302 lines
9.6 KiB
PHP
302 lines
9.6 KiB
PHP
<?php
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set_include_path(get_include_path().PATH_SEPARATOR.dirname(__FILE__).DIRECTORY_SEPARATOR.'libpy2php');
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require_once 'libpy2php.php';
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class PrimeModule
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{
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public function __construct()
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{
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$this->smallprimeset = array_unique($this->primesbelow(100000));
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$this->_smallprimeset = 100000;
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$this->smallprimes = $this->primesbelow(10000);
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}
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public function primesbelow($N)
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{
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$res = [];
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for ($i = 2; $i <= $N; $i++) {
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if ($i % 2 != 1 && $i != 2) {
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continue;
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}
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$d = 3;
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$x = sqrt($i);
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while ($i % $d != 0 && $d < $x) {
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$d += 2;
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}
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if ((($i % $d == 0 && $i != $d) * 1) == 0) {
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$res[] = $i;
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}
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}
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return $res;
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}
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public function isprime($n, $precision = 7)
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{
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if (($n == 1) || (($n % 2) == 0)) {
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return false;
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} elseif (($n < 1)) {
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throw new Exception('Out of bounds, first argument must be > 0');
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} elseif (($n < $this->_smallprimeset)) {
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return in_array($n, $this->smallprimeset);
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}
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$d = ($n - 1);
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$s = 0;
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while (($d % 2) == 0) {
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$d = floor($d / 2);
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$s++;
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}
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$break = false;
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foreach (pyjslib_range($precision) as $repeat) {
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$a = rand(2, ($n - 2));
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$x = posmod(pow($a, $d), $n);
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if (($x == 1) || ($x == ($n - 1))) {
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continue;
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}
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foreach (pyjslib_range($s - 1) as $r) {
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$x = posmod(pow($x, 2), $n);
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if (($x == 1)) {
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return false;
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}
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if (($x == ($n - 1))) {
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$break = true;
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}
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}
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if (!$break) {
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return false;
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}
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}
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return true;
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}
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// taken from https://github.com/enricostara/telegram-mt-node/blob/master/lib/security/pq-finder.js
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public function getpq($pq)
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{
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$p = 0;
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$q = 0;
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while ($pq != $p * $q && $p != 0) {
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for ($i = 0; $i < 3; $i++) {
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$q = new \phpseclib\Math\BigInteger((random_int(0, 128) & 15) + 17);
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$x = new \phpseclib\Math\BigInteger(random_int(0, 1000000000) + 1);
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$y = $x;
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$lim = 1 << ($i + 18);
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for ($j = 1; $j < $lim; $j++) {
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$a = $x;
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$b = $x;
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$c = $q;
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while (!$b->equals($zero)) {
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if ($b->powMod($one, $two)->equals($zero)) {
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$c = $c->add($a);
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if ($c->compare($pq) > 0) {
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$c = $c->subtract($pq);
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}
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}
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$a = $a->add($a);
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if ($a->compare($pq) > 0) {
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$a = $a->subtract($pq);
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}
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$b = $b->rightShift(1);
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}
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$x = $c;
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$z = ($y->compare($x) > 0) ? $y->subtract($x) : $x->subtract($y);
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$p = $z->gcd($pq);
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if (!$p->equals($one)) {
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break;
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}
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if (($j & ($j - 1)) === 0) {
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$y = $x;
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}
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}
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if (prime.gt(BigInteger.One())) {
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break;
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}
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}
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$q = $pq->divide(prime)[0];
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}
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$_pq = ($q->compare($p) > 0) ? [$p, $q] : [$q, $p];
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return $_pq;
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}
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public function pollard_brent($n)
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{
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$zero = new \phpseclib\Math\BigInteger(0);
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$one = new \phpseclib\Math\BigInteger(1);
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$two = new \phpseclib\Math\BigInteger(2);
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$three = new \phpseclib\Math\BigInteger(3);
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if ($n->powMod($one, $two)->toString() == '0') {
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return 2;
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}
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if ($n->powMod($one, $three)->toString() == '0') {
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return 3;
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}
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$big = new \phpseclib\Math\BigInteger();
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$max = $n->subtract($one);
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list($y, $c, $m) = [new \phpseclib\Math\BigInteger(87552211475113995), new \phpseclib\Math\BigInteger(330422027228888537), new \phpseclib\Math\BigInteger(226866727920975483)];
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//[$big->random($one, $max), $big->random($one, $max), $big->random($one, $max)];
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list($g, $r, $q) = [$one, $one, $one];
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while ($g->equals($one)) {
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$x = $y;
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$params = ['y' => $y, 'two' => $two, 'c' => $c, 'one' => $one, 'n' => $n];
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$r->loopforeach(function ($i, $params) {
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$params['y'] = $params['y']->powMod($params['two'], $params['n'])->add($params['c'])->powMod($params['one'], $params['n']);
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}, $params);
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each($params);
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$k = $zero;
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while ($k->compare($r) == -1 && $g->equals($one)) {
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$ys = $y;
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$params = ['x' => $x, 'y' => $y, 'two' => $two, 'c' => $c, 'one' => $one, 'n' => $n, 'q' => $q];
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$m->min($r->subtract($k))->loopforeach(function ($i, $params) {
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$params['y'] = $params['y']->powMod($params['two'], $params['n'])->add($params['c'])->powMod($params['one'], $params['n']);
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$params['q'] = $params['q']->multiply($params['x']->subtract($params['y'])->abs())->powMod($params['one'], $params['n']);
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}, $params);
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each($params);
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$g = $q->gcd($n);
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$k = $k->add($m);
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}
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$r = $r->multiply($two);
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}
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die;
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if ($g->equals($n)) {
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while (true) {
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$ys = $ys->powMod($two, $n)->add($c)->powMod($one, $n);
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$g = $x->subtract($ys)->abs()->gcd($n);
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if ($g->compare($one) == 1) {
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break;
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}
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}
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}
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return $g;
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}
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public function primefactors($pq, $sort = false)
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{
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if (function_exists('shell_exec')) {
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// Use the python version.
