examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/Formats/Keys/XML.php

+<?php
+
+/**
+ * XML Formatted DSA Key Handler
+ *
+ * While XKMS defines a private key format for RSA it does not do so for DSA. Quoting that standard:
+ *
+ * "[XKMS] does not specify private key parameters for the DSA signature algorithm since the algorithm only
+ *  supports signature modes and so the application of server generated keys and key recovery is of limited
+ *  value"
+ *
+ * PHP version 5
+ *
+ * @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 phpseclib3\Crypt\DSA\Formats\Keys;
+
+use phpseclib3\Common\Functions\Strings;
+use phpseclib3\Exception\BadConfigurationException;
+use phpseclib3\Math\BigInteger;
+
+/**
+ * XML Formatted DSA Key Handler
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class XML
+{
+    /**
+     * Break a public or private key down into its constituent components
+     *
+     * @param string $key
+     * @param string $password optional
+     * @return array
+     */
+    public static function load($key, $password = '')
+    {
+        if (!Strings::is_stringable($key)) {
+            throw new \UnexpectedValueException('Key should be a string - not a ' . gettype($key));
+        }
+
+        if (!class_exists('DOMDocument')) {
+            throw new BadConfigurationException('The dom extension is not setup correctly on this system');
+        }
+
+        $use_errors = libxml_use_internal_errors(true);
+
+        $dom = new \DOMDocument();
+        if (substr($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);
+        $keys = ['p', 'q', 'g', 'y', 'j', 'seed', 'pgencounter'];
+        foreach ($keys as $key) {
+            // $dom->getElementsByTagName($key) is case-sensitive
+            $temp = $xpath->query("//*[translate(local-name(), 'ABCDEFGHIJKLMNOPQRSTUVWXYZ','abcdefghijklmnopqrstuvwxyz')='$key']");
+            if (!$temp->length) {
+                continue;
+            }
+            $value = new BigInteger(Strings::base64_decode($temp->item(0)->nodeValue), 256);
+            switch ($key) {
+                case 'p': // a prime modulus meeting the [DSS] requirements
+                    // Parameters P, Q, and G can be public and common to a group of users. They might be known
+                    // from application context. As such, they are optional but P and Q must either both appear
+                    // or both be absent
+                    $components['p'] = $value;
+                    break;
+                case 'q': // an integer in the range 2**159 < Q < 2**160 which is a prime divisor of P-1
+                    $components['q'] = $value;
+                    break;
+                case 'g': // an integer with certain properties with respect to P and Q
+                    $components['g'] = $value;
+                    break;
+                case 'y': // G**X mod P (where X is part of the private key and not made public)
+                    $components['y'] = $value;
+                    // the remaining options do not do anything
+                case 'j': // (P - 1) / Q
+                    // Parameter J is available for inclusion solely for efficiency as it is calculatable from
+                    // P and Q
+                case 'seed': // a DSA prime generation seed
+                    // Parameters seed and pgenCounter are used in the DSA prime number generation algorithm
+                    // specified in [DSS]. As such, they are optional but must either both be present or both
+                    // be absent
+                case 'pgencounter': // a DSA prime generation counter
+            }
+        }
+
+        libxml_use_internal_errors($use_errors);
+
+        if (!isset($components['y'])) {
+            throw new \UnexpectedValueException('Key is missing y component');
+        }
+
+        switch (true) {
+            case !isset($components['p']):
+            case !isset($components['q']):
+            case !isset($components['g']):
+                return ['y' => $components['y']];
+        }
+
+        return $components;
+    }
+
+    /**
+     * Convert a public key to the appropriate format
+     *
+     * See https://www.w3.org/TR/xmldsig-core/#sec-DSAKeyValue
+     *
+     * @param \phpseclib3\Math\BigInteger $p
+     * @param \phpseclib3\Math\BigInteger $q
+     * @param \phpseclib3\Math\BigInteger $g
+     * @param \phpseclib3\Math\BigInteger $y
+     * @return string
+     */
+    public static function savePublicKey(BigInteger $p, BigInteger $q, BigInteger $g, BigInteger $y)
+    {
+        return "<DSAKeyValue>\r\n" .
+               '  <P>' . Strings::base64_encode($p->toBytes()) . "</P>\r\n" .
+               '  <Q>' . Strings::base64_encode($q->toBytes()) . "</Q>\r\n" .
+               '  <G>' . Strings::base64_encode($g->toBytes()) . "</G>\r\n" .
+               '  <Y>' . Strings::base64_encode($y->toBytes()) . "</Y>\r\n" .
+               '</DSAKeyValue>';
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/Formats/Signature/ASN1.php

+<?php
+
+/**
+ * ASN1 Signature Handler
+ *
+ * PHP version 5
+ *
+ * Handles signatures in the format described in
+ * https://tools.ietf.org/html/rfc3279#section-2.2.2
+ *
+ * @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 phpseclib3\Crypt\DSA\Formats\Signature;
+
+use phpseclib3\File\ASN1 as Encoder;
+use phpseclib3\File\ASN1\Maps;
+use phpseclib3\Math\BigInteger;
+
+/**
+ * ASN1 Signature Handler
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class ASN1
+{
+    /**
+     * Loads a signature
+     *
+     * @param string $sig
+     * @return array|bool
+     */
+    public static function load($sig)
+    {
+        if (!is_string($sig)) {
+            return false;
+        }
+
+        $decoded = Encoder::decodeBER($sig);
+        if (empty($decoded)) {
+            return false;
+        }
+        $components = Encoder::asn1map($decoded[0], Maps\DssSigValue::MAP);
+
+        return $components;
+    }
+
+    /**
+     * Returns a signature in the appropriate format
+     *
+     * @param \phpseclib3\Math\BigInteger $r
+     * @param \phpseclib3\Math\BigInteger $s
+     * @return string
+     */
+    public static function save(BigInteger $r, BigInteger $s)
+    {
+        return Encoder::encodeDER(compact('r', 's'), Maps\DssSigValue::MAP);
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/Formats/Signature/Raw.php

