diff --git a/phpseclib/Crypt/EC/BaseCurves/Montgomery.php b/phpseclib/Crypt/EC/BaseCurves/Montgomery.php
index 7c0daa6e..5fccb066 100644
--- a/phpseclib/Crypt/EC/BaseCurves/Montgomery.php
+++ b/phpseclib/Crypt/EC/BaseCurves/Montgomery.php
@@ -30,6 +30,7 @@ use phpseclib\Math\Common\FiniteField\Integer;
 use phpseclib\Common\Functions\Strings;
 use phpseclib\Math\PrimeField;
 use phpseclib\Math\BigInteger;
+use phpseclib\Crypt\EC\Curves\Curve25519;
 use phpseclib\Math\PrimeField\Integer as PrimeInteger;
 
 /**
@@ -202,7 +203,8 @@ class Montgomery extends Base
         $temp = $da->subtract($cb);
         $z5 = $x1->multiply($temp->multiply($temp));
         $x4 = $aa->multiply($bb);
-        $z4 = $e->multiply($bb->add($this->a24->multiply($e)));
+        $temp = static::class == Curve25519::class ? $bb : $aa;
+        $z4 = $e->multiply($temp->add($this->a24->multiply($e)));
 
         return [
             [$x4, $z4],
diff --git a/phpseclib/Crypt/EC/Curves/Curve25519.php b/phpseclib/Crypt/EC/Curves/Curve25519.php
index 2eeaf4af..0a90eb0d 100644
--- a/phpseclib/Crypt/EC/Curves/Curve25519.php
+++ b/phpseclib/Crypt/EC/Curves/Curve25519.php
@@ -36,7 +36,7 @@ class Curve25519 extends Montgomery
         );
         $this->setBasePoint(
             new BigInteger(9),
-            new BigInteger('14781619447589544791020593568409986887264606134616475288964881837755586237401', 16)
+            new BigInteger('14781619447589544791020593568409986887264606134616475288964881837755586237401')
         );
         */
     }
diff --git a/phpseclib/Crypt/EC/Curves/Curve448.php b/phpseclib/Crypt/EC/Curves/Curve448.php
new file mode 100644
index 00000000..d575cb74
--- /dev/null
+++ b/phpseclib/Crypt/EC/Curves/Curve448.php
@@ -0,0 +1,71 @@
+<?php
+
+/**
+ * Curve448
+ *
+ * PHP version 5 and 7
+ *
+ * @category  Crypt
+ * @package   EC
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2019 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ * @link      http://pear.php.net/package/Math_BigInteger
+ */
+
+namespace phpseclib\Crypt\EC\Curves;
+
+use phpseclib\Math\Common\FiniteField\Integer;
+use phpseclib\Crypt\EC\BaseCurves\Montgomery;
+use phpseclib\Math\BigInteger;
+
+class Curve448 extends Montgomery
+{
+    public function __construct()
+    {
+        // 2^448 - 2^224 - 1
+        $this->setModulo(new BigInteger(
+            'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE' .
+            'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF', 16));
+        $this->a24 = $this->factory->newInteger(new BigInteger('39081'));
+        $this->p = [$this->factory->newInteger(new BigInteger(5))];
+        // 2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d
+        $this->setOrder(new BigInteger(
+            '3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
+            '7CCA23E9C44EDB49AED63690216CC2728DC58F552378C292AB5844F3', 16));
+
+        /*
+        $this->setCoefficients(
+            new BigInteger('156326'), // a
+        );
+        $this->setBasePoint(
+            new BigInteger(5),
+            new BigInteger(
+                '355293926785568175264127502063783334808976399387714271831880898' .
+                '435169088786967410002932673765864550910142774147268105838985595290' .
+                '606362')
+        );
+        */
+    }
+
+    /**
+     * Multiply a point on the curve by a scalar
+     *
+     * Modifies the scalar as described at https://tools.ietf.org/html/rfc7748#page-8
+     *
+     * @return array
+     */
+    public function multiplyPoint(array $p, Integer $d)
+    {
+        //$r = strrev(sodium_crypto_scalarmult($d->toBytes(), strrev($p[0]->toBytes())));
+        //return [$this->factory->newInteger(new BigInteger($r, 256))];
+
+        $d = $d->toBytes();
+        $d[0] = $d[0] & "\xFC";
+        $d = strrev($d);
+        $d|= "\x80";
+        $d = $this->factory->newInteger(new BigInteger($d, 256));
+
+        return parent::multiplyPoint($p, $d);
+    }
+}
\ No newline at end of file
diff --git a/phpseclib/Crypt/EC/Formats/Keys/Curve25519Private.php b/phpseclib/Crypt/EC/Formats/Keys/MontgomeryPrivate.php
similarity index 69%
rename from phpseclib/Crypt/EC/Formats/Keys/Curve25519Private.php
rename to phpseclib/Crypt/EC/Formats/Keys/MontgomeryPrivate.php
index 79391f02..7ce0a49f 100644
--- a/phpseclib/Crypt/EC/Formats/Keys/Curve25519Private.php
+++ b/phpseclib/Crypt/EC/Formats/Keys/MontgomeryPrivate.php
@@ -1,7 +1,7 @@
 <?php
 
