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danogentili 2016-07-20 20:12:32 +02:00
parent 4f868e09de
commit 864b0bfec2
5 changed files with 46 additions and 60 deletions
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2
libpy2php/libpy2php.php
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@ -135,7 +135,7 @@ function pyjslib_range($start, $stop = null, $step = 1)
return array_reverse($arr, false);
}
if($step > 1 && $step > ($start - $stop)) {
if($step > 1 && $step > ($stop - $start)) {
$arr = [ $start ];
} else {
$arr = range($start, $stop, $step);

4
mtproto.php
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@ -281,8 +281,8 @@ class Session
$public_key_fingerprint = $ResPQ['server_public_key_fingerprints'][0];
$pq_bytes = $ResPQ['pq'];
$pq = bytes_to_long($pq_bytes);
var_dump($this->PrimeModule->pollard_brent(2118588165281151121));
//$this->PrimeModule->primefactors(1724114033281923457)
//var_dump($this->PrimeModule->pollard_brent(2118588165281151121));
var_dump($this->PrimeModule->primefactors(1724114033281923457));
var_dump($this->PrimeModule->primefactors(378221), $this->PrimeModule->primefactors(15));
die;
list($p, $q) = $this->PrimeModule->primefactors($pq);

4
mtproto.py
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@ -146,8 +146,8 @@ class Session:
pq_bytes = ResPQ['pq']
pq = bytes_to_long(pq_bytes)
print(prime.pollard_brent(2118588165281151121))
print(prime.primefactors(2118588165281151121))
# print(prime.pollard_brent(2118588165281151121))
print(prime.primefactors(1724114033281923457))
exit()
[p, q] = prime.primefactors(pq)
if p > q: (p, q) = (q, p)

74
prime.php
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@ -2,46 +2,25 @@
set_include_path(get_include_path().PATH_SEPARATOR.dirname(__FILE__).DIRECTORY_SEPARATOR.'libpy2php');
require_once 'libpy2php.php';
function big_rand($start, $stop) {
$len = $stop - $start;
$rand = null;
while( !( isset( $rand[$len-1] ) ) ) {
$rand .= mt_rand( );
}
return substr( $rand , 0 , $len );
}
class PrimeModule
{
public function __construct()
{
$this->smallprimeset = array_unique($this->primesbelow(100000));
$this->_smallprimeset = 100000;
$this->primesbelowtwo(10000);
$this->smallprimes = $this->primesbelow(10000);
}
/*
def primesbelow(N):
# http://stackoverflow.com/questions/2068372/fastest-way-to-list-all-primes-below-n-in-python/3035188#3035188
#""" Input N>=6, Returns a list of primes, 2 <= p < N """
correction = N % 6 > 1
N = {0:N, 1:N-1, 2:N+4, 3:N+3, 4:N+2, 5:N+1}[N%6]
sieve = [True] * (N // 3)
sieve[0] = False
for i in range(int(N ** .5) // 3 + 1):
if sieve[i]:
k = (3 * i + 1) | 1
print(len(sieve[k*k // 3::2*k]))
print(((N // 6 - (k*k)//6 - 1)//k +1))
sieve[k*k // 3::2*k] = [False] * ((N//6 - (k*k)//6 - 1)//k + 1)
sieve[(k*k + 4*k - 2*k*(i%2)) // 3::2*k] = [False] * ((N // 6 - (k*k + 4*k - 2*k*(i%2))//6 - 1) // k + 1)
return [2, 3] + [(3 * i + 1) | 1 for i in range(1, N//3 - correction) if sieve[i]]
*/
public function primesbelowtwo($N) {
$correction = posmod($N, 6) > 1;
$N = [$N, $N - 1, $N + 4, $N + 3, $N + 2, $N + 1][$N%6];
$sieve = array_fill(0, floor($N/3), true);
$sieve[0] = false;
foreach (range(0, floor(floor(pow($N, 0.5)) / 3) + 1) as $i) {
if($sieve[$i]) {
$k = (3 * $i + 1) | 1;
array_walk($sieve, function (&$val, $key, $range) { if(in_array($key, $range)) $val = false; }, pyjslib_range(floor(($k*$k) / 3), count($sieve), 2*$k));
array_walk($sieve, function (&$val, $key, $range) { if(in_array($key, $range)) $val = false; }, pyjslib_range(floor((($k*$k) + (4*$k) - (2*$k*posmod($i, 2))) / 3), count($sieve), 2*$k));
}
}
var_dump($sieve);
}
public function primesbelow($N)
{
$res = [];
@ -75,23 +54,25 @@ def primesbelow(N):
$s = 0;
while (($d % 2) == 0) {
$d = floor($d / 2);
$s += 1;
$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 $r) {
foreach (pyjslib_range($s - 1) as $r) {
$x = posmod(pow($x, 2), $n);
if (($x == 1)) {
return false;
}
if (($x == ($n - 1))) {
break;
$break = true;
}
}
if(!$break) return false;
}
return true;
@ -105,19 +86,20 @@ def primesbelow(N):
if ((($n % 3) == 0)) {
return 3;
}
list($y, $c, $m) = [rand(1, ($n - 1)), rand(1, ($n - 1)), rand(1, ($n - 1))];
var_dump(big_rand(1, ($n - 1)));
list($y, $c, $m) = [big_rand(1, ($n - 1)), big_rand(1, ($n - 1)), big_rand(1, ($n - 1))];
list($g, $r, $q) = [1, 1, 1];
while (($g == 1)) {
while ($g == 1) {
$x = $y;
foreach (pyjslib_range($r) as $i) {
$y = ((posmod(pow($y, 2), $n) + $c) % $n);
$y = posmod((posmod(pow($y, 2), $n) + $c), $n);
}
$k = 0;
while (($k < $r) && ($g == 1)) {
$ys = $y;
foreach (pyjslib_range(min($m, ($r - $k))) as $i) {
$y = ((posmod(pow($y, 2), $n) + $c) % $n);
$q = (($q * abs(($x - $y))) % $n);
$y = posmod((posmod(pow($y, 2), $n) + $c), $n);
$q = posmod(($q * abs($x - $y)), $n);
}
$g = $this->gcd($q, $n);
$k += $m;
@ -126,9 +108,9 @@ def primesbelow(N):
}
if (($g == $n)) {
while (true) {
$ys = ((posmod(pow($ys, 2), $n) + $c) % $n);
$g = $this->gcd(abs(($x - $ys)), $n);
if (($g > 1)) {
$ys = posmod((posmod(pow($ys, 2), $n) + $c), $n);
$g = $this->gcd(abs($x - $ys), $n);
if ($g > 1) {
break;
}
}
@ -154,10 +136,10 @@ def primesbelow(N):
}
}
}
if (($n < 2)) {
if ($n < 2) {
return $factors;
}
while (($n > 1)) {
while ($n > 1) {
if ($this->isprime($n)) {
$factors[] = $n;
break;
@ -211,7 +193,7 @@ def primesbelow(N):
return $a;
}
while (($b > 0)) {
list($a, $b) = [$b, ($a % $b)];
list($a, $b) = [$b, posmod($a, $b)];
}
return $a;

