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502 lines
16 KiB
502 lines
16 KiB
<?php
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/*
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* The MIT License (MIT)
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*
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* Copyright (c) 2013 John Judy
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy of
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* this software and associated documentation files (the "Software"), to deal in
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* the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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* the Software, and to permit persons to whom the Software is furnished to do so,
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* subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in all
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* copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
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* FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
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* COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
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* IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
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* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
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*/
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//ini_set('xdebug.max_nesting_level', 0);
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/**
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* A PHP implementation of the Python ED25519 library
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*
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* @author johnj
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*
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* @link http://ed25519.cr.yp.to/software.html Other ED25519 implementations this is referenced from
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*/
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defined( 'ABSPATH' ) || exit;
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class ed25519
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{
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public $b;
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public $q;
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public $l;
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public $d;
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public $I;
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public $By;
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public $Bx;
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public $B;
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private $gmp; // Is the GMP extension available?
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public function __construct()
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{
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$this->b = 256;
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$this->q = "57896044618658097711785492504343953926634992332820282019728792003956564819949"; //bcsub(bcpow(2, 255),19);
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$this->l = "7237005577332262213973186563042994240857116359379907606001950938285454250989"; //bcadd(bcpow(2,252),27742317777372353535851937790883648493);
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$this->d = "-4513249062541557337682894930092624173785641285191125241628941591882900924598840740"; //bcmul(-121665,$this->inv(121666));
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$this->I = "19681161376707505956807079304988542015446066515923890162744021073123829784752"; //$this->expmod(2, bcdiv((bcsub($this->q,1)),4),$this->q);
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$this->By = "46316835694926478169428394003475163141307993866256225615783033603165251855960"; //bcmul(4,$this->inv(5));
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$this->Bx = "15112221349535400772501151409588531511454012693041857206046113283949847762202"; //$this->xrecover($this->By);
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$this->B = array(
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"15112221349535400772501151409588531511454012693041857206046113283949847762202",
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"46316835694926478169428394003475163141307993866256225615783033603165251855960"
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); //array(bcmod($this->Bx,$this->q),bcmod($this->By,$this->q));
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$this->gmp = extension_loaded('gmp');
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}
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public function H($m)
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{
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return hash('sha512', $m, true);
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}
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//((n % M) + M) % M //python modulus craziness
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public function pymod($x, $m)
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{
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if ($this->gmp) {
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$mod = gmp_mod($x, $m);
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if ($mod < 0) {
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$mod = gmp_add($mod, $m);
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}
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} else {
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$mod = bcmod($x, $m);
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if ($mod < 0) {
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$mod = bcadd($mod, $m);
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}
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}
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return $mod;
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}
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public function expmod($b, $e, $m)
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{
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//if($e==0){return 1;}
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if ($this->gmp) {
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$t = gmp_powm($b, $e, $m);
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if ($t < 0) {
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$t = gmp_add($t, $m);
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}
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} else {
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$t = bcpowmod($b, $e, $m);
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if ($t[0] === '-') {
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$t = bcadd($t, $m);
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}
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}
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return $t;
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}
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public function inv($x)
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{
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if ($this->gmp) {
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return $this->expmod($x, gmp_sub($this->q, 2), $this->q);
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} else {
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return $this->expmod($x, bcsub($this->q, 2), $this->q);
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}
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}
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public function xrecover($y)
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{
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if ($this->gmp) {
