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Diffstat (limited to 'vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Montgomery.php')
-rw-r--r-- | vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Montgomery.php | 279 |
1 files changed, 279 insertions, 0 deletions
diff --git a/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Montgomery.php b/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Montgomery.php new file mode 100644 index 0000000..e3fa50b --- /dev/null +++ b/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/BaseCurves/Montgomery.php @@ -0,0 +1,279 @@ +<?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 <[email protected]> + * @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 <[email protected]> + */ +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)]; + } +} |