264 lines
7.5 KiB
PHP
264 lines
7.5 KiB
PHP
<?php
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/**
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* Ed448
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*
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* PHP version 5 and 7
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*
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* @author Jim Wigginton <terrafrost@php.net>
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* @copyright 2017 Jim Wigginton
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* @license http://www.opensource.org/licenses/mit-license.html MIT License
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*/
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declare(strict_types=1);
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namespace phpseclib3\Crypt\EC\Curves;
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use phpseclib3\Crypt\EC\BaseCurves\TwistedEdwards;
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use phpseclib3\Crypt\Hash;
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use phpseclib3\Crypt\Random;
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use phpseclib3\Math\BigInteger;
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class Ed448 extends TwistedEdwards
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{
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const HASH = 'shake256-912';
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const SIZE = 57;
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public function __construct()
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{
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// 2^448 - 2^224 - 1
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$this->setModulo(new BigInteger(
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'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE' .
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'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF',
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16
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));
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$this->setCoefficients(
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new BigInteger(1),
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// -39081
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new BigInteger('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFE' .
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'FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF6756', 16)
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);
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$this->setBasePoint(
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new BigInteger('4F1970C66BED0DED221D15A622BF36DA9E146570470F1767EA6DE324' .
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'A3D3A46412AE1AF72AB66511433B80E18B00938E2626A82BC70CC05E', 16),
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new BigInteger('693F46716EB6BC248876203756C9C7624BEA73736CA3984087789C1E' .
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'05A0C2D73AD3FF1CE67C39C4FDBD132C4ED7C8AD9808795BF230FA14', 16)
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);
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$this->setOrder(new BigInteger(
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'3FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF' .
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'7CCA23E9C44EDB49AED63690216CC2728DC58F552378C292AB5844F3',
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16
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));
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}
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/**
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* Recover X from Y
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*
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* Implements steps 2-4 at https://tools.ietf.org/html/rfc8032#section-5.2.3
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*
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* Used by EC\Keys\Common.php
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*
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* @param boolean $sign
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* @return object[]
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*/
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public function recoverX(BigInteger $y, bool $sign): array
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{
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$y = $this->factory->newInteger($y);
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$y2 = $y->multiply($y);
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$u = $y2->subtract($this->one);
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$v = $this->d->multiply($y2)->subtract($this->one);
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$x2 = $u->divide($v);
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if ($x2->equals($this->zero)) {
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if ($sign) {
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throw new \RuntimeException('Unable to recover X coordinate (x2 = 0)');
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}
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return clone $this->zero;
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}
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// find the square root
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$exp = $this->getModulo()->add(new BigInteger(1));
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$exp = $exp->bitwise_rightShift(2);
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$x = $x2->pow($exp);
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if (!$x->multiply($x)->subtract($x2)->equals($this->zero)) {
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throw new \RuntimeException('Unable to recover X coordinate');
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}
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if ($x->isOdd() != $sign) {
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$x = $x->negate();
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}
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return [$x, $y];
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}
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/**
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* Extract Secret Scalar
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*
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* Implements steps 1-3 at https://tools.ietf.org/html/rfc8032#section-5.2.5
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*
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* Used by the various key handlers
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*
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* @return \phpseclib3\Math\PrimeField\Integer
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*/
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public function extractSecret(string $str)
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{
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if (strlen($str) != 57) {
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throw new \LengthException('Private Key should be 57-bytes long');
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}
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// 1. Hash the 57-byte private key using SHAKE256(x, 114), storing the
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// digest in a 114-octet large buffer, denoted h. Only the lower 57
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// bytes are used for generating the public key.
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$hash = new Hash('shake256-912');
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$h = $hash->hash($str);
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$h = substr($h, 0, 57);
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// 2. Prune the buffer: The two least significant bits of the first
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// octet are cleared, all eight bits the last octet are cleared, and
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// the highest bit of the second to last octet is set.