+<?php
+
+/**
+ * Raw DSA Signature Handler
+ *
+ * PHP version 5
+ *
+ * @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 phpseclib3\Crypt\DSA\Formats\Signature;
+
+use phpseclib3\Crypt\Common\Formats\Signature\Raw as Progenitor;
+
+/**
+ * Raw DSA Signature Handler
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class Raw extends Progenitor
+{
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/Formats/Signature/SSH2.php

+<?php
+
+/**
+ * SSH2 Signature Handler
+ *
+ * PHP version 5
+ *
+ * Handles signatures in the format used by SSH2
+ *
+ * @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 phpseclib3\Crypt\DSA\Formats\Signature;
+
+use phpseclib3\Common\Functions\Strings;
+use phpseclib3\Math\BigInteger;
+
+/**
+ * SSH2 Signature Handler
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class SSH2
+{
+    /**
+     * Loads a signature
+     *
+     * @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) = $result;
+        if ($type != 'ssh-dss' || strlen($blob) != 40) {
+            return false;
+        }
+
+        return [
+            'r' => new BigInteger(substr($blob, 0, 20), 256),
+            's' => new BigInteger(substr($blob, 20), 256)
+        ];
+    }
+
+    /**
+     * Returns a signature in the appropriate format
+     *
+     * @param \phpseclib3\Math\BigInteger $r
+     * @param \phpseclib3\Math\BigInteger $s
+     * @return string
+     */
+    public static function save(BigInteger $r, BigInteger $s)
+    {
+        if ($r->getLength() > 160 || $s->getLength() > 160) {
+            return false;
+        }
+        return Strings::packSSH2(
+            'ss',
+            'ssh-dss',
+            str_pad($r->toBytes(), 20, "\0", STR_PAD_LEFT) .
+            str_pad($s->toBytes(), 20, "\0", STR_PAD_LEFT)
+        );
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/Parameters.php

+<?php
+
+/**
+ * DSA Parameters
+ *
+ * @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 phpseclib3\Crypt\DSA;
+
+use phpseclib3\Crypt\DSA;
+
+/**
+ * DSA Parameters
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class Parameters extends DSA
+{
+    /**
+     * Returns the parameters
+     *
+     * @param string $type
+     * @param array $options optional
+     * @return string
+     */
+    public function toString($type = 'PKCS1', array $options = [])
+    {
+        $type = self::validatePlugin('Keys', 'PKCS1', 'saveParameters');
+
+        return $type::saveParameters($this->p, $this->q, $this->g, $options);
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/PrivateKey.php

+<?php
+
+/**
+ * DSA Private Key
+ *
+ * @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 phpseclib3\Crypt\DSA;
+
+use phpseclib3\Crypt\Common;
+use phpseclib3\Crypt\DSA;
+use phpseclib3\Crypt\DSA\Formats\Signature\ASN1 as ASN1Signature;
+use phpseclib3\Math\BigInteger;
+
+/**
+ * DSA Private Key
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class PrivateKey extends DSA implements Common\PrivateKey
+{
+    use Common\Traits\PasswordProtected;
+
+    /**
+     * DSA secret exponent x
+     *
+     * @var \phpseclib3\Math\BigInteger
+     */
+    protected $x;
+
+    /**
+     * Returns the public key
+     *
+     * If you do "openssl rsa -in private.rsa -pubout -outform PEM" you get a PKCS8 formatted key
+     * that contains a publicKeyAlgorithm AlgorithmIdentifier and a publicKey BIT STRING.
+     * An AlgorithmIdentifier contains an OID and a parameters field. With RSA public keys this
+     * parameters field is NULL. With DSA PKCS8 public keys it is not - it contains the p, q and g
+     * variables. The publicKey BIT STRING contains, simply, the y variable. This can be verified
+     * by getting a DSA PKCS8 public key:
+     *
+     * "openssl dsa -in private.dsa -pubout -outform PEM"
+     *
+     * ie. just swap out rsa with dsa in the rsa command above.
+     *
+     * A PKCS1 public key corresponds to the publicKey portion of the PKCS8 key. In the case of RSA
+     * the publicKey portion /is/ the key. In the case of DSA it is not. You cannot verify a signature
+     * without the parameters and the PKCS1 DSA public key format does not include the parameters.
+     *
+     * @see self::getPrivateKey()
+     * @return mixed
+     */
+    public function getPublicKey()
+    {
+        $type = self::validatePlugin('Keys', 'PKCS8', 'savePublicKey');
+
+        if (!isset($this->y)) {
+            $this->y = $this->g->powMod($this->x, $this->p);
+        }
+
+        $key = $type::savePublicKey($this->p, $this->q, $this->g, $this->y);
+
+        return DSA::loadFormat('PKCS8', $key)
+            ->withHash($this->hash->getHash())
+            ->withSignatureFormat($this->shortFormat);
+    }
+
+    /**
+     * Create a signature
+     *
+     * @see self::verify()
+     * @param string $message
+     * @return mixed
+     */
+    public function sign($message)
+    {
+        $format = $this->sigFormat;
+
+        if (self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods())) {
+            $signature = '';
+            $result = openssl_sign($message, $signature, $this->toString('PKCS8'), $this->hash->getHash());
+
+            if ($result) {
+                if ($this->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);
+            list(, $r) = $r->divide($this->q);
+            if ($r->equals(self::$zero)) {
+                continue;
+            }
+            $kinv = $k->modInverse($this->q);
+            $temp = $h->add($this->x->multiply($r));
+            $temp = $kinv->multiply($temp);
+            list(, $s) = $temp->divide($this->q);
+            if (!$s->equals(self::$zero)) {
+                break;
+            }
+        }
+
+        // the following is an RFC6979 compliant implementation of deterministic DSA
+        // 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
+        /*
+        $h1 = $this->hash->hash($message);
+        $k = $this->computek($h1);
+        $r = $this->g->powMod($k, $this->p);
+        list(, $r) = $r->divide($this->q);
+        $kinv = $k->modInverse($this->q);
+        $h1 = $this->bits2int($h1);
+        $temp = $h1->add($this->x->multiply($r));
+        $temp = $kinv->multiply($temp);
+        list(, $s) = $temp->divide($this->q);
+        */
+
+        return $format::save($r, $s);
+    }
+
+    /**
+     * Returns the private key
+     *
+     * @param string $type
+     * @param array $options optional
+     * @return string
+     */
+    public function toString($type, array $options = [])
+    {
+        $type = self::validatePlugin('Keys', $type, 'savePrivateKey');
+
+        if (!isset($this->y)) {
+            $this->y = $this->g->powMod($this->x, $this->p);
+        }
+
+        return $type::savePrivateKey($this->p, $this->q, $this->g, $this->y, $this->x, $this->password, $options);
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/DSA/PublicKey.php