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$y2 = gmp_pow($y, 2);
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$xx = gmp_mul(gmp_sub($y2, 1), $this->inv(gmp_add(gmp_mul($this->d, $y2), 1)));
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$x = $this->expmod($xx, gmp_div(gmp_add($this->q, 3), 8, 0), $this->q);
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if ($this->pymod(gmp_sub(gmp_pow($x, 2), $xx), $this->q) != 0) {
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$x = $this->pymod(gmp_mul($x, $this->I), $this->q);
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}
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if (substr($x, -1)%2 != 0) {
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$x = gmp_sub($this->q, $x);
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}
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} else {
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$y2 = bcpow($y, 2);
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$xx = bcmul(bcsub($y2, 1), $this->inv(bcadd(bcmul($this->d, $y2), 1)));
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$x = $this->expmod($xx, bcdiv(bcadd($this->q, 3), 8, 0), $this->q);
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if ($this->pymod(bcsub(bcpow($x, 2), $xx), $this->q) != 0) {
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$x = $this->pymod(bcmul($x, $this->I), $this->q);
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}
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if (substr($x, -1)%2 != 0) {
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$x = bcsub($this->q, $x);
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}
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}
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return $x;
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}
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public function edwards($P, $Q)
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{
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if ($this->gmp) {
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list($x1, $y1) = $P;
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list($x2, $y2) = $Q;
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$xmul = gmp_mul($x1, $x2);
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$ymul = gmp_mul($y1, $y2);
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$com = gmp_mul($this->d, gmp_mul($xmul, $ymul));
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$x3 = gmp_mul(gmp_add(gmp_mul($x1, $y2), gmp_mul($x2, $y1)), $this->inv(gmp_add(1, $com)));
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$y3 = gmp_mul(gmp_add($ymul, $xmul), $this->inv(gmp_sub(1, $com)));
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return array($this->pymod($x3, $this->q), $this->pymod($y3, $this->q));
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} else {
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list($x1, $y1) = $P;
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list($x2, $y2) = $Q;
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$xmul = bcmul($x1, $x2);
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$ymul = bcmul($y1, $y2);
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$com = bcmul($this->d, bcmul($xmul, $ymul));
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$x3 = bcmul(bcadd(bcmul($x1, $y2), bcmul($x2, $y1)), $this->inv(bcadd(1, $com)));
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$y3 = bcmul(bcadd($ymul, $xmul), $this->inv(bcsub(1, $com)));
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return array($this->pymod($x3, $this->q), $this->pymod($y3, $this->q));
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}
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}
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public function scalarmult($P, $e)
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{
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if ($this->gmp) {
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if ($e == 0) {
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return array(0, 1);
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}
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$Q = $this->scalarmult($P, gmp_div($e, 2, 0));
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$Q = $this->edwards($Q, $Q);
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if (substr($e, -1)%2 == 1) {
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$Q = $this->edwards($Q, $P);
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}
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} else {
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if ($e == 0) {
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return array(0, 1);
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}
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$Q = $this->scalarmult($P, bcdiv($e, 2, 0));
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$Q = $this->edwards($Q, $Q);
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if (substr($e, -1)%2 == 1) {
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$Q = $this->edwards($Q, $P);
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}
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}
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return $Q;
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}
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public function scalarloop($P, $e)
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{
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if ($this->gmp) {
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$temp = array();
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$loopE = $e;
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while ($loopE > 0) {
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array_unshift($temp, $loopE);
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$loopE = gmp_div($loopE, 2, 0);
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}
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$Q = array();
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foreach ($temp as $e) {
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if ($e == 1) {
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$Q = $this->edwards(array(0, 1), $P);
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} elseif (substr($e, -1)%2 == 1) {
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$Q = $this->edwards($this->edwards($Q, $Q), $P);
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} else {
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$Q = $this->edwards($Q, $Q);
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}
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}
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} else {
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$temp = array();
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$loopE = $e;
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while ($loopE > 0) {
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array_unshift($temp, $loopE);
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$loopE = bcdiv($loopE, 2, 0);
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}
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$Q = array();
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foreach ($temp as $e) {
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if ($e == 1) {
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$Q = $this->edwards(array(0, 1), $P);
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} elseif (substr($e, -1)%2 == 1) {
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$Q = $this->edwards($this->edwards($Q, $Q), $P);
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} else {
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$Q = $this->edwards($Q, $Q);
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}
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}
