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Modifying prime function to make use of BigInteger functino
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danogentili
parent
9e08e6fe8f
commit
f524ae1121
@ -230,6 +230,7 @@ class Session
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$server_nonce = $ResPQ['server_nonce'];
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$public_key_fingerprint = $ResPQ['server_public_key_fingerprints'][0];
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$pq_bytes = $ResPQ['pq'];
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$pq = new \phpseclib\Math\BigInteger($pq_bytes, 256);
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var_dump($this->PrimeModule->primefactors($pq));
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die;
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@ -146,9 +146,8 @@ class Session:
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pq_bytes = ResPQ['pq']
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pq = bytes_to_long(pq_bytes)
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print(prime.pollard_brent(15))
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exit()
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print(prime.primefactors(1724114033281923457))
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exit()
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[p, q] = prime.primefactors(pq)
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if p > q: (p, q) = (q, p)
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assert p*q == pq and p < q
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73
prime.php
73
prime.php
@ -75,40 +75,47 @@ class PrimeModule
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public function pollard_brent($n)
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{
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if ((($n % 2) == 0)) {
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$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 % 3) == 0)) {
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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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$max = new \phpseclib\Math\BigInteger($n - 1);
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$min = new \phpseclib\Math\BigInteger(1);
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list($y, $c, $m) = [(int) $big->random($min, $max)->toString(), (int) $big->random($min, $max)->toString(), (int) $big->random($min, $max)->toString()];
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list($g, $r, $q) = [1, 1, 1];
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while ($g == 1) {
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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 = $y;
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foreach (pyjslib_range($r) as $i) {
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$y = posmod((posmod(pow($y, 2), $n) + $c), $n);
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$range = $r;
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while (!$range->equals($zero)) {
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$y = $y->powMod($two, $n)->add($c)->powMod($one, $n);
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$range = $range->subtract($one);
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}
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$k = 0;
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while (($k < $r) && ($g == 1)) {
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$k = $zero;
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while ($k->compare($r) == -1 && $g->equals($one)) {
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$ys = $y;
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foreach (pyjslib_range(min($m, ($r - $k))) as $i) {
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$y = posmod((posmod(pow($y, 2), $n) + $c), $n);
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$q = posmod(($q * abs($x - $y)), $n);
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$range = $big->min($m, $r->subtract($k));
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while (!$range->equals($zero)) {
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$y = $y->powMod($two, $n)->add($c)->powMod($one, $n);
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$q = $q->multiply($x->subtract($y)->abs())->powMod($one, $n);
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$range = $range->subtract($one);
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}
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$g = $this->gcd($q, $n);
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$k += $m;
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$g = $q->gcd($n);
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$k = $k->add($m);
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}
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$r *= 2;
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$r = $r->multiply($two);
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}
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if (($g == $n)) {
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if ($g->equals($n)) {
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while (true) {
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$ys = posmod((posmod(pow($ys, 2), $n) + $c), $n);
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$g = $this->gcd(abs($x - $ys), $n);
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if ($g > 1) {
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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($one) == 1) {
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break;
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}
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}
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@ -120,25 +127,29 @@ class PrimeModule
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public function primefactors($n, $sort = false)
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{
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$factors = [];
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$limit = $n->root()->add(1);
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$n = new \phpseclib\Math\BigInteger(1724114033281923457);
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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 $checker) {
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if (($limit < $checker)) {
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$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 % $checker) == 0) {
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while ($n->modPow($one, $checker)->toString() == "0") {
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$factors[] = $checker;
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$n = floor($n / $checker);
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$limit = ((int) (pow($n, 0.5)) + 1);
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if (($checker > $limit)) {
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$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 ($n < 2) {
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if ($n->compare($two) == -1) {
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return $factors;
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}
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while ($n > 1) {
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if ($this->isprime($n)) {
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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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26
prime.py
26
prime.py
@ -14,14 +14,7 @@ def primesbelow(N):
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k = (3 * i + 1) | 1
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sieve[k*k // 3::2*k] = [False] * ((N//6 - (k*k)//6 - 1)//k + 1)
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sieve[(k*k + 4*k - 2*k*(i%2)) // 3::2*k] = [False] * ((N // 6 - (k*k + 4*k - 2*k*(i%2))//6 - 1) // k + 1)
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result = []
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for i in range(1, N//3 - correction):
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if sieve[i]:
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result.append((3 * i + 1) | 1)
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return [2, 3] + result
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smallprimes = primesbelow(10000) # might seem low, but 1000*1000 = 1000000, so this will fully factor every composite < 1000000
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return [2, 3] + [(3 * i + 1) | 1 for i in range(1, N//3 - correction) if sieve[i]]
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smallprimeset = set(primesbelow(100000))
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_smallprimeset = 100000
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@ -47,12 +40,12 @@ def isprime(n, precision=7):
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x = pow(a, d, n)
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if x == 1 or x == n - 1: continue
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for r in range(s - 1):
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x = pow(x, 2, n)
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if x == 1: return False
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if x == n - 1: break
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else:
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return False
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else: return False
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return True
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@ -61,19 +54,24 @@ def pollard_brent(n):
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if n % 2 == 0: return 2
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if n % 3 == 0: return 3
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y, c, m = random.randint(1, n-1), random.randint(1, n-1), random.randint(1, n-1)
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y, c, m = 87552211475113995, 330422027228888537, 226866727920975483
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#random.randint(1, n-1), random.randint(1, n-1), random.randint(1, n-1)
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g, r, q = 1, 1, 1
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while g == 1:
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x = y
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for i in range(r):
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y = (pow(y, 2, n) + c) % n
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print(y)
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k = 0
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while k < r and g==1:
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ys = y
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print(min(m, r-k))
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for i in range(min(m, r-k)):
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y = (pow(y, 2, n) + c) % n
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q = q * abs(x-y) % n
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exit()
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g = gcd(q, n)
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k += m
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r *= 2
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@ -86,7 +84,7 @@ def pollard_brent(n):
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return g
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smallprimes = primesbelow(10000) # might seem low, but 1000*1000 = 1000000, so this will fully factor every composite < 1000000
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def primefactors(n, sort=False):
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factors = []
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@ -100,15 +98,17 @@ def primefactors(n, sort=False):
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if checker > limit: break
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if n < 2: return factors
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while n > 1:
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if isprime(n):
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factors.append(n)
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break
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print(pollard_brent(n))
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factor = pollard_brent(n) # trial division did not fully factor, switch to pollard-brent
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factors.extend(primefactors(factor)) # recurse to factor the not necessarily prime factor returned by pollard-brent
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n //= factor
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if sort: factors.sort()
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return factors
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def factorization(n):
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@ -1733,6 +1733,37 @@ class BigInteger
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break;
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}
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}
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/**
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* Return the minimum BigInteger between two BigIntegers.
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*
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*
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* @param \phpseclib\Math\BigInteger $a
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* @param \phpseclib\Math\BigInteger $b
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* @return \phpseclib\Math\BigInteger
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* @access public
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*/
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function min($a, $b) {
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if($a->compare($b) == "1") {
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return $b;
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}
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return $a;
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}
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/**
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* Return the maximum BigInteger between two BigIntegers.
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*
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*
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* @param \phpseclib\Math\BigInteger $a
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* @param \phpseclib\Math\BigInteger $b
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* @return \phpseclib\Math\BigInteger
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* @access public
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*/
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function max($a, $b) {
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if($a->compare($b) == "1") {
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return $a;
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}
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return $b;
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}
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/**
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* Divides a BigInteger by a regular integer
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*
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