+<?php
+
+/**
+ * DSA Public Key
+ *
+ * @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 phpseclib3\Crypt\DSA;
+
+use phpseclib3\Crypt\Common;
+use phpseclib3\Crypt\DSA;
+use phpseclib3\Crypt\DSA\Formats\Signature\ASN1 as ASN1Signature;
+
+/**
+ * DSA Public Key
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class PublicKey extends DSA implements Common\PublicKey
+{
+    use Common\Traits\Fingerprint;
+
+    /**
+     * Verify a signature
+     *
+     * @see self::verify()
+     * @param string $message
+     * @param string $signature
+     * @return mixed
+     */
+    public function verify($message, $signature)
+    {
+        $format = $this->sigFormat;
+
+        $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())) {
+            $sig = $format != 'ASN1' ? ASN1Signature::save($r, $s) : $signature;
+
+            $result = openssl_verify($message, $sig, $this->toString('PKCS8'), $this->hash->getHash());
+
+            if ($result != -1) {
+                return (bool) $result;
+            }
+        }
+
+        $q_1 = $this->q->subtract(self::$one);
+        if (!$r->between(self::$one, $q_1) || !$s->between(self::$one, $q_1)) {
+            return false;
+        }
+
+        $w = $s->modInverse($this->q);
+        $h = $this->hash->hash($message);
+        $h = $this->bits2int($h);
+        list(, $u1) = $h->multiply($w)->divide($this->q);
+        list(, $u2) = $r->multiply($w)->divide($this->q);
+        $v1 = $this->g->powMod($u1, $this->p);
+        $v2 = $this->y->powMod($u2, $this->p);
+        list(, $v) = $v1->multiply($v2)->divide($this->p);
+        list(, $v) = $v->divide($this->q);
+
+        return $v->equals($r);
+    }
+
+    /**
+     * Returns the public key
+     *
+     * @param string $type
+     * @param array $options optional
+     * @return string
+     */
+    public function toString($type, array $options = [])
+    {
+        $type = self::validatePlugin('Keys', $type, 'savePublicKey');
+
+        return $type::savePublicKey($this->p, $this->q, $this->g, $this->y, $options);
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC.php

