diff --git a/phpseclib/Math/BigInteger.php b/phpseclib/Math/BigInteger.php
index 1ed9e216..652d0b18 100644
--- a/phpseclib/Math/BigInteger.php
+++ b/phpseclib/Math/BigInteger.php
@@ -3048,19 +3048,31 @@ class BigInteger
     /**
      * Generate a random number
      *
-     * @param optional Integer $min
-     * @param optional Integer $max
+     * Returns a random number between $min and $max where $min and $max
+     * can be defined using one of the two methods:
+     *
+     * $min->random($max)
+     * $max->random($min)
+     *
+     * @param \phpseclib\Math\BigInteger $arg1
+     * @param optional \phpseclib\Math\BigInteger $arg2
      * @return \phpseclib\Math\BigInteger
      * @access public
+     * @internal The API for creating random numbers used to be $a->random($min, $max), where $a was a BigInteger object.
+     *           That method is still supported for BC purposes.
      */
-    function random($min = false, $max = false)
+    function random($arg1, $arg2 = false)
     {
-        if ($min === false) {
-            $min = new static(0);
+        if ($arg1 === false) {
+            return false;
         }
 
-        if ($max === false) {
-            $max = new static(0x7FFFFFFF);
+        if ($arg2 === false) {
+            $max = $arg1;
+            $min = $this;
+        } else {
+            $min = $arg1;
+            $max = $arg2;
         }
 
         $compare = $max->compare($min);
@@ -3123,21 +3135,25 @@ class BigInteger
      * If there's not a prime within the given range, false will be returned.  If more than $timeout seconds have elapsed,
      * give up and return false.
      *
-     * @param optional Integer $min
-     * @param optional Integer $max
+     * @param \phpseclib\Math\BigInteger $arg1
+     * @param optional \phpseclib\Math\BigInteger $arg2
      * @param optional Integer $timeout
-     * @return \phpseclib\Math\BigInteger
+     * @return Mixed
      * @access public
      * @internal See {@link http://www.cacr.math.uwaterloo.ca/hac/about/chap4.pdf#page=15 HAC 4.44}.
      */
-    function randomPrime($min = false, $max = false, $timeout = false)
+    function randomPrime($arg1, $arg2 = false, $timeout = false)
     {
-        if ($min === false) {
-            $min = new static(0);
+        if ($arg1 === false) {
+            return false;
         }
 
-        if ($max === false) {
-            $max = new static(0x7FFFFFFF);
+        if ($arg2 === false) {
+            $max = $arg1;
+            $min = $this;
+        } else {
+            $min = $arg1;
+            $max = $arg2;
         }
 
         $compare = $max->compare($min);
@@ -3249,7 +3265,7 @@ class BigInteger
      * $t parameter is distributability.  BigInteger::randomPrime() can be distributed across multiple pageloads
      * on a website instead of just one.
      *
-     * @param optional Integer $t
+     * @param optional \phpseclib\Math\BigInteger $t
      * @return Boolean
      * @access public
      * @internal Uses the
diff --git a/tests/Unit/Math/BigInteger/TestCase.php b/tests/Unit/Math/BigInteger/TestCase.php
index 69459ca2..b0947667 100644
--- a/tests/Unit/Math/BigInteger/TestCase.php
+++ b/tests/Unit/Math/BigInteger/TestCase.php
@@ -266,6 +266,34 @@ abstract class Unit_Math_BigInteger_TestCase extends PhpseclibTestCase
         $this->assertSame('18446744073709551616', (string) $y);
     }
 
+    public function testRandomTwoArgument()
+    {
+        $min = $this->getInstance(0);
+        $max = $this->getInstance('18446744073709551616');
+
+        $rand1 = $min->random($min, $max);
+        // technically $rand1 can equal $min but with the $min and $max we've
+        // chosen it's just not that likely
+        $this->assertTrue($rand1->compare($min) > 0);
+        $this->assertTrue($rand1->compare($max) < 0);
+    }
+
+    public function testRandomOneArgument()
+    {
+        $min = $this->getInstance(0);
+        $max = $this->getInstance('18446744073709551616');
+
+        $rand1 = $min->random($max);
+        $this->assertTrue($rand1->compare($min) > 0);
+        $this->assertTrue($rand1->compare($max) < 0);
+
+        $rand2 = $max->random($min);
+        $this->assertTrue($rand2->compare($min) > 0);
+        $this->assertTrue($rand2->compare($max) < 0);
+
+        $this->assertFalse($rand1->equals($rand2));
+    }
+
     /**
     * @group github279
     */