/**
* Performs RSA Blinding
*
* Protects against timing attacks by employing RSA Blinding.
* Returns $x->modPow($this->exponents[$i], $this->primes[$i])
*
* @access private
* @param MathBigInteger $x
* @param MathBigInteger $r
* @param Integer $i
* @return MathBigInteger
*/
function _blind($x, $r, $i)
{
$x = $x->multiply($r->modPow($this->publicExponent, $this->primes[$i]));
$x = $x->modPow($this->exponents[$i], $this->primes[$i]);
$r = $r->modInverse($this->primes[$i]);
$x = $x->multiply($r);
list(, $x) = $x->divide($this->primes[$i]);
return $x;
}
/**
* 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;
}