+<?php
+
+/**
+ * Pure-PHP implementation of EC.
+ *
+ * PHP version 5
+ *
+ * Here's an example of how to create signatures and verify signatures with this library:
+ * <code>
+ * <?php
+ * include 'vendor/autoload.php';
+ *
+ * $private = \phpseclib3\Crypt\EC::createKey('secp256k1');
+ * $public = $private->getPublicKey();
+ *
+ * $plaintext = 'terrafrost';
+ *
+ * $signature = $private->sign($plaintext);
+ *
+ * echo $public->verify($plaintext, $signature) ? 'verified' : 'unverified';
+ * ?>
+ * </code>
+ *
+ * @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 phpseclib3\Crypt;
+
+use phpseclib3\Crypt\Common\AsymmetricKey;
+use phpseclib3\Crypt\EC\BaseCurves\Montgomery as MontgomeryCurve;
+use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards as TwistedEdwardsCurve;
+use phpseclib3\Crypt\EC\Curves\Curve25519;
+use phpseclib3\Crypt\EC\Curves\Ed25519;
+use phpseclib3\Crypt\EC\Curves\Ed448;
+use phpseclib3\Crypt\EC\Formats\Keys\PKCS1;
+use phpseclib3\Crypt\EC\Parameters;
+use phpseclib3\Crypt\EC\PrivateKey;
+use phpseclib3\Crypt\EC\PublicKey;
+use phpseclib3\Exception\UnsupportedAlgorithmException;
+use phpseclib3\Exception\UnsupportedCurveException;
+use phpseclib3\Exception\UnsupportedOperationException;
+use phpseclib3\File\ASN1;
+use phpseclib3\File\ASN1\Maps\ECParameters;
+use phpseclib3\Math\BigInteger;
+
+/**
+ * Pure-PHP implementation of EC.
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class EC extends AsymmetricKey
+{
+    /**
+     * Algorithm Name
+     *
+     * @var string
+     */
+    const ALGORITHM = 'EC';
+
+    /**
+     * Public Key QA
+     *
+     * @var object[]
+     */
+    protected $QA;
+
+    /**
+     * Curve
+     *
+     * @var \phpseclib3\Crypt\EC\BaseCurves\Base
+     */
+    protected $curve;
+
+    /**
+     * Signature Format
+     *
+     * @var string
+     */
+    protected $format;
+
+    /**
+     * Signature Format (Short)
+     *
+     * @var string
+     */
+    protected $shortFormat;
+
+    /**
+     * Curve Name
+     *
+     * @var string
+     */
+    private $curveName;
+
+    /**
+     * Curve Order
+     *
+     * Used for deterministic ECDSA
+     *
+     * @var \phpseclib3\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 \phpseclib3\Math\BigInteger
+     */
+    protected $x;
+
+    /**
+     * Context
+     *
+     * @var string
+     */
+    protected $context;
+
+    /**
+     * Signature Format
+     *
+     * @var string
+     */
+    protected $sigFormat;
+
+    /**
+     * Create public / private key pair.
+     *
+     * @param string $curve
+     * @return \phpseclib3\Crypt\EC\PrivateKey
+     */
+    public static function createKey($curve)
+    {
+        self::initialize_static_variables();
+
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
+        $curve = strtolower($curve);
+        if (self::$engines['libsodium'] && $curve == 'ed25519' && function_exists('sodium_crypto_sign_keypair')) {
+            $kp = sodium_crypto_sign_keypair();
+
+            $privatekey = EC::loadFormat('libsodium', sodium_crypto_sign_secretkey($kp));
+            //$publickey = EC::loadFormat('libsodium', sodium_crypto_sign_publickey($kp));
+
+            $privatekey->curveName = 'Ed25519';
+            //$publickey->curveName = $curve;
+
+            return $privatekey;
+        }
+
+        $privatekey = new PrivateKey();
+
+        $curveName = $curve;
+        if (preg_match('#(?:^curve|^ed)\d+$#', $curveName)) {
+            $curveName = ucfirst($curveName);
+        } elseif (substr($curveName, 0, 10) == 'brainpoolp') {
+            $curveName = 'brainpoolP' . substr($curveName, 10);
+        }
+        $curve = '\phpseclib3\Crypt\EC\Curves\\' . $curveName;
+
+        if (!class_exists($curve)) {
+            throw new UnsupportedCurveException('Named Curve of ' . $curveName . ' is not supported');
+        }
+
+        $reflect = new \ReflectionClass($curve);
+        $curveName = $reflect->isFinal() ?
+            $reflect->getParentClass()->getShortName() :
+            $reflect->getShortName();
+
+        $curve = new $curve();
+        if ($curve instanceof TwistedEdwardsCurve) {
+            $arr = $curve->extractSecret(Random::string($curve instanceof Ed448 ? 57 : 32));
+            $privatekey->dA = $dA = $arr['dA'];
+            $privatekey->secret = $arr['secret'];
+        } else {
+            $privatekey->dA = $dA = $curve->createRandomMultiplier();
+        }
+        if ($curve instanceof Curve25519 && self::$engines['libsodium']) {
+            //$r = pack('H*', '0900000000000000000000000000000000000000000000000000000000000000');
+            //$QA = sodium_crypto_scalarmult($dA->toBytes(), $r);
+            $QA = sodium_crypto_box_publickey_from_secretkey($dA->toBytes());
+            $privatekey->QA = [$curve->convertInteger(new BigInteger(strrev($QA), 256))];
+        } else {
+            $privatekey->QA = $curve->multiplyPoint($curve->getBasePoint(), $dA);
+        }
+        $privatekey->curve = $curve;
+
+        //$publickey = clone $privatekey;
+        //unset($publickey->dA);
+        //unset($publickey->x);
+
+        $privatekey->curveName = $curveName;
+        //$publickey->curveName = $curveName;
+
+        if ($privatekey->curve instanceof TwistedEdwardsCurve) {
+            return $privatekey->withHash($curve::HASH);
+        }
+
+        return $privatekey;
+    }
+
+    /**
+     * OnLoad Handler
+     *
+     * @return bool
+     */
+    protected static function onLoad(array $components)
+    {
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+
+        if (!isset($components['dA']) && !isset($components['QA'])) {
+            $new = new Parameters();
+            $new->curve = $components['curve'];
+            return $new;
+        }
+
+        $new = isset($components['dA']) ?
+            new PrivateKey() :
+            new PublicKey();
+        $new->curve = $components['curve'];
+        $new->QA = $components['QA'];
+
+        if (isset($components['dA'])) {
+            $new->dA = $components['dA'];
+            $new->secret = $components['secret'];
+        }
+
+        if ($new->curve instanceof TwistedEdwardsCurve) {
+            return $new->withHash($components['curve']::HASH);
+        }
+
+        return $new;
+    }
+
+    /**
+     * Constructor
+     *
+     * PublicKey and PrivateKey objects can only be created from abstract RSA class
+     */
+    protected function __construct()
+    {
+        $this->sigFormat = self::validatePlugin('Signature', 'ASN1');
+        $this->shortFormat = 'ASN1';
+
+        parent::__construct();
+    }
+
+    /**
+     * Returns the curve
+     *
+     * Returns a string if it's a named curve, an array if not
+     *
+     * @return string|array
+     */
+    public function getCurve()
+    {
+        if ($this->curveName) {
+            return $this->curveName;
+        }
+
+        if ($this->curve instanceof MontgomeryCurve) {
+            $this->curveName = $this->curve instanceof Curve25519 ? 'Curve25519' : 'Curve448';
+            return $this->curveName;
+        }
+
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            $this->curveName = $this->curve instanceof Ed25519 ? 'Ed25519' : 'Ed448';
+            return $this->curveName;
+        }
+
+        $params = $this->getParameters()->toString('PKCS8', ['namedCurve' => true]);
+        $decoded = ASN1::extractBER($params);
+        $decoded = ASN1::decodeBER($decoded);
+        $decoded = ASN1::asn1map($decoded[0], ECParameters::MAP);
+        if (isset($decoded['namedCurve'])) {
+            $this->curveName = $decoded['namedCurve'];
+            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"
+     *
+     * @return int
+     */
+    public function getLength()
+    {
+        return $this->curve->getLength();
+    }
+
+    /**
+     * Returns the current engine being used
+     *
+     * @see self::useInternalEngine()
+     * @see self::useBestEngine()
+     * @return string
+     */
+    public function getEngine()
+    {
+        if (!isset(self::$engines['PHP'])) {
+            self::useBestEngine();
+        }
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            return $this->curve instanceof Ed25519 && self::$engines['libsodium'] && !isset($this->context) ?
+                'libsodium' : 'PHP';
+        }
+
+        return self::$engines['OpenSSL'] && in_array($this->hash->getHash(), openssl_get_md_methods()) ?
+            'OpenSSL' : 'PHP';
+    }
+
+    /**
+     * Returns the public key coordinates as a string
+     *
+     * Used by ECDH
+     *
+     * @return string
+     */
+    public function getEncodedCoordinates()
+    {
+        if ($this->curve instanceof MontgomeryCurve) {
+            return strrev($this->QA[0]->toBytes(true));
+        }
+        if ($this->curve instanceof TwistedEdwardsCurve) {
+            return $this->curve->encodePoint($this->QA);
+        }
+        return "\4" . $this->QA[0]->toBytes(true) . $this->QA[1]->toBytes(true);
+    }
+
+    /**
+     * Returns the parameters
+     *
+     * @see self::getPublicKey()
+     * @param string $type optional
+     * @return mixed
+     */
+    public function getParameters($type = 'PKCS1')
+    {
+        $type = self::validatePlugin('Keys', $type, 'saveParameters');
+
+        $key = $type::saveParameters($this->curve);
+
+        return EC::load($key, 'PKCS1')
+            ->withHash($this->hash->getHash())
+            ->withSignatureFormat($this->shortFormat);
+    }
+
+    /**
+     * Determines the signature padding mode
+     *
+     * Valid values are: ASN1, SSH2, Raw
+     *
+     * @param string $format
+     */
+    public function withSignatureFormat($format)
+    {
+        if ($this->curve instanceof MontgomeryCurve) {
+            throw new UnsupportedOperationException('Montgomery Curves cannot be used to create signatures');
+        }
+
+        $new = clone $this;
+        $new->shortFormat = $format;
+        $new->sigFormat = self::validatePlugin('Signature', $format);
+        return $new;
+    }
+
+    /**
+     * Returns the signature format currently being used
+     *
+     */
+    public function getSignatureFormat()
+    {
+        return $this->shortFormat;
+    }
+
+    /**
+     * Sets the context
+     *
+     * Used by Ed25519 / Ed448.
+     *
+     * @see self::sign()
+     * @see self::verify()
+     * @param string $context optional
+     */
+    public function withContext($context = null)
+    {
+        if (!$this->curve instanceof TwistedEdwardsCurve) {
+            throw new UnsupportedCurveException('Only Ed25519 and Ed448 support contexts');
+        }
+
+        $new = clone $this;
+        if (!isset($context)) {
+            $new->context = null;
+            return $new;
+        }
+        if (!is_string($context)) {
+            throw new \InvalidArgumentException('setContext expects a string');
+        }
+        if (strlen($context) > 255) {
+            throw new \LengthException('The context is supposed to be, at most, 255 bytes long');
+        }
+        $new->context = $context;
+        return $new;
+    }
+
+    /**
+     * Returns the signature format currently being used
+     *
+     */
+    public function getContext()
+    {
+        return $this->context;
+    }
+
+    /**
+     * Determines which hashing function should be used
+     *
+     * @param string $hash
+     */
+    public function withHash($hash)
+    {
+        if ($this->curve instanceof MontgomeryCurve) {
+            throw new UnsupportedOperationException('Montgomery Curves cannot be used to create signatures');
+        }
+        if ($this->curve instanceof Ed25519 && $hash != 'sha512') {
+            throw new UnsupportedAlgorithmException('Ed25519 only supports sha512 as a hash');
+        }
+        if ($this->curve instanceof Ed448 && $hash != 'shake256-912') {
+            throw new UnsupportedAlgorithmException('Ed448 only supports shake256 with a length of 114 bytes');
+        }
+
+        return parent::withHash($hash);
+    }
+
+    /**
+     * __toString() magic method
+     *
+     * @return string
+     */
+    public function __toString()
+    {
+        if ($this->curve instanceof MontgomeryCurve) {
+            return '';
+        }
+
+        return parent::__toString();
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Base.php