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$res = explode(' ', shell_exec('python getpq.py '.$pq));
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if (count($res) == 2) {
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return $res;
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}
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}
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// Else do factorization with wolfram alpha :)))))
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$query = 'Do prime factorization of '.$pq;
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$params = [
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'async' => true,
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'banners' => 'raw',
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'debuggingdata' => false,
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'format' => 'moutput',
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'formattimeout' => 8,
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'input' => $query,
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'output' => 'JSON',
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'proxycode' => json_decode(file_get_contents('http://www.wolframalpha.com/api/v1/code'), true)['code'],
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];
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$url = 'https://www.wolframalpha.com/input/json.jsp?'.http_build_query($params);
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$ch = curl_init();
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curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
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curl_setopt($ch, CURLOPT_HTTPHEADER, ['Referer: https://www.wolframalpha.com/input/?i='.urlencode($query)]);
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curl_setopt($ch, CURLOPT_URL, $url);
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$res = json_decode(curl_exec($ch), true);
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curl_close($ch);
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foreach ($res['queryresult']['pods'] as $cur) {
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if ($cur['id'] == 'Divisors') {
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$res = explode(', ', preg_replace(["/{\d+, /", "/, \d+}$/"], '', $cur['subpods'][0]['moutput']));
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break;
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}
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}
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if (count($res) == 2) {
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return $res;
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}
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$factors = [];
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$one = new \phpseclib\Math\BigInteger(1);
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$two = new \phpseclib\Math\BigInteger(2);
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$limit = $n->root()->add($one);
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foreach ($this->smallprimes as $checker) {
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$checker = new \phpseclib\Math\BigInteger($checker);
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if ($limit->compare($checker) == -1) {
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break;
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}
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while ($n->modPow($one, $checker)->toString() == '0') {
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$factors[] = $checker;
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$n = $n->divide($checker)[0];
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$limit = $n->root()->add($one);
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if ($limit->compare($checker) == -1) {
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break;
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}
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}
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}
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if ($n->compare($two) == -1) {
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return $factors;
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}
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while ($n->compare($two) == 1) {
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if ($n->isprime()) {
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$factors[] = $n;
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break;
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}
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$factor = $this->pollard_brent($n);
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$factors[] = $this->primefactors($factor);
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$n = floor($n / $factor);
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}
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if ($sort) {
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$factors = sort($factors);
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}
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return $factors;
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}
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public function factorization($n)
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{
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$factors = [];
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foreach (primefactors($n) as $p1) {
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if (isset($factors[$p1])) {
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$factors[$p1] += 1;
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} else {
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$factors[$p1] = 1;
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}
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}
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return $factors;
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}
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public function totient($n)
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{
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$totients = [];
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if (($n == 0)) {
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return 1;
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}
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if (isset($totients[$n])) {
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return $totients[$n];
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}
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$tot = 1;
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foreach (factorization($n) as $p => $exp) {
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$tot *= (($p - 1) * pow($p, ($exp - 1)));
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}
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$totients[$n] = $tot;
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return $tot;
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}
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public function gcd($a, $b)
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{
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if (($a == $b)) {
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return $a;
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}
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while (($b > 0)) {
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list($a, $b) = [$b, posmod($a, $b)];
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}
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return $a;
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}
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public function lcm($a, $b)
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{
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return floor(abs(($a * $b)) / $this->gcd($a, $b));
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}
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}
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