/**
returns RSA key pair with length $bit_len
*/
function generate_key_pair($bit_len)
{
// generate two primes p and q
$p_len = (int) ($bit_len / 2) + 1;
$q_len = $bit_len - $p_len;
$p = get_prime($p_len);
$q = get_prime($q_len);
// $n - is shared modulus
$n = bi_mul($p, $q);
// generate public ($e) and private ($d) keys
$pq = bi_mul(bi_dec($p), bi_dec($q));
do {
$e = bi_rand($q_len, 'microtime_generator');
} while (!bi_is_zero(bi_dec(bi_gcd($e, $pq))));
$d = bi_invmod($e, $pq);
return array('n' => bi_serialize($n), 'public_key' => bi_serialize($e), 'private_key' => bi_serialize($d));
}
/**
* Finds greatest common divider (GCD) of $num1 and $num2
*
* @param big_int resource $num1
* @param big_int resource $num2
* @return big_int resource
* @access public
*/
function GCD($num1, $num2)
{
return bi_gcd($num1, $num2);
}
*/
echo '<h3>other functions</h3>' . "\n";
/*
attention: second parameter of bi_pow() must have
integer type (not BIG_INT!)
*/
$c = bi_pow($a, 4);
echo 'pow($a, 4) = [', bi_to_str($c), "]<br/>\n";
// argument of bi_fact() must have integer type (not BIG_INT)
$c = bi_fact(100);
echo '100! = [', bi_to_str($c), "]<br/>\n";
$c = bi_sqrt($a);
echo 'sqrt($a) = [', bi_to_str($c), "]<br/>\n";
$c = bi_sqrt_rem($a);
echo 'sqrt_rem($a) = [', bi_to_str($c), "]<br/>\n";
$c = bi_gcd($a, $b);
echo 'GCD($a, $b) = [', bi_to_str($c), "]<br/>\n";
// Miller-Rabin primality test of $a
echo 'miller_test($a, $b) = ', bi_miller_test($a, $b), "<br/>\n";
// primality test of $a
echo 'is_prime($a) = ', bi_is_prime($a), "<br/>\n";
// Jacobi symbol ($a|$b)
echo 'jacobi($a, $b) = ', bi_jacobi($a, $b), "<br/>\n";
$c = bi_div_extended($a, $b);
echo '$a = $b * ', bi_to_str($c[0]), ' + ', bi_to_str($c[1]), "<br/>\n";
$c = bi_gcd_extended($a, $b);
echo 'abs($a) * ', bi_to_str($c[1]), ' + abs($b) * ', bi_to_str($c[2]), ' = ', bi_to_str($c[0]), "<br/>\n";
// serialize $a into sequence of bytes
$str = bi_serialize($a);
echo '$str = serialize($a) = [', base64_encode($str), "]<br/>\n";
// unserialize $a from sequence of bytes