+<?php
+
+/**
+ * Curve methods common to all curves
+ *
+ * PHP version 5 and 7
+ *
+ * @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 phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Math\BigInteger;
+
+/**
+ * Base
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+abstract class Base
+{
+    /**
+     * The Order
+     *
+     * @var BigInteger
+     */
+    protected $order;
+
+    /**
+     * Finite Field Integer factory
+     *
+     * @var \phpseclib3\Math\FiniteField\Integer
+     */
+    protected $factory;
+
+    /**
+     * Returns a random integer
+     *
+     * @return object
+     */
+    public function randomInteger()
+    {
+        return $this->factory->randomInteger();
+    }
+
+    /**
+     * Converts a BigInteger to a \phpseclib3\Math\FiniteField\Integer 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, BigInteger $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 BigInteger
+     */
+    public function createRandomMultiplier()
+    {
+        static $one;
+        if (!isset($one)) {
+            $one = new BigInteger(1);
+        }
+
+        return BigInteger::randomRange($one, $this->order->subtract($one));
+    }
+
+    /**
+     * Performs range check
+     */
+    public function rangeCheck(BigInteger $x)
+    {
+        static $zero;
+        if (!isset($zero)) {
+            $zero = new BigInteger();
+        }
+
+        if (!isset($this->order)) {
+            throw new \RuntimeException('setOrder needs to be called before this method');
+        }
+        if ($x->compare($this->order) > 0 || $x->compare($zero) <= 0) {
+            throw new \RangeException('x must be between 1 and the order of the curve');
+        }
+    }
+
+    /**
+     * Sets the Order
+     */
+    public function setOrder(BigInteger $order)
+    {
+        $this->order = $order;
+    }
+
+    /**
+     * Returns the Order
+     *
+     * @return \phpseclib3\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);
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Binary.php