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$h[0] = $h[0] & chr(0xFC);
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$h = strrev($h);
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$h[0] = "\0";
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$h[1] = $h[1] | chr(0x80);
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// 3. Interpret the buffer as the little-endian integer, forming a
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// secret scalar s.
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$dA = new BigInteger($h, 256);
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$dA->secret = $str;
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return $dA;
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}
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/**
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* Encode a point as a string
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*/
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public function encodePoint(array $point): string
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{
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[$x, $y] = $point;
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$y = "\0" . $y->toBytes();
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if ($x->isOdd()) {
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$y[0] = $y[0] | chr(0x80);
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}
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$y = strrev($y);
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return $y;
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}
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/**
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* Creates a random scalar multiplier
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*/
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public function createRandomMultiplier(): BigInteger
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{
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return $this->extractSecret(Random::string(57));
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}
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/**
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* Converts an affine point to an extended homogeneous coordinate
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*
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* From https://tools.ietf.org/html/rfc8032#section-5.2.4 :
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*
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* A point (x,y) is represented in extended homogeneous coordinates (X, Y, Z, T),
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* with x = X/Z, y = Y/Z, x * y = T/Z.
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*
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* @return \phpseclib3\Math\PrimeField\Integer[]
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*/
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public function convertToInternal(array $p): array
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{
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if (empty($p)) {
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return [clone $this->zero, clone $this->one, clone $this->one];
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}
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if (isset($p[2])) {
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return $p;
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}
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$p[2] = clone $this->one;
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return $p;
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}
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/**
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* Doubles a point on a curve
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*
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* @return FiniteField[]
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*/
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public function doublePoint(array $p): array
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{
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if (!isset($this->factory)) {
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throw new \RuntimeException('setModulo needs to be called before this method');
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}
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if (!count($p)) {
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return [];
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}
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if (!isset($p[2])) {
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throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
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}
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// from https://tools.ietf.org/html/rfc8032#page-18
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[$x1, $y1, $z1] = $p;
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$b = $x1->add($y1);
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$b = $b->multiply($b);
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$c = $x1->multiply($x1);
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$d = $y1->multiply($y1);
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$e = $c->add($d);
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$h = $z1->multiply($z1);
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$j = $e->subtract($this->two->multiply($h));
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$x3 = $b->subtract($e)->multiply($j);
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$y3 = $c->subtract($d)->multiply($e);
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$z3 = $e->multiply($j);
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return [$x3, $y3, $z3];
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}
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/**
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* Adds two points on the curve
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*
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* @return FiniteField[]
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*/
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public function addPoint(array $p, array $q): array
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{
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if (!isset($this->factory)) {
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throw new \RuntimeException('setModulo needs to be called before this method');
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}
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if (!count($p) || !count($q)) {
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if (count($q)) {
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return $q;
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}
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if (count($p)) {
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return $p;
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}
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return [];
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}
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if (!isset($p[2]) || !isset($q[2])) {
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throw new \RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa');
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}
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if ($p[0]->equals($q[0])) {
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return !$p[1]->equals($q[1]) ? [] : $this->doublePoint($p);
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}
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// from https://tools.ietf.org/html/rfc8032#page-17
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[$x1, $y1, $z1] = $p;
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[$x2, $y2, $z2] = $q;
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$a = $z1->multiply($z2);
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$b = $a->multiply($a);
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$c = $x1->multiply($x2);
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$d = $y1->multiply($y2);
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$e = $this->d->multiply($c)->multiply($d);
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$f = $b->subtract($e);
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$g = $b->add($e);
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$h = $x1->add($y1)->multiply($x2->add($y2));
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$x3 = $a->multiply($f)->multiply($h->subtract($c)->subtract($d));
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$y3 = $a->multiply($g)->multiply($d->subtract($c));
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$z3 = $f->multiply($g);
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return [$x3, $y3, $z3];
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}
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}
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