diff options
Diffstat (limited to 'vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed448.php')
| -rw-r--r-- | vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed448.php | 273 |
1 files changed, 273 insertions, 0 deletions
diff --git a/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed448.php b/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed448.php new file mode 100644 index 0000000..5451f90 --- /dev/null +++ b/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/Ed448.php @@ -0,0 +1,273 @@ +<?php + +/** + * Ed448 + * + * PHP version 5 and 7 + * + * @author Jim Wigginton <[email protected]> + * @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]; + } +} |