+<?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
+ *
+ * @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 phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Math\BigInteger;
+use phpseclib3\Math\BinaryField;
+use phpseclib3\Math\BinaryField\Integer as BinaryInteger;
+
+/**
+ * Curves over y^2 + x*y = x^3 + a*x^2 + b
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class Binary extends Base
+{
+    /**
+     * Binary Field Integer factory
+     *
+     * @var \phpseclib3\Math\BinaryField
+     */
+    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 \phpseclib3\Math\BigInteger
+     */
+    public function getModulo()
+    {
+        return $this->modulo;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib3\Math\PrimeField\Integer
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib3\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 \phpseclib3\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 \phpseclib3\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (isset($p[2])) {
+            return $p;
+        }
+
+        $p[2] = clone $this->one;
+        $p['fresh'] = true;
+        return $p;
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/KoblitzPrime.php

+<?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
+ *
+ * @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 phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Math\BigInteger;
+use phpseclib3\Math\PrimeField;
+
+/**
+ * Curves over y^2 = x^3 + b
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class KoblitzPrime extends Prime
+{
+    /**
+     * Basis
+     *
+     * @var list<array{a: BigInteger, b: BigInteger}>
+     */
+    protected $basis;
+
+    /**
+     * Beta
+     *
+     * @var PrimeField\Integer
+     */
+    protected $beta;
+
+    // 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://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/curve/short.js#L219
+     *
+     * @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 $u
+     * @param BigInteger $v
+     * @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]
+        ];
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Montgomery.php

