/**
* Create public / private key pair
*
* Returns an array with the following three elements:
* - 'privatekey': The private key.
* - 'publickey': The public key.
* - 'partialkey': A partially computed key (if the execution time exceeded $timeout).
* Will need to be passed back to CryptRSA::createKey() as the third parameter for further processing.
*
* @access public
* @param optional Integer $bits
* @param optional Integer $timeout
* @param optional MathBigInteger $p
*/
function createKey($bits = 1024, $timeout = false, $partial = array())
{
if (!defined('CRYPT_RSA_EXPONENT')) {
// http://en.wikipedia.org/wiki/65537_%28number%29
define('CRYPT_RSA_EXPONENT', '65537');
}
// per <http://cseweb.ucsd.edu/~hovav/dist/survey.pdf#page=5>, this number ought not result in primes smaller
// than 256 bits. as a consequence if the key you're trying to create is 1024 bits and you've set CRYPT_RSA_SMALLEST_PRIME
// to 384 bits then you're going to get a 384 bit prime and a 640 bit prime (384 + 1024 % 384). at least if
// CRYPT_RSA_MODE is set to CRYPT_RSA_MODE_INTERNAL. if CRYPT_RSA_MODE is set to CRYPT_RSA_MODE_OPENSSL then
// CRYPT_RSA_SMALLEST_PRIME is ignored (ie. multi-prime RSA support is more intended as a way to speed up RSA key
// generation when there's a chance neither gmp nor OpenSSL are installed)
if (!defined('CRYPT_RSA_SMALLEST_PRIME')) {
define('CRYPT_RSA_SMALLEST_PRIME', 4096);
}
// OpenSSL uses 65537 as the exponent and requires RSA keys be 384 bits minimum
if (CRYPT_RSA_MODE == CRYPT_RSA_MODE_OPENSSL && $bits >= 384 && CRYPT_RSA_EXPONENT == 65537) {
$inst = Configuration::getInstance();
$cnfPath = Utils::path_concat($inst->get('base_path'), $inst->get('var_path'), 'openssl.cnf');
$rsa = openssl_pkey_new(array('private_key_bits' => $bits, 'config' => $cnfPath));
openssl_pkey_export($rsa, $privatekey, NULL, array('config' => $cnfPath));
$publickey = openssl_pkey_get_details($rsa);
$publickey = $publickey['key'];
$privatekey = call_user_func_array(array($this, '_convertPrivateKey'), array_values($this->_parseKey($privatekey, CRYPT_RSA_PRIVATE_FORMAT_PKCS1)));
$publickey = call_user_func_array(array($this, '_convertPublicKey'), array_values($this->_parseKey($publickey, CRYPT_RSA_PUBLIC_FORMAT_PKCS1)));
// clear the buffer of error strings stemming from a minimalistic openssl.cnf
while (openssl_error_string() !== false) {
}
return array('privatekey' => $privatekey, 'publickey' => $publickey, 'partialkey' => false);
}
static $e;
if (!isset($e)) {
$e = new MathBigInteger(CRYPT_RSA_EXPONENT);
}
extract($this->_generateMinMax($bits));
$absoluteMin = $min;
$temp = $bits >> 1;
// divide by two to see how many bits P and Q would be
if ($temp > CRYPT_RSA_SMALLEST_PRIME) {
$num_primes = floor($bits / CRYPT_RSA_SMALLEST_PRIME);
$temp = CRYPT_RSA_SMALLEST_PRIME;
} else {
$num_primes = 2;
}
extract($this->_generateMinMax($temp + $bits % $temp));
$finalMax = $max;
extract($this->_generateMinMax($temp));
$generator = new MathBigInteger();
$generator->setRandomGenerator('crypt_random');
$n = $this->one->copy();
if (!empty($partial)) {
extract(unserialize($partial));
} else {
$exponents = $coefficients = $primes = array();
$lcm = array('top' => $this->one->copy(), 'bottom' => false);
}
$start = time();
$i0 = count($primes) + 1;
do {
for ($i = $i0; $i <= $num_primes; $i++) {