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}
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return $Q;
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}
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public function bitsToString($bits)
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{
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$string = '';
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for ($i = 0; $i < $this->b/8; $i++) {
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$sum = 0;
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for ($j = 0; $j < 8; $j++) {
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$bit = $bits[$i*8+$j];
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$sum += (int) $bit << $j;
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}
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$string .= chr($sum);
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}
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return $string;
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}
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public function dec2bin_i($decimal_i)
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{
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if ($this->gmp) {
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$binary_i = '';
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do {
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$binary_i = substr($decimal_i, -1)%2 .$binary_i;
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$decimal_i = gmp_div($decimal_i, '2', 0);
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} while (gmp_cmp($decimal_i, '0'));
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} else {
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$binary_i = '';
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do {
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$binary_i = substr($decimal_i, -1)%2 .$binary_i;
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$decimal_i = bcdiv($decimal_i, '2', 0);
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} while (bccomp($decimal_i, '0'));
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}
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return ($binary_i);
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}
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public function encodeint($y)
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{
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$bits = substr(str_pad(strrev($this->dec2bin_i($y)), $this->b, '0', STR_PAD_RIGHT), 0, $this->b);
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return $this->bitsToString($bits);
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}
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public function encodepoint($P)
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{
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list($x, $y) = $P;
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$bits = substr(str_pad(strrev($this->dec2bin_i($y)), $this->b-1, '0', STR_PAD_RIGHT), 0, $this->b-1);
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$bits .= (substr($x, -1)%2 == 1 ? '1' : '0');
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return $this->bitsToString($bits);
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}
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public function bit($h, $i)
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{
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if ($this->gmp) {
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return (ord($h[(int) gmp_div($i, 8, 0)]) >> substr($i, -3)%8) & 1;
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} else {
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return (ord($h[(int) bcdiv($i, 8, 0)]) >> substr($i, -3)%8) & 1;
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}
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}
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/**
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* Generates the public key of a given private key
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*
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* @param string $sk the secret key
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*
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* @return string
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*/
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public function publickey($sk)
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{
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if ($this->gmp) {
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$h = $this->H($sk);
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$sum = 0;
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for ($i = 3; $i < $this->b-2; $i++) {
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$sum = gmp_add($sum, gmp_mul(gmp_pow(2, $i), $this->bit($h, $i)));
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}
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$a = gmp_add(gmp_pow(2, $this->b-2), $sum);
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$A = $this->scalarmult($this->B, $a);
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$data = $this->encodepoint($A);
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} else {
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$h = $this->H($sk);
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$sum = 0;
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for ($i = 3; $i < $this->b-2; $i++) {
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$sum = bcadd($sum, bcmul(bcpow(2, $i), $this->bit($h, $i)));
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}
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$a = bcadd(bcpow(2, $this->b-2), $sum);
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$A = $this->scalarmult($this->B, $a);
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$data = $this->encodepoint($A);
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}
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return $data;
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}
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public function Hint($m)
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{
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if ($this->gmp) {
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$h = $this->H($m);
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$sum = 0;
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for ($i = 0; $i < $this->b*2; $i++) {
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$sum = gmp_add($sum, gmp_mul(gmp_pow(2, $i), $this->bit($h, $i)));
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}
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} else {
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$h = $this->H($m);
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$sum = 0;
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for ($i = 0; $i < $this->b*2; $i++) {
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$sum = bcadd($sum, bcmul(bcpow(2, $i), $this->bit($h, $i)));
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}
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}
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return $sum;
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}
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public function signature($m, $sk, $pk)
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{
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if ($this->gmp) {
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$h = $this->H($sk);
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$a = gmp_pow(2, (gmp_sub($this->b, 2)));
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for ($i = 3; $i < $this->b-2; $i++) {
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$a = gmp_add($a, gmp_mul(gmp_pow(2, $i), $this->bit($h, $i)));
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}
