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MadelineProto/src/danog/MadelineProto/PrimeModule.php

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<?php
/*
Copyright 2016 Daniil Gentili
(https://daniil.it)
This file is part of MadelineProto.
MadelineProto is free software: you can redistribute it and/or modify it under the terms of the GNU Affero General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
The PWRTelegram API is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
See the GNU Affero General Public License for more details.
You should have received a copy of the GNU General Public License along with the MadelineProto.
If not, see <http://www.gnu.org/licenses/>.
*/
namespace danog\MadelineProto;
class PrimeModule
{
public function __construct()
{
$this->smallprimeset = array_unique($this->primesbelow(100000));
$this->_smallprimeset = 100000;
$this->smallprimes = $this->primesbelow(10000);
}
public function primesbelow($N)
{
$res = [];
for ($i = 2; $i <= $N; $i++) {
if ($i % 2 != 1 && $i != 2) {
continue;
}
$d = 3;
$x = sqrt($i);
while ($i % $d != 0 && $d < $x) {
$d += 2;
}
if ((($i % $d == 0 && $i != $d) * 1) == 0) {
$res[] = $i;
}
}
return $res;
}
public function isprime($n, $precision = 7)
{
if (($n == 1) || (($n % 2) == 0)) {
return false;
} elseif (($n < 1)) {
throw new Exception('Out of bounds, first argument must be > 0');
} elseif (($n < $this->_smallprimeset)) {
return in_array($n, $this->smallprimeset);
}
$d = ($n - 1);
$s = 0;
while (($d % 2) == 0) {
$d = floor($d / 2);
$s++;
}
$break = false;
foreach (pyjslib_range($precision) as $repeat) {
$a = rand(2, ($n - 2));
$x = posmod(pow($a, $d), $n);
if (($x == 1) || ($x == ($n - 1))) {
continue;
}
foreach (pyjslib_range($s - 1) as $r) {
$x = posmod(pow($x, 2), $n);
if (($x == 1)) {
return false;
}
if (($x == ($n - 1))) {
$break = true;
}
}
if (!$break) {
return false;
}
}
return true;
}
// taken from https://github.com/enricostara/telegram-mt-node/blob/master/lib/security/pq-finder.js
public function getpq($pq)
{
$p = 0;
$q = 0;
while ($pq != $p * $q && $p != 0) {
for ($i = 0; $i < 3; $i++) {
$q = new \phpseclib\Math\BigInteger((random_int(0, 128) & 15) + 17);
$x = new \phpseclib\Math\BigInteger(random_int(0, 1000000000) + 1);
$y = $x;
$lim = 1 << ($i + 18);
for ($j = 1; $j < $lim; $j++) {
$a = $x;
$b = $x;
$c = $q;
while (!$b->equals($zero)) {
if ($b->powMod($one, $two)->equals($zero)) {
$c = $c->add($a);
if ($c->compare($pq) > 0) {
$c = $c->subtract($pq);
}
}
$a = $a->add($a);
if ($a->compare($pq) > 0) {
$a = $a->subtract($pq);
}
$b = $b->rightShift(1);
}
$x = $c;
$z = ($y->compare($x) > 0) ? $y->subtract($x) : $x->subtract($y);
$p = $z->gcd($pq);
if (!$p->equals($one)) {
break;
}
if (($j & ($j - 1)) === 0) {
$y = $x;
}
}
if (prime.gt(BigInteger.One())) {
break;
}
}
$q = $pq->divide(prime)[0];
}
$_pq = ($q->compare($p) > 0) ? [$p, $q] : [$q, $p];
return $_pq;
}
public function pollard_brent($n)
{
$zero = new \phpseclib\Math\BigInteger(0);
$one = new \phpseclib\Math\BigInteger(1);
$two = new \phpseclib\Math\BigInteger(2);
$three = new \phpseclib\Math\BigInteger(3);
if ($n->powMod($one, $two)->toString() == '0') {
return 2;
}
if ($n->powMod($one, $three)->toString() == '0') {
return 3;
}
$big = new \phpseclib\Math\BigInteger();
$max = $n->subtract($one);
list($y, $c, $m) = [new \phpseclib\Math\BigInteger(87552211475113995), new \phpseclib\Math\BigInteger(330422027228888537), new \phpseclib\Math\BigInteger(226866727920975483)];
//[$big->random($one, $max), $big->random($one, $max), $big->random($one, $max)];
list($g, $r, $q) = [$one, $one, $one];
while ($g->equals($one)) {
$x = $y;
