328 lines
9.9 KiB
PHP
328 lines
9.9 KiB
PHP
<?php
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/**
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* Ed25519
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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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use phpseclib3\Math\PrimeField\Integer;
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class Ed25519 extends TwistedEdwards
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{
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const HASH = 'sha512';
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/*
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Per https://tools.ietf.org/html/rfc8032#page-6 EdDSA has several parameters, one of which is b:
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2. An integer b with 2^(b-1) > p. EdDSA public keys have exactly b
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bits, and EdDSA signatures have exactly 2*b bits. b is
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recommended to be a multiple of 8, so public key and signature
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lengths are an integral number of octets.
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SIZE corresponds to b
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*/
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const SIZE = 32;
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public function __construct()
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{
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// 2^255 - 19
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$this->setModulo(new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFED', 16));
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$this->setCoefficients(
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// -1
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new BigInteger('7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEC', 16), // a
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// -121665/121666
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new BigInteger('52036CEE2B6FFE738CC740797779E89800700A4D4141D8AB75EB4DCA135978A3', 16) // d
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);
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$this->setBasePoint(
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new BigInteger('216936D3CD6E53FEC0A4E231FDD6DC5C692CC7609525A7B2C9562D608F25D51A', 16),
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new BigInteger('6666666666666666666666666666666666666666666666666666666666666658', 16)
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);
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$this->setOrder(new BigInteger('1000000000000000000000000000000014DEF9DEA2F79CD65812631A5CF5D3ED', 16));
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// algorithm 14.47 from http://cacr.uwaterloo.ca/hac/about/chap14.pdf#page=16
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/*
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$this->setReduction(function($x) {
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$parts = $x->bitwise_split(255);
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$className = $this->className;
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if (count($parts) > 2) {
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list(, $r) = $x->divide($className::$modulo);
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return $r;
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}
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$zero = new BigInteger();
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$c = new BigInteger(19);
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switch (count($parts)) {
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case 2:
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list($qi, $ri) = $parts;
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break;
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case 1:
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$qi = $zero;
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list($ri) = $parts;
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break;
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case 0:
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return $zero;
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}
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$r = $ri;
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while ($qi->compare($zero) > 0) {
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$temp = $qi->multiply($c)->bitwise_split(255);
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if (count($temp) == 2) {
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list($qi, $ri) = $temp;
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} else {
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$qi = $zero;
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list($ri) = $temp;
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}
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$r = $r->add($ri);
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}
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while ($r->compare($className::$modulo) > 0) {
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$r = $r->subtract($className::$modulo);
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}
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return $r;
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});
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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-5.1.3
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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)->add($this->one);
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$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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/* we don't do $x2->squareRoot() because, quoting from
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https://tools.ietf.org/html/rfc8032#section-5.1.1:
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"For point decoding or "decompression", square roots modulo p are
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needed. They can be computed using the Tonelli-Shanks algorithm or
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the special case for p = 5 (mod 8). To find a square root of a,
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first compute the candidate root x = a^((p+3)/8) (mod p)."
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*/
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$exp = $this->getModulo()->add(new BigInteger(3));
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$exp = $exp->bitwise_rightShift(3);
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$x = $x2->pow($exp);
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// If v x^2 = -u (mod p), set x <-- x * 2^((p-1)/4), which is a square root.
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if (!$x->multiply($x)->subtract($x2)->equals($this->zero)) {
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$temp = $this->getModulo()->subtract(new BigInteger(1));
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$temp = $temp->bitwise_rightShift(2);
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$temp = $this->two->pow($temp);
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$x = $x->multiply($temp);
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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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}
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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-5.1.5
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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) != 32) {
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throw new \LengthException('Private Key should be 32-bytes long');
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}
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// 1. Hash the 32-byte private key using SHA-512, storing the digest in
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// a 64-octet large buffer, denoted h. Only the lower 32 bytes are
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// used for generating the public key.
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$hash = new Hash('sha512');
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$h = $hash->hash($str);
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$h = substr($h, 0, 32);
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// 2. Prune the buffer: The lowest three bits of the first octet are
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// cleared, the highest bit of the last octet is cleared, and the
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// second highest bit of the last octet is set.
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$h[0] = $h[0] & chr(0xF8);
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$h = strrev($h);
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$h[0] = ($h[0] & chr(0x3F)) | chr(0x40);
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// 3. Interpret the buffer as the little-endian integer, forming a
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// secret scalar s.
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$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 = $y->toBytes();
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$y[0] = $y[0] & chr(0x7F);
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if ($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(32));
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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-5.1.4 :
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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, clone $this->zero];
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}
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if (isset($p[2])) {
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return $p;
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}
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$p[2] = clone $this->one;
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$p[3] = $p[0]->multiply($p[1]);
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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-12
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[$x1, $y1, $z1, $t1] = $p;
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$a = $x1->multiply($x1);
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$b = $y1->multiply($y1);
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$c = $this->two->multiply($z1)->multiply($z1);
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$h = $a->add($b);
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$temp = $x1->add($y1);
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$e = $h->subtract($temp->multiply($temp));
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$g = $a->subtract($b);
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$f = $c->add($g);
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$x3 = $e->multiply($f);
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$y3 = $g->multiply($h);
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$t3 = $e->multiply($h);
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$z3 = $f->multiply($g);
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return [$x3, $y3, $z3, $t3];
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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-12
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[$x1, $y1, $z1, $t1] = $p;
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[$x2, $y2, $z2, $t2] = $q;
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$a = $y1->subtract($x1)->multiply($y2->subtract($x2));
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$b = $y1->add($x1)->multiply($y2->add($x2));
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$c = $t1->multiply($this->two)->multiply($this->d)->multiply($t2);
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$d = $z1->multiply($this->two)->multiply($z2);
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$e = $b->subtract($a);
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$f = $d->subtract($c);
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$g = $d->add($c);
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$h = $b->add($a);
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$x3 = $e->multiply($f);
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$y3 = $g->multiply($h);
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$t3 = $e->multiply($h);
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$z3 = $f->multiply($g);
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return [$x3, $y3, $z3, $t3];
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}
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}
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