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$r = $this->Hint(substr($h, $this->b/8, ($this->b/4-$this->b/8)).$m);
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$R = $this->scalarmult($this->B, $r);
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$encR = $this->encodepoint($R);
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$S = $this->pymod(gmp_add($r, gmp_mul($this->Hint($encR.$pk.$m), $a)), $this->l);
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} else {
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$h = $this->H($sk);
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$a = bcpow(2, (bcsub($this->b, 2)));
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for ($i = 3; $i < $this->b-2; $i++) {
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$a = bcadd($a, bcmul(bcpow(2, $i), $this->bit($h, $i)));
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}
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$r = $this->Hint(substr($h, $this->b/8, ($this->b/4-$this->b/8)).$m);
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$R = $this->scalarmult($this->B, $r);
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$encR = $this->encodepoint($R);
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$S = $this->pymod(bcadd($r, bcmul($this->Hint($encR.$pk.$m), $a)), $this->l);
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}
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return $encR.$this->encodeint($S);
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}
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public function isoncurve($P)
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{
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if ($this->gmp) {
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list($x, $y) = $P;
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$x2 = gmp_pow($x, 2);
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$y2 = gmp_pow($y, 2);
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return $this->pymod(gmp_sub(gmp_sub(gmp_sub($y2, $x2), 1), gmp_mul($this->d, gmp_mul($x2, $y2))), $this->q) == 0;
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} else {
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list($x, $y) = $P;
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$x2 = bcpow($x, 2);
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$y2 = bcpow($y, 2);
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return $this->pymod(bcsub(bcsub(bcsub($y2, $x2), 1), bcmul($this->d, bcmul($x2, $y2))), $this->q) == 0;
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}
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}
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public function decodeint($s)
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{
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if ($this->gmp) {
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$sum = 0;
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for ($i = 0; $i < $this->b; $i++) {
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$sum = gmp_add($sum, gmp_mul(gmp_pow(2, $i), $this->bit($s, $i)));
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}
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} else {
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$sum = 0;
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for ($i = 0; $i < $this->b; $i++) {
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$sum = bcadd($sum, bcmul(bcpow(2, $i), $this->bit($s, $i)));
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}
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}
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return $sum;
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}
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/*
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* def decodepoint(s):
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y = sum(2**i * bit(s,i) for i in range(0,b-1))
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x = xrecover(y)
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if x & 1 != bit(s,b-1): x = q-x
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P = [x,y]
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if not isoncurve(P): raise Exception("decoding point that is not on curve")
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return P
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*/
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public function decodepoint($s)
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{
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if ($this->gmp) {
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$y = 0;
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for ($i = 0; $i < $this->b-1; $i++) {
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$y = gmp_add($y, gmp_mul(gmp_pow(2, $i), $this->bit($s, $i)));
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}
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$x = $this->xrecover($y);
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if (substr($x, -1)%2 != $this->bit($s, $this->b-1)) {
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$x = gmp_sub($this->q, $x);
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}
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$P = array($x, $y);
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if (!$this->isoncurve($P)) {
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throw new \Exception("Decoding point that is not on curve");
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}
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} else {
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$y = 0;
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for ($i = 0; $i < $this->b-1; $i++) {
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$y = bcadd($y, bcmul(bcpow(2, $i), $this->bit($s, $i)));
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}
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$x = $this->xrecover($y);
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if (substr($x, -1)%2 != $this->bit($s, $this->b-1)) {
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$x = bcsub($this->q, $x);
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}
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$P = array($x, $y);
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if (!$this->isoncurve($P)) {
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throw new \Exception("Decoding point that is not on curve");
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}
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}
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return $P;
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}
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|
|
|
public function checkvalid($s, $m, $pk)
|
|
{
|
|
if (strlen($s) != $this->b/4) {
|
|
throw new \Exception('Signature length is wrong');
|
|
}
|
|
if (strlen($pk) != $this->b/8) {
|
|
throw new \Exception('Public key length is wrong: '.strlen($pk));
|
|
}
|
|
$R = $this->decodepoint(substr($s, 0, $this->b/8));
|
|
try {
|
|
$A = $this->decodepoint($pk);
|
|
} catch (\Exception $e) {
|
|
return false;
|
|
}
|
|
$S = $this->decodeint(substr($s, $this->b/8, $this->b/4));
|
|
$h = $this->Hint($this->encodepoint($R).$pk.$m);
|
|
|
|
return $this->scalarmult($this->B, $S) == $this->edwards($R, $this->scalarmult($A, $h));
|
|
}
|
|
|
|
// The code below is by the Monero-Integrations team
|
|
|
|
public function scalarmult_base($e)
|
|
{
|
|
if ($this->gmp) {
|
|
if ($e == 0) {
|
|
return array(0, 1);
|
|
}
|
|
$Q = $this->scalarmult($this->B, gmp_div($e, 2, 0));
|
|
$Q = $this->edwards($Q, $Q);
|
|
if (substr($e, -1)%2 == 1) {
|
|
$Q = $this->edwards($Q, $this->B);
|
|
}
|
|
} else {
|
|
if ($e == 0) {
|
|
return array(0, 1);
|
|
}
|
|
$Q = $this->scalarmult($this->B, bcdiv($e, 2, 0));
|
|
$Q = $this->edwards($Q, $Q);
|
|
if (substr($e, -1)%2 == 1) {
|
|
$Q = $this->edwards($Q, $this->B);
|
|
}
|
|
}
|
|
|
|
return $Q;
|
|
}
|
|
}
|