if ($timeout !== false) {
$timeout -= time() - $start;
$start = time();
if ($timeout <= 0) {
return array('privatekey' => '', 'publickey' => '', 'partialkey' => serialize(array('primes' => $primes, 'coefficients' => $coefficients, 'lcm' => $lcm, 'exponents' => $exponents)));
}
}
if ($i == $num_primes) {
list($min, $temp) = $absoluteMin->divide($n);
if (!$temp->equals($this->zero)) {
$min = $min->add($this->one);
// ie. ceil()
}
$primes[$i] = $generator->randomPrime($min, $finalMax, $timeout);
} else {
$primes[$i] = $generator->randomPrime($min, $max, $timeout);
}
if ($primes[$i] === false) {
// if we've reached the timeout
if (count($primes) > 1) {
$partialkey = '';
} else {
array_pop($primes);
$partialkey = serialize(array('primes' => $primes, 'coefficients' => $coefficients, 'lcm' => $lcm, 'exponents' => $exponents));
}
return array('privatekey' => '', 'publickey' => '', 'partialkey' => $partialkey);
}
// the first coefficient is calculated differently from the rest
// ie. instead of being $primes[1]->modInverse($primes[2]), it's $primes[2]->modInverse($primes[1])
if ($i > 2) {
$coefficients[$i] = $n->modInverse($primes[$i]);
}
$n = $n->multiply($primes[$i]);
$temp = $primes[$i]->subtract($this->one);
// textbook RSA implementations use Euler's totient function instead of the least common multiple.
// see http://en.wikipedia.org/wiki/Euler%27s_totient_function
$lcm['top'] = $lcm['top']->multiply($temp);
$lcm['bottom'] = $lcm['bottom'] === false ? $temp : $lcm['bottom']->gcd($temp);
$exponents[$i] = $e->modInverse($temp);
}
list($lcm) = $lcm['top']->divide($lcm['bottom']);
$gcd = $lcm->gcd($e);
$i0 = 1;
} while (!$gcd->equals($this->one));
$d = $e->modInverse($lcm);
$coefficients[2] = $primes[2]->modInverse($primes[1]);
// from <http://tools.ietf.org/html/rfc3447#appendix-A.1.2>:
// RSAPrivateKey ::= SEQUENCE {
// version Version,
// modulus INTEGER, -- n
// publicExponent INTEGER, -- e
// privateExponent INTEGER, -- d
// prime1 INTEGER, -- p
// prime2 INTEGER, -- q
// exponent1 INTEGER, -- d mod (p-1)
// exponent2 INTEGER, -- d mod (q-1)
// coefficient INTEGER, -- (inverse of q) mod p
// otherPrimeInfos OtherPrimeInfos OPTIONAL
// }
return array('privatekey' => $this->_convertPrivateKey($n, $e, $d, $primes, $exponents, $coefficients), 'publickey' => $this->_convertPublicKey($n, $e), 'partialkey' => false);
}
/**
* DSA verify
*
* @param string $message message
* @param string $hash_alg hash algorithm
* @param MathBigInteger $r r
* @param MathBigInteger $s s
* @param MathBigInteger $p p
* @param MathBigInteger $q q
* @param MathBigInteger $g g
* @param MathBigInteger $y public key
* @return bool
*/
public static function verify($message, $hash_alg, $r, $s, $p, $q, $g, $y)
{
$hash = new CryptHash($hash_alg);
$hash_m = new MathBigInteger($hash->hash($message), 256);
$w = $s->modInverse($q);
$hash_m_mul = $hash_m->multiply($w);
$u1_base = $hash_m_mul->divide($q);
$u1 = $u1_base[1];
$r_mul = $r->multiply($w);
$u2_base = $r_mul->divide($q);
$u2 = $u2_base[1];
$g_pow = $g->modPow($u1, $p);
$y_pow = $y->modPow($u2, $p);
$g_pow_mul = $g_pow->multiply($y_pow);
$g_pow_mul_mod_base = $g_pow_mul->divide($p);
$g_pow_mul_mod = $g_pow_mul_mod_base[1];
$v_base = $g_pow_mul_mod->divide($q);
$v = $v_base[1];
return $v->compare($r) == 0;
}