+<?php
+
+/**
+ * Curves over y^2 = x^3 + a*x + x
+ *
+ * Technically, a Montgomery curve has a coefficient for y^2 but for Curve25519 and Curve448 that
+ * coefficient is 1.
+ *
+ * Curve25519 and Curve448 do not make use of the y coordinate, which makes it unsuitable for use
+ * with ECDSA / EdDSA. A few other differences between Curve25519 and Ed25519 are discussed at
+ * https://crypto.stackexchange.com/a/43058/4520
+ *
+ * More info:
+ *
+ * https://en.wikipedia.org/wiki/Montgomery_curve
+ *
+ * PHP version 5 and 7
+ *
+ * @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 phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Crypt\EC\Curves\Curve25519;
+use phpseclib3\Math\BigInteger;
+use phpseclib3\Math\PrimeField;
+use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
+
+/**
+ * Curves over y^2 = x^3 + a*x + x
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class Montgomery extends Base
+{
+    /**
+     * Prime Field Integer factory
+     *
+     * @var \phpseclib3\Math\PrimeField
+     */
+    protected $factory;
+
+    /**
+     * Cofficient for x
+     *
+     * @var object
+     */
+    protected $a;
+
+    /**
+     * Constant used for point doubling
+     *
+     * @var object
+     */
+    protected $a24;
+
+    /**
+     * The Number Zero
+     *
+     * @var object
+     */
+    protected $zero;
+
+    /**
+     * The Number One
+     *
+     * @var object
+     */
+    protected $one;
+
+    /**
+     * Base Point
+     *
+     * @var object
+     */
+    protected $p;
+
+    /**
+     * 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->zero = $this->factory->newInteger(new BigInteger());
+        $this->one = $this->factory->newInteger(new BigInteger(1));
+    }
+
+    /**
+     * Set coefficients a
+     */
+    public function setCoefficients(BigInteger $a)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+        $this->a = $this->factory->newInteger($a);
+        $two = $this->factory->newInteger(new BigInteger(2));
+        $four = $this->factory->newInteger(new BigInteger(4));
+        $this->a24 = $this->a->subtract($two)->divide($four);
+    }
+
+    /**
+     * 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;
+    }
+
+    /**
+     * Doubles and adds a point on a curve
+     *
+     * See https://tools.ietf.org/html/draft-ietf-tls-curve25519-01#appendix-A.1.3
+     *
+     * @return FiniteField[][]
+     */
+    private function doubleAndAddPoint(array $p, array $q, PrimeInteger $x1)
+    {
+        if (!isset($this->factory)) {
+            throw new \RuntimeException('setModulo needs to be called before this method');
+        }
+
+        if (!count($p) || !count($q)) {
+            return [];
+        }
+
+        if (!isset($p[1])) {
+            throw new \RuntimeException('Affine coordinates need to be manually converted to XZ coordinates');
+        }
+
+        list($x2, $z2) = $p;
+        list($x3, $z3) = $q;
+
+        $a = $x2->add($z2);
+        $aa = $a->multiply($a);
+        $b = $x2->subtract($z2);
+        $bb = $b->multiply($b);
+        $e = $aa->subtract($bb);
+        $c = $x3->add($z3);
+        $d = $x3->subtract($z3);
+        $da = $d->multiply($a);
+        $cb = $c->multiply($b);
+        $temp = $da->add($cb);
+        $x5 = $temp->multiply($temp);
+        $temp = $da->subtract($cb);
+        $z5 = $x1->multiply($temp->multiply($temp));
+        $x4 = $aa->multiply($bb);
+        $temp = static::class == Curve25519::class ? $bb : $aa;
+        $z4 = $e->multiply($temp->add($this->a24->multiply($e)));
+
+        return [
+            [$x4, $z4],
+            [$x5, $z5]
+        ];
+    }
+
+    /**
+     * 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, BigInteger $d)
+    {
+        $p1 = [$this->one, $this->zero];
+        $alreadyInternal = isset($x[1]);
+        $p2 = $this->convertToInternal($p);
+        $x = $p[0];
+
+        $b = $d->toBits();
+        $b = str_pad($b, 256, '0', STR_PAD_LEFT);
+        for ($i = 0; $i < strlen($b); $i++) {
+            $b_i = (int) $b[$i];
+            if ($b_i) {
+                list($p2, $p1) = $this->doubleAndAddPoint($p2, $p1, $x);
+            } else {
+                list($p1, $p2) = $this->doubleAndAddPoint($p1, $p2, $x);
+            }
+        }
+
+        return $alreadyInternal ? $p1 : $this->convertToAffine($p1);
+    }
+
+    /**
+     * Converts an affine point to an XZ coordinate
+     *
+     * From https://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html
+     *
+     * XZ coordinates represent x y as X Z satsfying the following equations:
+     *
+     *   x=X/Z
+     *
+     * @return \phpseclib3\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (empty($p)) {
+            return [clone $this->zero, clone $this->one];
+        }
+
+        if (isset($p[1])) {
+            return $p;
+        }
+
+        $p[1] = clone $this->one;
+
+        return $p;
+    }
+
+    /**
+     * Returns the affine point
+     *
+     * @return \phpseclib3\Math\PrimeField\Integer[]
+     */
+    public function convertToAffine(array $p)
+    {
+        if (!isset($p[1])) {
+            return $p;
+        }
+        list($x, $z) = $p;
+        return [$x->divide($z)];
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Prime.php

+<?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
+ *
+ * @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 phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Common\Functions\Strings;
+use phpseclib3\Math\BigInteger;
+use phpseclib3\Math\Common\FiniteField\Integer;
+use phpseclib3\Math\PrimeField;
+use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
+
+/**
+ * Curves over y^2 = x^3 + a*x + b
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+class Prime extends Base
+{
+    /**
+     * Prime Field Integer factory
+     *
+     * @var \phpseclib3\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 \phpseclib3\Math\BigInteger
+     */
+    public function getModulo()
+    {
+        return $this->modulo;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib3\Math\PrimeField\Integer
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib3\Math\PrimeField\Integer
+     */
+    public function getB()
+    {
+        return $this->b;
+    }
+
+    /**
+     * Multiply and Add Points
+     *
+     * Adapted from:
+     * https://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/curve/base.js#L125
+     *
+     * @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://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/curve/base.js#L351
+     *
+     * @return int[]
+     */
+    private function getNAFPoints(array $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://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/utils.js#L96
+     *
+     * @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 \phpseclib3\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 \phpseclib3\Math\PrimeField\Integer[]
+     */
+    public function convertToInternal(array $p)
+    {
+        if (isset($p[2])) {
+            return $p;
+        }
+
+        $p[2] = clone $this->one;
+        $p['fresh'] = true;
+        return $p;
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/TwistedEdwards.php

+<?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
+ *
+ * @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 phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Math\BigInteger;
+use phpseclib3\Math\PrimeField;
+use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
+
+/**
+ * Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
+ *
+ * @author  Jim Wigginton <terrafrost@php.net>
+ */
+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 \phpseclib3\Math\PrimeField\Integer
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return \phpseclib3\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 \phpseclib3\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 \phpseclib3\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);
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Curve25519.php

