/**
* Exponentiate with or without Chinese Remainder Theorem
*
* See {@link http://tools.ietf.org/html/rfc3447#section-5.1.1 RFC3447#section-5.1.2}.
*
* @access private
* @param MathBigInteger $x
* @return MathBigInteger
*/
function _exponentiate($x)
{
if (empty($this->primes) || empty($this->coefficients) || empty($this->exponents)) {
return $x->modPow($this->exponent, $this->modulus);
}
$num_primes = count($this->primes);
if (defined('CRYPT_RSA_DISABLE_BLINDING')) {
$m_i = array(1 => $x->modPow($this->exponents[1], $this->primes[1]), 2 => $x->modPow($this->exponents[2], $this->primes[2]));
$h = $m_i[1]->subtract($m_i[2]);
$h = $h->multiply($this->coefficients[2]);
list(, $h) = $h->divide($this->primes[1]);
$m = $m_i[2]->add($h->multiply($this->primes[2]));
$r = $this->primes[1];
for ($i = 3; $i <= $num_primes; $i++) {
$m_i = $x->modPow($this->exponents[$i], $this->primes[$i]);
$r = $r->multiply($this->primes[$i - 1]);
$h = $m_i->subtract($m);
$h = $h->multiply($this->coefficients[$i]);
list(, $h) = $h->divide($this->primes[$i]);
$m = $m->add($r->multiply($h));
}
} else {
$smallest = $this->primes[1];
for ($i = 2; $i <= $num_primes; $i++) {
if ($smallest->compare($this->primes[$i]) > 0) {
$smallest = $this->primes[$i];
}
}
$one = new MathBigInteger(1);
$one->setRandomGenerator('crypt_random');
$r = $one->random($one, $smallest->subtract($one));
$m_i = array(1 => $this->_blind($x, $r, 1), 2 => $this->_blind($x, $r, 2));
$h = $m_i[1]->subtract($m_i[2]);
$h = $h->multiply($this->coefficients[2]);
list(, $h) = $h->divide($this->primes[1]);
$m = $m_i[2]->add($h->multiply($this->primes[2]));
$r = $this->primes[1];
for ($i = 3; $i <= $num_primes; $i++) {
$m_i = $this->_blind($x, $r, $i);
$r = $r->multiply($this->primes[$i - 1]);
$h = $m_i->subtract($m);
$h = $h->multiply($this->coefficients[$i]);
list(, $h) = $h->divide($this->primes[$i]);
$m = $m->add($r->multiply($h));
}
}
return $m;
}