/**
* Decompress Public Key
*
* Accepts a y_byte, 02 or 03 indicating whether the Y coordinate is
* odd or even, and $passpoint, which is simply a hexadecimal X coordinate.
* Using this data, it is possible to deconstruct the original
* uncompressed public key.
*
* @param $key
* @return array|bool
*/
public static function decompress_public_key($key)
{
$y_byte = substr($key, 0, 2);
$x_coordinate = substr($key, 2);
$x = gmp_strval(gmp_init($x_coordinate, 16), 10);
$curve = \SECcurve::curve_secp256k1();
$generator = \SECcurve::generator_secp256k1();
try {
$x3 = \NumberTheory::modular_exp($x, 3, $curve->getPrime());
$y2 = gmp_add($x3, $curve->getB());
$y0 = \NumberTheory::square_root_mod_prime(gmp_strval($y2, 10), $curve->getPrime());
if ($y0 == FALSE) {
return FALSE;
}
$y1 = gmp_strval(gmp_sub($curve->getPrime(), $y0), 10);
$y_coordinate = $y_byte == '02' ? \gmp_Utils::gmp_mod2(gmp_init($y0, 10), 2) == '0' ? $y0 : $y1 : (\gmp_Utils::gmp_mod2(gmp_init($y0, 10), 2) !== '0' ? $y0 : $y1);
$y_coordinate = str_pad(gmp_strval($y_coordinate, 16), 64, '0', STR_PAD_LEFT);
$point = new \Point($curve, gmp_strval(gmp_init($x_coordinate, 16), 10), gmp_strval(gmp_init($y_coordinate, 16), 10), $generator->getOrder());
} catch (\Exception $e) {
return FALSE;
}
return array('x' => $x_coordinate, 'y' => $y_coordinate, 'point' => $point, 'public_key' => '04' . $x_coordinate . $y_coordinate);
}
public static function bcmath_squareRootModP($prime, $verbose = false)
{
$start_time = microtime(true);
if ($verbose) {
echo "Testing primes for modulus " . $prime . "<br />";
}
flush();
$squares = array();
for ($root = 0; bccomp($root, bcadd(1, bcdiv($prime, 2))) < 0; $root = bcadd($root, 1)) {
$sq = bcpowmod($root, 2, $prime);
$calculated = NumberTheory::square_root_mod_prime($sq, $prime);
$calc_sq = bcpowmod($calculated, 2, $prime);
if (bccomp($calculated, $root) != 0 && bccomp(bcsub($prime, $calculated), $root) != 0) {
$error_tally++;
echo "FAILED TO FIND " . $root . " AS sqrt(" . $sq . ") mod {$prime} . Said {$calculated} (" . ($prime - $calculated) . ") <br />\n";
flush();
} else {
if ($verbose) {
echo "SUCCESS TO FIND " . $root . " AS sqrt(" . $sq . ") mod {$prime} . Said {$calculated} (" . ($prime - $calculated) . ") <br />\n";
}
flush();
}
}
$end_time = microtime(true);
$time_res = $end_time - $start_time;
echo "<br />Square roots mod " . $prime . " took: " . $time_res . " seconds. <br />";
flush();
}
public function decompress_public_key($key)
{
// Initialize
$y_byte = substr($key, 0, 2);
$x_coordinate = substr($key, 2);
// Set variables
$x = gmp_strval(gmp_init($x_coordinate, 16), 10);
$curve = SECcurve::curve_secp256k1();
$generator = SECcurve::generator_secp256k1();
// Decode
try {
$x3 = NumberTheory::modular_exp($x, 3, $curve->getPrime());
$y2 = gmp_add($x3, $curve->getB());
$y0 = NumberTheory::square_root_mod_prime(gmp_strval($y2, 10), $curve->getPrime());
if ($y0 === false) {
return false;
}
$y1 = gmp_strval(gmp_sub($curve->getPrime(), $y0), 10);
$y_coordinate = $y_byte == '02' ? gmp_Utils::gmp_mod2(gmp_init($y0, 10), 2) == '0' ? $y0 : $y1 : (gmp_Utils::gmp_mod2(gmp_init($y0, 10), 2) !== '0' ? $y0 : $y1);
$y_coordinate = str_pad(gmp_strval($y_coordinate, 16), 64, '0', STR_PAD_LEFT);
$point = new Point($curve, gmp_strval(gmp_init($x_coordinate, 16), 10), gmp_strval(gmp_init($y_coordinate, 16), 10), $generator->getOrder());
} catch (Exception $e) {
return false;
}
// Return
return array('x' => $x_coordinate, 'y' => $y_coordinate, 'point' => $point, 'public_key' => '04' . $x_coordinate . $y_coordinate);
}