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qa-tool/htdocs/oidc/phpseclib/Crypt/EC/BaseCurves/TwistedEdwards.php

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+<?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
+ */
+
+declare(strict_types=1);
+
+namespace phpseclib3\Crypt\EC\BaseCurves;
+
+use phpseclib3\Exception\RuntimeException;
+use phpseclib3\Exception\UnexpectedValueException;
+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): void
+    {
+        $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 $d): void
+    {
+        if (!isset($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, $y): void
+    {
+        switch (true) {
+            case !$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 PrimeInteger
+     */
+    public function getA()
+    {
+        return $this->a;
+    }
+
+    /**
+     * Returns the a coefficient
+     *
+     * @return PrimeInteger
+     */
+    public function getD()
+    {
+        return $this->d;
+    }
+
+    /**
+     * Retrieve the base point as an array
+     */
+    public function getBasePoint(): array
+    {
+        if (!isset($this->factory)) {
+            throw new RuntimeException('setModulo needs to be called before this method');
+        }
+        /*
+        if (!isset($this->p)) {
+            throw new \phpseclib3\Exception\RuntimeException('setBasePoint needs to be called before this method');
+        }
+        */
+        return $this->p;
+    }
+
+    /**
+     * Returns the affine point
+     *
+     * @return PrimeInteger[]
+     */
+    public function convertToAffine(array $p): array
+    {
+        if (!isset($p[2])) {
+            return $p;
+        }
+        [$x, $y, $z] = $p;
+        $z = $this->one->divide($z);
+        return [
+            $x->multiply($z),
+            $y->multiply($z),
+        ];
+    }
+
+    /**
+     * Returns the modulo
+     */
+    public function getModulo(): BigInteger
+    {
+        return $this->modulo;
+    }
+
+    /**
+     * Tests whether or not the x / y values satisfy the equation
+     *
+     * @return boolean
+     */
+    public function verifyPoint(array $p): bool
+    {
+        [$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);
+    }
+}