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Direktori : /home2/selectio/public_html/3-idiots/vendor/phpseclib/phpseclib/phpseclib/Crypt/EC/Curves/ |
Current File : /home2/selectio/public_html/3-idiots/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]; } }