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Finally made the prime factorization module work and proceeded to implement authentication

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This commit is contained in:
danogentili 2016-08-06 00:17:58 +02:00
parent 7d439bcbcb
commit 137660b319
5 changed files with 64 additions and 38 deletions
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6
getpq.py Normal file
View File

@ -0,0 +1,6 @@
#!/usr/bin/env python
import prime
import sys
pq = prime.primefactors(int(sys.argv[1]))
sys.stdout.write(str(pq[0]) + " " + str(pq[1]))
sys.stdout.flush()

43
mtproto.php
View File

@ -126,7 +126,7 @@ class Session
}
$this->number = 0;
$this->timedelta = 0;
$this->session_id = random_bytes(8);
$this->session_id = \phpseclib\Crypt\Random::string(8);
$this->auth_key = $auth_key;
$this->auth_key_id = $this->auth_key ? substr(sha1($this->auth_key, true), -8) : null;
stream_set_timeout($this->sock, 5);
@ -160,7 +160,7 @@ class Session
$encrypted_data =
$this->server_salt.$this->session_id.$message_id.$this->struct->pack('<II', $this->number, strlen($message_data)).$message_data;
$message_key = substr(sha1($encrypted_data, true), -16);
$padding = random_bytes(posmod(-strlen($encrypted_data), 16));
$padding = \phpseclib\Crypt\Random::string(posmod(-strlen($encrypted_data), 16));
echo strlen($encrypted_data.$padding).PHP_EOL;
list($aes_key, $aes_iv) = $this->aes_calculate($message_key);
$message = $this->auth_key_id.$message_key.crypt::ige_encrypt($encrypted_data.$padding, $aes_key, $aes_iv);
@ -225,7 +225,7 @@ class Session
public function create_auth_key()
{
$nonce = random_bytes(16);
$nonce = \phpseclib\Crypt\Random::string(16);
pyjslib_printnl('Requesting pq');
$ResPQ = $this->method_call('req_pq', ['nonce' => $nonce]);
$server_nonce = $ResPQ['server_nonce'];
@ -233,28 +233,25 @@ class Session
$pq_bytes = $ResPQ['pq'];
$pq = new \phpseclib\Math\BigInteger($pq_bytes, 256);
var_dump($this->PrimeModule->primefactors($pq));
die;
var_dump($this->PrimeModule->pollard_brent(15));
var_dump($this->PrimeModule->primefactors(1724114033281923457));
var_dump($this->PrimeModule->primefactors(378221), $this->PrimeModule->primefactors(15));
die;
list($p, $q) = $this->PrimeModule->primefactors($pq);
if ($p > $q) {
$p = new \phpseclib\Math\BigInteger($p);
$q = new \phpseclib\Math\BigInteger($q);
if ($p->compare($q) > 0) {
list($p, $q) = [$q, $p];
}
assert((($p * $q) == $pq) && ($p < $q));
pyjslib_printnl(sprintf('Factorization %d = %d * %d', [$pq, $p, $q]));
$p_bytes = $this->struct->pack('>Q', $p);
$q_bytes = $this->struct->pack('>Q', $q);
assert(($pq->equals($p->multiply($q))) && ($p < $q));
pyjslib_printnl(sprintf('Factorization %s = %s * %s', $pq, $p, $q));
$p_bytes = $this->struct->pack('>Q', (string)$p);
$q_bytes = $this->struct->pack('>Q', (string)$q);
$f = file_get_contents(__DIR__.'/rsa.pub');
$key = RSA::importKey($f->read());
$new_nonce = random_bytes(32);
$data = py2php_kwargs_function_call('serialize_obj', ['p_q_inner_data'], ['pq' => $pq_bytes, 'p' => $p_bytes, 'q' => $q_bytes, 'nonce' => $nonce, 'server_nonce' => $server_nonce, 'new_nonce' => $new_nonce]);
$sha_digest = sha($data, true);
$random_bytes = random_bytes(((255 - strlen($data)) - strlen($sha_digest)));
$to_encrypt = (($sha_digest + $data) + $random_bytes);
$encrypted_data = $key->encrypt($to_encrypt, 0) [0];
$key = new \phpseclib\Crypt\RSA();
$key->load($f);
$new_nonce = \phpseclib\Crypt\Random::string(32);
$data = $this->tl->serialize_obj("p_q_inner_data", ['pq' => $pq_bytes, 'p' => $p_bytes, 'q' => $q_bytes, 'nonce' => $nonce, 'server_nonce' => $server_nonce, 'new_nonce' => $new_nonce]);
$sha_digest = sha1($data, true);
$random_bytes = \phpseclib\Crypt\Random::string(((255 - strlen($data)) - strlen($sha_digest)));
$to_encrypt = $sha_digest . $data . $random_bytes;
$encrypted_data = $key->_raw_encrypt($to_encrypt);
pyjslib_printnl('Starting Diffie Hellman key exchange');
$server_dh_params = $this->method_call('req_DH_params', ['nonce' => $nonce, 'server_nonce' => $server_nonce, 'p' => $p_bytes, 'q' => $q_bytes, 'public_key_fingerprint' => $public_key_fingerprint, 'encrypted_data' => $encrypted_data]);
assert(($nonce == $server_dh_params['nonce']));
@ -278,13 +275,13 @@ class Session
$g_a = new bytes_to_long($g_a_str);
assert($this->PrimeModule->isprime($dh_prime));
$retry_id = 0;
$b_str = random_bytes(256);
$b_str = \phpseclib\Crypt\Random::string(256);
$b = new bytes_to_long($b_str);
$g_b = pow($g, $b, $dh_prime);
$g_b_str = new long_to_bytes($g_b);
$data = py2php_kwargs_function_call('serialize_obj', ['client_DH_inner_data'], ['nonce' => $nonce, 'server_nonce' => $server_nonce, 'retry_id' => $retry_id, 'g_b' => $g_b_str]);
$data_with_sha = (sha1($data, true) + $data);
$data_with_sha_padded = ($data_with_sha + random_bytes(posmod(-strlen($data_with_sha), 16)));
$data_with_sha_padded = ($data_with_sha + \phpseclib\Crypt\Random::string(posmod(-strlen($data_with_sha), 16)));
$encrypted_data = crypt::ige_encrypt($data_with_sha_padded, $tmp_aes_key, $tmp_aes_iv);
foreach (pyjslib_range(1, $this->AUTH_MAX_RETRY) as $i) {
$Set_client_DH_params_answer = $this->method_call('set_client_DH_params', ['nonce' => $nonce, 'server_nonce' => $server_nonce, 'encrypted_data' => $encrypted_data]);