 /**
- * Curve25519 Private Key Handler
+ * Montgomery Private Key Handler
  *
  * "Naked" Curve25519 private keys can pretty much be any sequence of random 32x bytes so unless
  * we have a "hidden" key handler pretty much every 32 byte string will be loaded as a curve25519
@@ -23,17 +23,19 @@
 namespace phpseclib\Crypt\EC\Formats\Keys;
 
 use phpseclib\Crypt\EC\Curves\Curve25519;
+use phpseclib\Crypt\EC\Curves\Curve448;
+use phpseclib\Crypt\EC\BaseCurves\Montgomery as MontgomeryCurve;
 use phpseclib\Math\Common\FiniteField\Integer;
 use phpseclib\Math\BigInteger;
 
 /**
- * Curve25519 Private Key Handler
+ * Montgomery Curve Private Key Handler
  *
  * @package EC
  * @author  Jim Wigginton <terrafrost@php.net>
  * @access  public
  */
-abstract class Curve25519Private
+abstract class MontgomeryPrivate
 {
     /**
      * Is invisible flag
@@ -52,10 +54,19 @@ abstract class Curve25519Private
      */
     public static function load($key, $password = '')
     {
-        $curve = new Curve25519();
+        switch (strlen($key)) {
+            case 32:
+                $curve = new Curve25519;
+                break;
+            case 56:
+                $curve = new Curve448;
+                break;
+            default:
+                throw new \LengthException('The only supported lengths are 32 and 56');
+        }
 
         $components = ['curve' => $curve];
-        $components['dA'] = $components['curve']->convertInteger(new BigInteger($key, -256));
+        $components['dA'] = $components['curve']->convertInteger(new BigInteger($key, 256));
         // note that EC::getEncodedCoordinates does some additional "magic" (it does strrev on the result)
         $components['QA'] = $components['curve']->multiplyPoint($components['curve']->getBasePoint(), $components['dA']);
 
@@ -66,13 +77,13 @@ abstract class Curve25519Private
      * Convert an EC public key to the appropriate format
      *
      * @access public
-     * @param \phpseclib\Crypt\EC\Curves\Curve25519 $curve
+     * @param \phpseclib\Crypt\EC\Curves\MontgomeryCurve $curve
      * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
      * @return string
      */
-    public static function savePublicKey(Curve25519 $curve, array $publicKey)
+    public static function savePublicKey(MontgomeryCurve $curve, array $publicKey)
     {
-        return strrev($publicKey[0]->toBytes(true));
+        return strrev($publicKey[0]->toBytes());
     }
 
     /**
@@ -80,13 +91,13 @@ abstract class Curve25519Private
      *
      * @access public
      * @param \phpseclib\Math\Common\FiniteField\Integer $privateKey
-     * @param \phpseclib\Crypt\EC\Curves\Curve25519 $curve
+     * @param \phpseclib\Crypt\EC\Curves\Montgomery $curve
      * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
      * @param string $password optional
      * @return string
      */
-    public static function savePrivateKey(Integer $privateKey, Curve25519 $curve, array $publicKey, $password = '')
+    public static function savePrivateKey(Integer $privateKey, MontgomeryCurve $curve, array $publicKey, $password = '')
     {
-        return $privateKey->toBytes(true);
+        return $privateKey->toBytes();
     }
 }
diff --git a/phpseclib/Crypt/EC/Formats/Keys/Curve25519Public.php b/phpseclib/Crypt/EC/Formats/Keys/MontgomeryPublic.php
similarity index 62%
rename from phpseclib/Crypt/EC/Formats/Keys/Curve25519Public.php
rename to phpseclib/Crypt/EC/Formats/Keys/MontgomeryPublic.php
index 22828f1a..35f2b5b9 100644
--- a/phpseclib/Crypt/EC/Formats/Keys/Curve25519Public.php
+++ b/phpseclib/Crypt/EC/Formats/Keys/MontgomeryPublic.php
@@ -1,7 +1,7 @@
 <?php
 
 /**
- * Curve25519 Public Key Handler
+ * Montgomery Public Key Handler
  *
  * PHP version 5
  *
@@ -16,17 +16,19 @@
 namespace phpseclib\Crypt\EC\Formats\Keys;
 
 use phpseclib\Crypt\EC\Curves\Curve25519;
+use phpseclib\Crypt\EC\Curves\Curve448;
+use phpseclib\Crypt\EC\BaseCurves\Montgomery as MontgomeryCurve;
 use phpseclib\Math\Common\FiniteField\Integer;
 use phpseclib\Math\BigInteger;
 
 /**
- * Curve25519 Public Key Handler
+ * Montgomery Public Key Handler
  *
  * @package EC
  * @author  Jim Wigginton <terrafrost@php.net>
  * @access  public
  */
-abstract class Curve25519Public
+abstract class MontgomeryPublic
 {
     /**
      * Is invisible flag
@@ -45,10 +47,19 @@ abstract class Curve25519Public
      */
     public static function load($key, $password = '')
     {
-        $curve = new Curve25519();
+        switch (strlen($key)) {
+            case 32:
+                $curve = new Curve25519;
+                break;
+            case 56:
+                $curve = new Curve448;
+                break;
+            default:
+                throw new \LengthException('The only supported lengths are 32 and 56');
+        }
 
         $components = ['curve' => $curve];
-        $components['QA'] = [$components['curve']->convertInteger(new BigInteger(strrev($key), -256))];
+        $components['QA'] = [$components['curve']->convertInteger(new BigInteger(strrev($key), 256))];
 
         return $components;
     }
@@ -57,12 +68,12 @@ abstract class Curve25519Public
      * Convert an EC public key to the appropriate format
      *
      * @access public
-     * @param \phpseclib\Crypt\EC\Curves\Curve25519 $curve
+     * @param \phpseclib\Crypt\EC\Curves\Montgomery $curve
      * @param \phpseclib\Math\Common\FiniteField\Integer[] $publicKey
      * @return string
      */
-    public static function savePublicKey(Curve25519 $curve, array $publicKey)
+    public static function savePublicKey(MontgomeryCurve $curve, array $publicKey)
     {
-        return strrev($publicKey[0]->toBytes(true));
+        return strrev($publicKey[0]->toBytes());
     }
 }
diff --git a/phpseclib/Crypt/EC/PrivateKey.php b/phpseclib/Crypt/EC/PrivateKey.php
index e50819fa..4c22a6ed 100644
--- a/phpseclib/Crypt/EC/PrivateKey.php
+++ b/phpseclib/Crypt/EC/PrivateKey.php
@@ -235,9 +235,7 @@ class PrivateKey extends EC implements Common\PrivateKey
     {
         $format = 'PKCS8';
         if ($this->curve instanceof MontgomeryCurve) {
-            $format = $this->curve instanceof Curve25519 ?
-                'Curve25519Public' :
-                'Curve448Public';
+            $format = 'MontgomeryPublic';
         }
 
         $type = self::validatePlugin('Keys', $format, 'savePublicKey');
diff --git a/tests/Unit/Crypt/DHTest.php b/tests/Unit/Crypt/DHTest.php
index 2c90185f..951f1c33 100644
--- a/tests/Unit/Crypt/DHTest.php
+++ b/tests/Unit/Crypt/DHTest.php
@@ -153,11 +153,11 @@ Q3ADAIcv9LEmTBnSAOsCs1K9ExAmSv/T2/4+9dW28UYb+p/uV477d1wf+nCWS6VU
         $aes->setIV(substr($key, 16, 16));
 
         $encrypted =
-            $ourEphemeralPublic->toString('Curve25519Public') .
+            $ourEphemeralPublic->toString('MontgomeryPublic') .
             $aes->encrypt($plaintext);
 
