/** * 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; }