5A899FA5AE9F24117C4B1FE649286651ECE45B3DC2007CB8A163BF05' . 
+                         '98DA48361C55D39A69163FA8FD24CF5F83655D23DCA3AD961C62F356208552BB' . 
+                         '9ED529077096966D670C354E4ABC9804F1746C08CA18217C32905E462E36CE3B' . 
+                         'E39E772C180E86039B2783A2EC07A28FB5C55DF06F4C52C9DE2BCBF695581718' . 
+                         '3995497CEA956AE515D2261898FA051015728E5A8AACAA68FFFFFFFFFFFFFFFF';
+                break;
         }
 
-        $p = new Math_BigInteger($p, 256);
+        // For both diffie-hellman-group1-sha1 and diffie-hellman-group14-sha1
+        // the generator field element is 2 (decimal) and the hash function is sha1.
+        $g = new Math_BigInteger(2);
+        $prime = new Math_BigInteger($prime, 16);
+        $kexHash = new Crypt_Hash('sha1');
         //$q = $p->bitwise_rightShift(1);
 
         /* To increase the speed of the key exchange, both client and server may
@@ -1201,14 +1202,12 @@ class Net_SSH2 {
            [VAN-OORSCHOT].
 
            -- http://tools.ietf.org/html/rfc4419#section-6.2 */
-        $q = new Math_BigInteger(1);
-        $q = $q->bitwise_leftShift(16 * $keyLength); // 2 * 8 * $keyLength
-        $q = $q->subtract(new Math_BigInteger(1));
+        $one = new Math_BigInteger(1);
+        $keyLength = min($keyLength, $kexHash->getLength());
+        $max = $one->bitwise_leftShift(16 * $keyLength)->subtract($one); // 2 * 8 * $keyLength
 
-        $g = new Math_BigInteger(2);
-        $x = new Math_BigInteger();
-        $x = $x->random(new Math_BigInteger(1), $q);
-        $e = $g->modPow($x, $p);
+        $x = $one->random($one, $max);
+        $e = $g->modPow($x, $prime);
 
         $eBytes = $e->toBytes(true);
         $data = pack('CNa*', NET_SSH2_MSG_KEXDH_INIT, strlen($eBytes), $eBytes);
@@ -1246,7 +1245,7 @@ class Net_SSH2 {
         $temp = unpack('Nlength', $this->_string_shift($this->signature, 4));
         $this->signature_format = $this->_string_shift($this->signature, $temp['length']);
 
-        $key = $f->modPow($x, $p);
+        $key = $f->modPow($x, $prime);
         $keyBytes = $key->toBytes(true);
 
         $this->exchange_hash = pack('Na*Na*Na*Na*Na*Na*Na*Na*',
@@ -1256,7 +1255,7 @@ class Net_SSH2 {
             $eBytes, strlen($fBytes), $fBytes, strlen($keyBytes), $keyBytes
         );
 
-        $this->exchange_hash = pack('H*', $hash($this->exchange_hash));
+        $this->exchange_hash = $kexHash->hash($this->exchange_hash);
 
         if ($this->session_id === false) {
             $this->session_id = $this->exchange_hash;
@@ -1455,15 +1454,15 @@ class Net_SSH2 {
             $this->encrypt->enableContinuousBuffer();
             $this->encrypt->disablePadding();
 
-            $iv = pack('H*', $hash($keyBytes . $this->exchange_hash . 'A' . $this->session_id));
+            $iv = $kexHash->hash($keyBytes . $this->exchange_hash . 'A' . $this->session_id);
             while ($this->encrypt_block_size > strlen($iv)) {
-                $iv.= pack('H*', $hash($keyBytes . $this->exchange_hash . $iv));
+                $iv.= $kexHash->hash($keyBytes . $this->exchange_hash . $iv);
             }
             $this->encrypt->setIV(substr($iv, 0, $this->encrypt_block_size));
 
-            $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'C' . $this->session_id));
+            $key = $kexHash->hash($keyBytes . $this->exchange_hash . 'C' . $this->session_id);
             while ($encryptKeyLength > strlen($key)) {
-                $key.= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
+                $key.= $kexHash->hash($keyBytes . $this->exchange_hash . $key);
             }
             $this->encrypt->setKey(substr($key, 0, $encryptKeyLength));
         }
@@ -1472,15 +1471,15 @@ class Net_SSH2 {
             $this->decrypt->enableContinuousBuffer();
             $this->decrypt->disablePadding();
 
-            $iv = pack('H*', $hash($keyBytes . $this->exchange_hash . 'B' . $this->session_id));
+            $iv = $kexHash->hash($keyBytes . $this->exchange_hash . 'B' . $this->session_id);
             while ($this->decrypt_block_size > strlen($iv)) {
-                $iv.= pack('H*', $hash($keyBytes . $this->exchange_hash . $iv));
+                $iv.= $kexHash->hash($keyBytes . $this->exchange_hash . $iv);
             }
             $this->decrypt->setIV(substr($iv, 0, $this->decrypt_block_size));
 
-            $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'D' . $this->session_id));
+            $key = $kexHash->hash($keyBytes . $this->exchange_hash . 'D' . $this->session_id);
             while ($decryptKeyLength > strlen($key)) {
-                $key.= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
+                $key.= $kexHash->hash($keyBytes . $this->exchange_hash . $key);
             }
             $this->decrypt->setKey(substr($key, 0, $decryptKeyLength));
         }
@@ -1554,15 +1553,15 @@ class Net_SSH2 {
                 $this->hmac_size = 12;
         }
 
-        $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'E' . $this->session_id));
+        $key = $kexHash->hash($keyBytes . $this->exchange_hash . 'E' . $this->session_id);
         while ($createKeyLength > strlen($key)) {
-            $key.= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
+            $key.= $kexHash->hash($keyBytes . $this->exchange_hash . $key);
         }
         $this->hmac_create->setKey(substr($key, 0, $createKeyLength));
 
-        $key = pack('H*', $hash($keyBytes . $this->exchange_hash . 'F' . $this->session_id));
+        $key = $kexHash->hash($keyBytes . $this->exchange_hash . 'F' . $this->session_id);
         while ($checkKeyLength > strlen($key)) {
-            $key.= pack('H*', $hash($keyBytes . $this->exchange_hash . $key));
+            $key.= $kexHash->hash($keyBytes . $this->exchange_hash . $key);
         }
         $this->hmac_check->setKey(substr($key, 0, $checkKeyLength));