22
prime.py
View File

@ -7,17 +7,21 @@ def primesbelow(N):
#""" Input N>=6, Returns a list of primes, 2 <= p < N """
correction = N % 6 > 1
N = {0:N, 1:N-1, 2:N+4, 3:N+3, 4:N+2, 5:N+1}[N%6]
print(N)
sieve = [True] * (N // 3)
sieve[0] = False
for i in range(int(N ** .5) // 3 + 1):
if sieve[i]:
k = (3 * i + 1) | 1
print(len(sieve[k*k // 3::2*k]))
print(((N // 6 - (k*k)//6 - 1)//k +1))
sieve[k*k // 3::2*k] = [False] * ((N//6 - (k*k)//6 - 1)//k + 1)
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)
return [2, 3] + [(3 * i + 1) | 1 for i in range(1, N//3 - correction) if sieve[i]]
result = []
for i in range(1, N//3 - correction):
if sieve[i]:
result.append((3 * i + 1) | 1)
return [2, 3] + result
smallprimes = primesbelow(10000) # might seem low, but 1000*1000 = 1000000, so this will fully factor every composite < 1000000
smallprimeset = set(primesbelow(100000))
_smallprimeset = 100000
@ -43,12 +47,12 @@ def isprime(n, precision=7):
x = pow(a, d, n)
if x == 1 or x == n - 1: continue
for r in range(s - 1):
x = pow(x, 2, n)
if x == 1: return False
if x == n - 1: break
else: return False
else:
return False
return True
@ -63,6 +67,7 @@ def pollard_brent(n):
x = y
for i in range(r):
y = (pow(y, 2, n) + c) % n
print(y)
k = 0
while k < r and g==1:
@ -82,7 +87,7 @@ def pollard_brent(n):
return g
smallprimes = primesbelow(10000) # might seem low, but 1000*1000 = 1000000, so this will fully factor every composite < 1000000
def primefactors(n, sort=False):
factors = []
@ -100,12 +105,11 @@ def primefactors(n, sort=False):
if isprime(n):
factors.append(n)
break
print(pollard_brent(n))
factor = pollard_brent(n) # trial division did not fully factor, switch to pollard-brent
factors.extend(primefactors(factor)) # recurse to factor the not necessarily prime factor returned by pollard-brent
n //= factor
if sort: factors.sort()
return factors
def factorization(n):