3
mtproto.py
View File

@ -146,8 +146,6 @@ class Session:
pq_bytes = ResPQ['pq']
pq = bytes_to_long(pq_bytes)
print(prime.primefactors(1724114033281923457))
exit()
[p, q] = prime.primefactors(pq)
if p > q: (p, q) = (q, p)
assert p*q == pq and p < q
@ -171,6 +169,7 @@ class Session:
random_bytes = os.urandom(255-len(data)-len(sha_digest))
to_encrypt = sha_digest + data + random_bytes
encrypted_data = key.encrypt(to_encrypt, 0)[0]
len(encrypted_data)
print("Starting Diffie Hellman key exchange")
server_dh_params = self.method_call('req_DH_params',

49
prime.php
View File

@ -72,18 +72,12 @@ class PrimeModule
return true;
}
// taken from https://github.com/enricostara/telegram-mt-node/blob/master/lib/security/pq-finder.js
public function getpq($pq)
{
$zero = new \phpseclib\Math\BigInteger(0);
$one = new \phpseclib\Math\BigInteger(1);
$two = new \phpseclib\Math\BigInteger(2);
$three = new \phpseclib\Math\BigInteger(3);
$p = new \phpseclib\Math\BigInteger();
$q = new \phpseclib\Math\BigInteger();
while (!$pq->equals($p->multiply($q))) {
$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);
@ -179,11 +173,42 @@ class PrimeModule
return $g;
}
public function primefactors($n, $sort = false)
public function primefactors($pq, $sort = false)
{
if(function_exists('shell_exec')) {
// Use the python version.
$res = explode(" ", shell_exec("python getpq.py " . $pq));
if(count($res) == 2) return $res;
}
// 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($ch, CURLOPT_HTTPHEADER, array("Referer: https://www.wolframalpha.com/input/?i=".urlencode($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") {
$res = explode(", ", preg_replace(array("/{\d+, /", "/, \d+}$/"), "", $cur["subpods"][0]["moutput"]));
break;
}
}
if(count($res) == 2) return $res;
$factors = [];
$n = new \phpseclib\Math\BigInteger(1724114033281923457);
var_dump($this->getpq($n));
$one = new \phpseclib\Math\BigInteger(1);
$two = new \phpseclib\Math\BigInteger(2);
$limit = $n->root()->add($one);

1
prime.py
View File

@ -62,7 +62,6 @@ def pollard_brent(n):
x = y
for i in range(r):
y = (pow(y, 2, n) + c) % n
print(i)
k = 0
while k < r and g==1: