/**
* 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 Math_BigInteger $x
* @return Math_BigInteger
*/
function _exponentiate($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 Math_BigInteger(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;
}
/**
* generation of a position, logoot algorithm
* @param <Object> $start is the previous logootPosition
* @param <Object> $end is the next logootPosition
* @param <Integer> $N number of positions generated (should be 1 in our case)
* @param <Object> $sid session id
* @return <Object> a logootPosition between $start and $end
*/
private function getLogootPosition($start, $end, $N, $sid)
{
$result = array();
$Id_Max = LogootId::IdMax();
$Id_Min = LogootId::IdMin();
$i = 0;
$pos = array();
$currentPosition = new LogootPosition($pos);
// voir constructeur
$inf = new Math_BigInteger("0");
$sup = new Math_BigInteger("0");
$isInf = false;
while (true) {
$inf = new Math_BigInteger($start->get($i)->getInt());
if ($isInf == true) {
$sup = new Math_BigInteger(INT_MAX);
} else {
$sup = new Math_BigInteger($end->get($i)->getInt());
}
$tmpVal = $sup->subtract($inf);
$tmpVal1 = $tmpVal->subtract(new Math_BigInteger("1"));
if ($tmpVal1->compare($N) > 0) {
// inf = start.get(i).getInteger();
// sup = end.get(i).getInteger();
break;
}
$currentPosition->add($start->get($i));
$i++;
if ($i == $start->size()) {
$start->add($Id_Min);
}
if ($i == $end->size()) {
$end->add($Id_Max);
}
if ($inf->compare($sup) < 0) {
$isInf = true;
}
}
$binf = $inf->add(new Math_BigInteger("1"));
$bsup = $sup->subtract(new Math_BigInteger("1"));
$slot = $bsup->subtract($binf);
$stepTmp = $slot->divide($N);
$step = $stepTmp[0];
// quotient, [1] is the remainder
$old = clone $currentPosition;
if ($step->compare(new Math_BigInteger(INT_MAX)) > 0) {
$lstep = new Math_BigInteger(INT_MAX);
$r = clone $currentPosition;
$tmpVal2 = $inf->random($inf, $sup);
$r->set($i, $tmpVal2->toString(), $sid);
$result[] = $r;
// result est une arraylist<Position>
return $result;
} else {
$lstep = $step;
}
if ($lstep->compare(new Math_BigInteger("0")) == 0) {
$lstep = new Math_BigInteger("1");
}
$p = clone $currentPosition;
$p->set($i, $inf->toString(), $sid);
$tmpVal3 = (int) $N->toString();
for ($j = 0; $j < $tmpVal3; $j++) {
$r = clone $p;
if (!($lstep->compare(new Math_BigInteger("1")) == 0)) {
$tmpVal4 = new Math_BigInteger($p->get($i)->getInt());
$tmpVal5 = $tmpVal4->add($lstep);
// max
$tmpVal6 = new Math_BigInteger($p->get($i)->getInt());
// min
$add = $tmpVal6->random($tmpVal6, $tmpVal5);
$r->set($i, $add->toString(), $sid);
} else {
$r->add1($i, new Math_BigInteger("1"), $sid);
}
$result[] = clone $r;
// voir
$old = clone $r;
$tmpVal7 = new Math_BigInteger($p->get($i)->getInt());
$tmpVal7 = $tmpVal7->add($lstep);
$p->set($i, $tmpVal7->toString(), $sid);
}
return $result;
}
