diff --git a/phpseclib/Crypt/Random.php b/phpseclib/Crypt/Random.php
index bb968374..964bd2e8 100644
--- a/phpseclib/Crypt/Random.php
+++ b/phpseclib/Crypt/Random.php
@@ -68,9 +68,8 @@ if (!function_exists('crypt_random_string')) {
     function crypt_random_string($length)
     {
         if (CRYPT_RANDOM_IS_WINDOWS) {
-            // method 1. prior to PHP 5.3 this would call rand() on windows hence the function_exists('class_alias') call.
-            // ie. class_alias is a function that was introduced in PHP 5.3
-            if (function_exists('mcrypt_create_iv') && function_exists('class_alias')) {
+            // method 1. prior to PHP 5.3, mcrypt_create_iv() would call rand() on windows
+            if (extension_loaded('mcrypt') && version_compare(PHP_VERSION, '5.3.0', '>=')) {
                 return mcrypt_create_iv($length);
             }
             // method 2. openssl_random_pseudo_bytes was introduced in PHP 5.3.0 but prior to PHP 5.3.4 there was,
@@ -86,12 +85,12 @@ if (!function_exists('crypt_random_string')) {
             // https://github.com/php/php-src/blob/7014a0eb6d1611151a286c0ff4f2238f92c120d6/win32/winutil.c#L80
             //
             // we're calling it, all the same, in the off chance that the mcrypt extension is not available
-            if (function_exists('openssl_random_pseudo_bytes') && version_compare(PHP_VERSION, '5.3.4', '>=')) {
+            if (extension_loaded('openssl') && version_compare(PHP_VERSION, '5.3.4', '>=')) {
                 return openssl_random_pseudo_bytes($length);
             }
         } else {
             // method 1. the fastest
-            if (function_exists('openssl_random_pseudo_bytes')) {
+            if (extension_loaded('openssl') && version_compare(PHP_VERSION, '5.3.0', '>=')) {
                 return openssl_random_pseudo_bytes($length);
             }
             // method 2
@@ -109,7 +108,7 @@ if (!function_exists('crypt_random_string')) {
             // surprisingly slower than method 2. maybe that's because mcrypt_create_iv does a bunch of error checking that we're
             // not doing. regardless, this'll only be called if this PHP script couldn't open /dev/urandom due to open_basedir
             // restrictions or some such
-            if (function_exists('mcrypt_create_iv')) {
+            if (extension_loaded('mcrypt')) {
                 return mcrypt_create_iv($length, MCRYPT_DEV_URANDOM);
             }
         }
diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php
index 94362a69..b1057c88 100644
--- a/phpseclib/Math/BigInteger.php
+++ b/phpseclib/Math/BigInteger.php
@@ -266,7 +266,7 @@ class Math_BigInteger
             }
         }
 
-        if (function_exists('openssl_public_encrypt') && !defined('MATH_BIGINTEGER_OPENSSL_DISABLE') && !defined('MATH_BIGINTEGER_OPENSSL_ENABLED')) {
+        if (extension_loaded('openssl') && !defined('MATH_BIGINTEGER_OPENSSL_DISABLE') && !defined('MATH_BIGINTEGER_OPENSSL_ENABLED')) {
             // some versions of XAMPP have mismatched versions of OpenSSL which causes it not to work
             ob_start();
             @phpinfo();
@@ -3236,7 +3236,7 @@ class Math_BigInteger
         $x = $this->random($min, $max);
 
         // gmp_nextprime() requires PHP 5 >= 5.2.0 per <http://php.net/gmp-nextprime>.
-        if (MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_GMP && function_exists('gmp_nextprime')) {
+        if (MATH_BIGINTEGER_MODE == MATH_BIGINTEGER_MODE_GMP && (extension_loaded('gmp') && version_compare(PHP_VERSION, '5.2.0', '>='))) {
             $p = new Math_BigInteger();
             $p->value = gmp_nextprime($x->value);
 
diff --git a/tests/PhpseclibTestCase.php b/tests/PhpseclibTestCase.php
index 4dc28b9a..12dbb548 100644
--- a/tests/PhpseclibTestCase.php
+++ b/tests/PhpseclibTestCase.php
@@ -59,7 +59,7 @@ abstract class PhpseclibTestCase extends PHPUnit_Framework_TestCase
             $value = constant($constant);
 
             if ($value !== $expected) {
-                if (function_exists('runkit_constant_redefine')) {
+                if (extension_loaded('runkit')) {
                     if (!runkit_constant_redefine($constant, $expected)) {
                         self::markTestSkipped(sprintf(
                             "Failed to redefine constant %s to %s",
@@ -88,7 +88,7 @@ abstract class PhpseclibTestCase extends PHPUnit_Framework_TestCase
      */
     protected static function reRequireFile($filename)
     {
-        if (function_exists('runkit_import')) {
+        if (extension_loaded('runkit')) {
             $result = runkit_import(
                 $filename,
                 RUNKIT_IMPORT_FUNCTIONS |
diff --git a/tests/Unit/Math/BigInteger/InternalOpenSSLTest.php b/tests/Unit/Math/BigInteger/InternalOpenSSLTest.php
index 7f86fd63..4b297d9f 100644
--- a/tests/Unit/Math/BigInteger/InternalOpenSSLTest.php
+++ b/tests/Unit/Math/BigInteger/InternalOpenSSLTest.php
@@ -9,7 +9,7 @@ class Unit_Math_BigInteger_InternalOpenSSLTest extends Unit_Math_BigInteger_Test
 {
     public static function setUpBeforeClass()
     {
-        if (!function_exists('openssl_public_encrypt')) {
+        if (!extension_loaded('openssl')) {
             self::markTestSkipped('openssl_public_encrypt() function is not available.');
         }