+<?php
+
+/**
+ * Curve25519
+ *
+ * PHP version 5 and 7
+ *
+ * @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 phpseclib3\Crypt\EC\Curves;
+
+use phpseclib3\Crypt\EC\BaseCurves\Montgomery;
+use phpseclib3\Math\BigInteger;
+
+class Curve25519 extends Montgomery
+{
+    public function __construct()
+    {
+        // 2^255 - 19
+        $this->setModulo(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED', 16));
+        $this->a24 = $this->factory->newInteger(new BigInteger('121666'));
+        $this->p = [$this->factory->newInteger(new BigInteger(9))];
+        // 2^252 + 0x14def9dea2f79cd65812631a5cf5d3ed
+        $this->setOrder(new BigInteger('1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED', 16));
+
+        /*
+        $this->setCoefficients(
+            new BigInteger('486662'), // a
+        );
+        $this->setBasePoint(
+            new BigInteger(9),
+            new BigInteger('14781619447589544791020593568409986887264606134616475288964881837755586237401')
+        );
+        */
+    }
+
+    /**
+     * 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, BigInteger $d)
+    {
+        //$r = strrev(sodium_crypto_scalarmult($d->toBytes(), strrev($p[0]->toBytes())));
+        //return [$this->factory->newInteger(new BigInteger($r, 256))];
+
+        $d = $d->toBytes();
+        $d &= "\xF8" . str_repeat("\xFF", 30) . "\x7F";
+        $d = strrev($d);
+        $d |= "\x40";
+        $d = new BigInteger($d, -256);
+
+        return parent::multiplyPoint($p, $d);
+    }
+
+    /**
+     * Creates a random scalar multiplier
+     *
+     * @return BigInteger
+     */
+    public function createRandomMultiplier()
+    {
+        return BigInteger::random(256);
+    }
+
+    /**
+     * Performs range check
+     */
+    public function rangeCheck(BigInteger $x)
+    {
+        if ($x->getLength() > 256 || $x->isNegative()) {
+            throw new \RangeException('x must be a positive integer less than 256 bytes in length');
+        }
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Curve448.php

+<?php
+
+/**
+ * Curve448
+ *
+ * PHP version 5 and 7
+ *
+ * @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 phpseclib3\Crypt\EC\Curves;
+
+use phpseclib3\Crypt\EC\BaseCurves\Montgomery;
+use phpseclib3\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, BigInteger $d)
+    {
+        //$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";
+        $d = new BigInteger($d, 256);
+
+        return parent::multiplyPoint($p, $d);
+    }
+
+    /**
+     * Creates a random scalar multiplier
+     *
+     * @return BigInteger
+     */
+    public function createRandomMultiplier()
+    {
+        return BigInteger::random(446);
+    }
+
+    /**
+     * Performs range check
+     */
+    public function rangeCheck(BigInteger $x)
+    {
+        if ($x->getLength() > 448 || $x->isNegative()) {
+            throw new \RangeException('x must be a positive integer less than 446 bytes in length');
+        }
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed25519.php

+<?php
+
+/**
+ * Ed25519
+ *
+ * PHP version 5 and 7
+ *
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib3\Crypt\EC\Curves;
+
+use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards;
+use phpseclib3\Crypt\Hash;
+use phpseclib3\Crypt\Random;
+use phpseclib3\Math\BigInteger;
+
+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 EC\Keys\Common.php
+     *
+     * @param BigInteger $y
+     * @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 $str
+     * @return array
+     */
+    public function extractSecret($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);
+
+        return [
+            'dA' => $dA,
+            'secret' => $str
+        ];
+    }
+
+    /**
+     * Encode a point as a string
+     *
+     * @param array $point
+     * @return string
+     */
+    public function encodePoint($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 \phpseclib3\Math\PrimeField\Integer
+     */
+    public function createRandomMultiplier()
+    {
+        return $this->extractSecret(Random::string(32))['dA'];
+    }
+
+    /**
+     * 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 \phpseclib3\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];
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed448.php

+<?php
+
+/**
+ * Ed448
+ *
+ * PHP version 5 and 7
+ *
+ * @author    Jim Wigginton <terrafrost@php.net>
+ * @copyright 2017 Jim Wigginton
+ * @license   http://www.opensource.org/licenses/mit-license.html  MIT License
+ */
+
+namespace phpseclib3\Crypt\EC\Curves;
+
+use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards;
+use phpseclib3\Crypt\Hash;
+use phpseclib3\Crypt\Random;
+use phpseclib3\Math\BigInteger;
+
+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 EC\Keys\Common.php
+     *
+     * @param BigInteger $y
+     * @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 $str
+     * @return array
+     */
+    public function extractSecret($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);
+
+        return [
+            'dA' => $dA,
+            'secret' => $str
+        ];
+
+        $dA->secret = $str;
+        return $dA;
+    }
+
+    /**
+     * Encode a point as a string
+     *
+     * @param array $point
+     * @return string
+     */
+    public function encodePoint($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 \phpseclib3\Math\PrimeField\Integer
+     */
+    public function createRandomMultiplier()
+    {
+        return $this->extractSecret(Random::string(57))['dA'];
+    }
+
+    /**
+     * 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 \phpseclib3\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];
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/brainpoolP160r1.php

+<?php
+
+/**
+ * brainpoolP160r1
+ *
+ * PHP version 5 and 7
+ *
+ * @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 phpseclib3\Crypt\EC\Curves;
+
+use phpseclib3\Crypt\EC\BaseCurves\Prime;
+use phpseclib3\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));
+    }
+}

examples/rabbitmq/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/brainpoolP160t1.php

+<?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
+ *
+ * @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 phpseclib3\Crypt\EC\Curves;
+
+use phpseclib3\Crypt\EC\BaseCurves\Prime;
+use phpseclib3\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));
+    }
+}