         $theirPublic = substr($encrypted, 0, 32);
-        $theirPublic = EC::loadFormat('Curve25519Public', $theirPublic);
+        $theirPublic = EC::loadFormat('MontgomeryPublic', $theirPublic);
 
         $ourPrivate = $theirPrivate;
 
@@ -205,20 +205,20 @@ Q3ADAIcv9LEmTBnSAOsCs1K9ExAmSv/T2/4+9dW28UYb+p/uV477d1wf+nCWS6VU
     {
         // utilizing test vector from https://tools.ietf.org/html/rfc7748#section-6.1
 
-        $alicePrivate = EC::loadFormat('Curve25519Private', pack('H*', '77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a'));
-        $bobPrivate = EC::loadFormat('Curve25519Private', pack('H*', '5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb'));
+        $alicePrivate = EC::loadFormat('MontgomeryPrivate', pack('H*', '77076d0a7318a57d3c16c17251b26645df4c2f87ebc0992ab177fba51db92c2a'));
+        $bobPrivate = EC::loadFormat('MontgomeryPrivate', pack('H*', '5dab087e624a8a4b79e17f8b83800ee66f3bb1292618b6fd1c2f8b27ff88e0eb'));
 
         $alicePublic = $alicePrivate->getPublicKey();
         $bobPublic = $bobPrivate->getPublicKey();
 
         $this->assertSame(
             '8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a',
-            bin2hex($alicePublic->toString('Curve25519Public'))
+            bin2hex($alicePublic->toString('MontgomeryPublic'))
         );
 
         $this->assertSame(
             'de9edb7d7b7dc1b4d35b61c2ece435373f8343c85b78674dadfc7e146f882b4f',
-            bin2hex($bobPublic->toString('Curve25519Public'))
+            bin2hex($bobPublic->toString('MontgomeryPublic'))
         );
 
         $expected = pack('H*', '4a5d9d5ba4ce2de1728e3bf480350f25e07e21c947d19e3376f09b3c1e161742');
@@ -226,4 +226,41 @@ Q3ADAIcv9LEmTBnSAOsCs1K9ExAmSv/T2/4+9dW28UYb+p/uV477d1wf+nCWS6VU
         $this->assertSame($expected, DH::computeSecret($alicePrivate, $bobPublic));
         $this->assertSame($expected, DH::computeSecret($bobPrivate, $alicePublic));
     }
+
+    public function testCurve448()
+    {
+        // utilizing test vector from https://tools.ietf.org/html/rfc7748#section-6.2
+
+        $alicePrivate = EC::loadFormat('MontgomeryPrivate', pack('H*',
+            '9a8f4925d1519f5775cf46b04b5800d4ee9ee8bae8bc5565d498c28d' .
+            'd9c9baf574a9419744897391006382a6f127ab1d9ac2d8c0a598726b'
+        ));
+        $bobPrivate = EC::loadFormat('MontgomeryPrivate', pack('H*',
+            '1c306a7ac2a0e2e0990b294470cba339e6453772b075811d8fad0d1d' .
+            '6927c120bb5ee8972b0d3e21374c9c921b09d1b0366f10b65173992d'
+        ));
+
+        $alicePublic = $alicePrivate->getPublicKey();
+        $bobPublic = $bobPrivate->getPublicKey();
+
+        $this->assertSame(
+            '9b08f7cc31b7e3e67d22d5aea121074a273bd2b83de09c63faa73d2c' .
+            '22c5d9bbc836647241d953d40c5b12da88120d53177f80e532c41fa0',
+            bin2hex($alicePublic->toString('MontgomeryPublic'))
+        );
+
+        $this->assertSame(
+            '3eb7a829b0cd20f5bcfc0b599b6feccf6da4627107bdb0d4f345b430' .
+            '27d8b972fc3e34fb4232a13ca706dcb57aec3dae07bdc1c67bf33609',
+            bin2hex($bobPublic->toString('MontgomeryPublic'))
+        );
+
+        $expected = pack('H*',
+            '07fff4181ac6cc95ec1c16a94a0f74d12da232ce40a77552281d282b' .
+            'b60c0b56fd2464c335543936521c24403085d59a449a5037514a879d'
+        );
+
+        $this->assertSame($expected, DH::computeSecret($alicePrivate, $bobPublic));
+        $this->assertSame($expected, DH::computeSecret($bobPrivate, $alicePublic));
+    }
 }