$params = ['y' => $y, 'two' => $two, 'c' => $c, 'one' => $one, 'n' => $n];
$r->loopforeach(function ($i, $params) {
$params['y'] = $params['y']->powMod($params['two'], $params['n'])->add($params['c'])->powMod($params['one'], $params['n']);
}, $params);
each($params);
$k = $zero;
while ($k->compare($r) == -1 && $g->equals($one)) {
$ys = $y;
$params = ['x' => $x, 'y' => $y, 'two' => $two, 'c' => $c, 'one' => $one, 'n' => $n, 'q' => $q];
$m->min($r->subtract($k))->loopforeach(function ($i, $params) {
$params['y'] = $params['y']->powMod($params['two'], $params['n'])->add($params['c'])->powMod($params['one'], $params['n']);
$params['q'] = $params['q']->multiply($params['x']->subtract($params['y'])->abs())->powMod($params['one'], $params['n']);
}, $params);
each($params);
$g = $q->gcd($n);
$k = $k->add($m);
}
$r = $r->multiply($two);
}
die;
if ($g->equals($n)) {
while (true) {
$ys = $ys->powMod($two, $n)->add($c)->powMod($one, $n);
$g = $x->subtract($ys)->abs()->gcd($n);
if ($g->compare($one) == 1) {
break;
}
}
}
return $g;
}
public function primefactors($pq, $sort = false)
{
if (function_exists('shell_exec')) {
try {
// Use the python version.
$res = explode(' ', shell_exec('python '.__DIR__.'/getpq.py '.$pq));
if (count($res) == 2) {
return $res;
}
} catch (ErrorException $e) {
}
}
// Else do factorization with wolfram alpha :)))))
$query = 'Do prime factorization of '.$pq;
$params = [
'async' => true,
'banners' => 'raw',
'debuggingdata' => false,
'format' => 'moutput',
'formattimeout' => 8,
'input' => $query,
'output' => 'JSON',
'proxycode' => json_decode(file_get_contents('http://www.wolframalpha.com/api/v1/code'), true)['code'],
];
$url = 'https://www.wolframalpha.com/input/json.jsp?'.http_build_query($params);
$ch = curl_init();
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_HTTPHEADER, ['Referer: https://www.wolframalpha.com/input/?i='.urlencode($query)]);
curl_setopt($ch, CURLOPT_URL, $url);
$res = json_decode(curl_exec($ch), true);
curl_close($ch);
foreach ($res['queryresult']['pods'] as $cur) {
if ($cur['id'] == 'Divisors') {
$res = explode(', ', preg_replace(["/{\d+, /", "/, \d+}$/"], '', $cur['subpods'][0]['moutput']));
break;
}
}
if (count($res) == 2) {
return $res;
}
$factors = [];
$one = new \phpseclib\Math\BigInteger(1);
$two = new \phpseclib\Math\BigInteger(2);
$limit = $n->root()->add($one);
foreach ($this->smallprimes as $checker) {
$checker = new \phpseclib\Math\BigInteger($checker);
if ($limit->compare($checker) == -1) {
break;
}
while ($n->modPow($one, $checker)->toString() == '0') {
$factors[] = $checker;
$n = $n->divide($checker)[0];
$limit = $n->root()->add($one);
if ($limit->compare($checker) == -1) {
break;
}
}
}
if ($n->compare($two) == -1) {
return $factors;
}
while ($n->compare($two) == 1) {
if ($n->isprime()) {
$factors[] = $n;
break;
}
$factor = $this->pollard_brent($n);
$factors[] = $this->primefactors($factor);
$n = floor($n / $factor);
}
if ($sort) {
$factors = sort($factors);
}
return $factors;
}
public function factorization($n)
{
$factors = [];
foreach (primefactors($n) as $p1) {
if (isset($factors[$p1])) {
$factors[$p1] += 1;
} else {
$factors[$p1] = 1;
}
}
return $factors;
}
public function totient($n)
{
$totients = [];
if (($n == 0)) {
return 1;
}
if (isset($totients[$n])) {
return $totients[$n];
}
$tot = 1;
foreach (factorization($n) as $p => $exp) {
$tot *= (($p - 1) * pow($p, ($exp - 1)));
}
$totients[$n] = $tot;
return $tot;
}
public function gcd($a, $b)
{
if (($a == $b)) {
return $a;
}
while (($b > 0)) {
list($a, $b) = [$b, posmod($a, $b)];
}
return $a;
}
public function lcm($a, $b)
{
return floor(abs(($a * $b)) / $this->gcd($a, $b));
}
}
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