function powmod($base, $exponent, $modulus)
{
if (function_exists('gmp_powm')) {
// fast
return gmp_strval(gmp_powm($base, $exponent, $modulus));
}
if (function_exists('bi_powmod')) {
// not tested
return bi_sto_str(bi_powmod($base, $exponent, $modulus));
}
if (function_exists('bcpowmod')) {
// slow
return bcpowmod($base, $exponent, $modulus);
}
// emulation, slow
$square = bcmod($base, $modulus);
$result = 1;
while (bccomp($exponent, 0) > 0) {
if (bcmod($exponent, 2)) {
$result = bcmod(bcmul($result, $square), $modulus);
}
$square = bcmod(bcmul($square, $square), $modulus);
$exponent = bcdiv($exponent, 2);
}
return $result;
}
/**
encrypts / decrypts $text with key ($e, $n)
*/
function encrypt_text($text, $e, $n)
{
$tmp = bi_unserialize($text);
$e = bi_unserialize($e);
$n = bi_unserialize($n);
if (bi_cmp($tmp, $n) >= 0) {
die('$text is too long to encrypt by key with length ' . bi_bit_len($n) . ' bits' . "<br/>\n");
}
return bi_serialize(bi_powmod($tmp, $e, $n));
}
/**
* Calculates pow($num, $pow) (mod $mod)
*
* @param big_int resource $num
* @param big_int resource $pow
* @param big_int resource $mod
* @return big_int resource
* @access public
*/
function powmod($num, $pow, $mod)
{
return bi_powmod($num, $pow, $mod);
}
/**
* Generates the secret key using the private key and prime
*
* @param string Public key passed in by the request
*
* @return string String containing the shared secret
*/
function fetch_shared_secret($foreignpubkey)
{
$this->secret = bi_powmod($foreignpubkey, $this->privatekey, $this->prime);
return $this->secret;
}
public static function powmod($x, $y, $m)
{
switch (BigInt::support()) {
case 'gmp':
return gmp_powm($x, $y, $m);
case 'big_int':
return bi_powmod($x, $y, $m);
case 'bcmath':
return bcpowmod($x, $y, $m);
case '':
default:
return BigInt::_powmod($x, $y, $m);
}
}
function bcpowmod($a, $b, $c)
{
return bi_to_str(bi_powmod($a, $b, $c));
}
function powm($base, $exponent, $modulus)
{
if (function_exists('gmp_powm')) {
return gmp_strval(gmp_powm($base, $exponent, $modulus));
} else {
if (function_exists('bi_powmod')) {
return bi_sto_str(bi_powmod($base, $exponent, $modulus));
} else {
if (function_exists('bcpowmod')) {
return bcpowmod($base, $exponent, $modulus);
} else {
if (preg_match("/^\\d+,\\d+,\\d+\$/", "{$base},{$exponent},{$modulus}")) {
//@FIX: this is insecure - a bi-directional proc_open() is required
if (is_executable("/usr/bin/python")) {
$r = trim(`python -c "print pow({$base}, {$exponent}, {$modulus})"`);
} else {
$r = trim(`perl -e "use Math::BigInt; print Math::BigInt->new('{$base}')->bmodpow('{$exponent}', '{$modulus}')->bstr();"`);
}
if (preg_match("/^\\d+\$/", $r)) {
return $r;
}
}
}
}
}
trigger_error("powmod: unsupported or non-integer argument", E_USER_ERROR);
}
function bigint_powmod($x, $y, $m)
{
return bi_powmod($x, $y, $m);
}
/*
functions for modular arithmetic calculations
*/
echo '<h3>modular arithmetic functions</h3>' . "\n";
// find next pseudoprime number after $c
$modulus = bi_next_prime($c);
echo '$modulus = next_prime($c) = [', bi_to_str($modulus), "]<br/>\n";
$c = bi_addmod($a, $b, $modulus);
echo '$a + $b (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_submod($a, $b, $modulus);
echo '$a - $b (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_mulmod($a, $b, $modulus);
echo '$a * $b (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_divmod($a, $b, $modulus);
echo '$a / $b (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_powmod($a, $b, $modulus);
echo 'pow($a, $b) (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_factmod(1000, $modulus);
echo '1000! (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_absmod(-1, $modulus);
echo '-1 (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_invmod($a, $modulus);
echo '1 / $a (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
$c = bi_sqrmod($a, $modulus);
echo 'sqr($a) (mod $modulus) = [', bi_to_str($c), "]<br/>\n";
echo 'cmp($a, $b) (mod $modulus) = ', bi_cmpmod($a, $b, $modulus), "<br/>\n";
/*
other functions
*/
echo '<h3>other functions</h3>' . "\n";
/*
/**
* Raise an arbitrary precision number to another, reduced by a specified modulus
*
* @param string $base The left operand, as a string.
* @param string $exp The right operand, as a string.
* @param string $mod The modulus, as a string.
* @access public
* @return string|null Returns the result as a string, or <b>NULL</b> if modulus is 0.
*/
public function powmod($base, $exp, $mod)
{
return bi_powmod($base, $exp, $mod);
}