/**
* @param $a
* @param $p
* @return int|string
*/
public function squareRootModP($a, $p)
{
if (0 <= $a && $a < $p && 1 < $p) {
if ($a == 0) {
return 0;
}
if ($p == 2) {
return $a;
}
$jac = $this->adapter->jacobi($a, $p);
if ($jac == -1) {
throw new \LogicException($a . " has no square root modulo " . $p);
}
if ($this->adapter->mod($p, 4) == 3) {
return $this->adapter->powmod($a, $this->adapter->div($this->adapter->add($p, 1), 4), $p);
}
if ($this->adapter->mod($p, 8) == 5) {
$d = $this->adapter->powmod($a, $this->adapter->div($this->adapter->sub($p, 1), 4), $p);
if ($d == 1) {
return $this->adapter->powmod($a, $this->adapter->div($this->adapter->add($p, 3), 8), $p);
}
if ($d == $p - 1) {
return $this->adapter->mod($this->adapter->mul($this->adapter->mul(2, $a), $this->adapter->powmod($this->adapter->mul(4, $a), $this->adapter->div($this->adapter->sub($p, 5), 8), $p)), $p);
}
//shouldn't get here
}
for ($b = 2; $b < $p; $b++) {
if ($this->adapter->jacobi($this->adapter->sub($this->adapter->mul($b, $b), $this->adapter->mul(4, $a)), $p) == -1) {
$f = array($a, -$b, 1);
$ff = $this->polynomialPowMod(array(0, 1), $this->adapter->div($this->adapter->add($p, 1), 2), $f, $p);
if ($ff[1] == 0) {
return $ff[0];
}
// if we got here no b was found
}
}
}
throw new \InvalidArgumentException('Unable to calculate square root mod p!');
}
/**
* @param $dividend
* @param $divisor
* @return int|string
*/
public function div($dividend, $divisor)
{
return $this->adapter->mod($this->adapter->mul($dividend, $this->adapter->inverseMod($divisor, $this->modulus)), $this->modulus);
}