/**
* Validate Public Key
*
* Validates a public key by attempting to create a point on the
* secp256k1 curve.
*
* @param string $public_key
* @return boolean
*/
public static function validate_public_key($public_key)
{
if (strlen($public_key) == '66') {
// Compressed key
// Attempt to decompress the public key. If the point is not
// generated, or the function fails, then the key is invalid.
$decompressed = self::decompress_public_key($public_key);
return $decompressed == TRUE;
} else {
if (strlen($public_key) == '130') {
// Uncompressed key, try to create the point
$curve = \SECcurve::curve_secp256k1();
$generator = \SECcurve::generator_secp256k1();
$x = substr($public_key, 2, 64);
$y = substr($public_key, 66, 64);
// Attempt to create the point. Point returns false in the
// constructor if anything is invalid.
try {
$point = new \Point($curve, gmp_strval(gmp_init($x, 16), 10), gmp_strval(gmp_init($y, 16), 10), $generator->getOrder());
} catch (\Exception $e) {
return FALSE;
}
return TRUE;
}
}
return FALSE;
}
/**
* Public Key From MPK
*
* This function is used to generate a public key from the supplied
* $mpk - the master public key, and an $iteration indicating which
* address in the sequence should be generated.
*
* @param string $mpk
* @param int $iteration
* @return string
*/
public static function public_key_from_mpk($mpk, $iteration, $change = 0, $compressed = FALSE)
{
$change = $change == 0 ? '0' : '1';
// Generate the curve, and the generator point.
$curve = \SECcurve::curve_secp256k1();
$gen = \SECcurve::generator_secp256k1();
// Prepare the input values, by converting the MPK to X and Y coordinates
$x = gmp_init(substr($mpk, 0, 64), 16);
$y = gmp_init(substr($mpk, 64, 64), 16);
// Generate a scalar from the $iteration and $mpk
$z = gmp_init(hash('sha256', hash('sha256', "{$iteration}:{$change}:" . pack('H*', $mpk), TRUE)), 16);
try {
// Add the Point defined by $x and $y, to the result of EC multiplication of $z by $gen
$pt = \Point::add(new \Point($curve, $x, $y), \Point::mul($z, $gen));
// Generate the uncompressed public key.
$keystr = '04' . str_pad(gmp_strval($pt->x, 16), 64, '0', STR_PAD_LEFT) . str_pad(gmp_strval($pt->y, 16), 64, '0', STR_PAD_LEFT);
} catch (Exception $e) {
throw new ErrorException($e->getMessage());
}
return $compressed == TRUE ? BitcoinLib::compress_public_key($keystr) : $keystr;
}
public function decompress_public_key($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);
}
/**
* CKD
*
* This recursive function accepts $master, a parent extended key,
* and an array of address bytes (the $address_definition tuple). It
* pop's the next value from the $address_definition tuple and
* generates the desired key. If the $address_definition tuple is
* empty, then it returns the key. If not, then it calls itself again
* with the new key and the tuple with the remaining key indexes to
* generate, but will terminate with an array containing the desired
* key at index 0, and it's human readable definition in the second.
*
* @param string $master
* @param array $address_definition
* @return array
*/
public static function CKD($master, $address_definition, $generated = array())
{
$previous = self::import($master);
if ($previous['type'] == 'private') {
$private_key = $previous['key'];
$public_key = BitcoinLib::private_key_to_public_key($private_key, TRUE);
} else {
if ($previous['type'] == 'public') {
$public_key = $previous['key'];
} else {
// Exception here?
return FALSE;
}
}
$fingerprint = substr(hash('ripemd160', hash('sha256', pack("H*", $public_key), TRUE)), 0, 8);
$i = array_pop($address_definition);
$is_prime = self::check_is_prime_hex($i);
if ($is_prime == 1) {
if ($previous['type'] == 'public') {
return FALSE;
}
// Cannot derive private from public key - Exception here?
$data = '00' . $private_key . $i;
} else {
if ($is_prime == 0) {
$data = $public_key . $i;
}
}
if (!isset($data)) {
return FALSE;
}
$I = hash_hmac('sha512', pack("H*", $data), pack("H*", $previous['chain_code']));
$I_l = substr($I, 0, 64);
$I_r = substr($I, 64, 64);
if (self::check_valid_hmac_key($I_l) == FALSE) {
// Check the key is in a valid range.
// calculate the next i in the sequence, and start over with that.
$new_i = self::calc_address_bytes(self::get_address_number($i) + 1, $is_prime);
array_push($address_definition, $new_i);
return self::CKD($master, $address_definition, $generated);
}
// Keep a record of the address being built. Done after error
// checking so only valid keys get to this point.
if (count($generated) == 0 && $previous['depth'] == 0) {
array_push($generated, $previous['type'] == 'private' ? 'm' : 'M');
}
array_push($generated, self::get_address_number($i, $is_prime) . ($is_prime == 1 ? "'" : NULL));
$g = \SECcurve::generator_secp256k1();
$n = $g->getOrder();
if ($previous['type'] == 'private') {
// (Il + kpar) mod n
$key = str_pad(gmp_strval(\gmp_Utils::gmp_mod2(gmp_add(gmp_init($I_l, 16), gmp_init($private_key, 16)), $n), 16), 64, '0', STR_PAD_LEFT);
} else {
if ($previous['type'] == 'public') {
// newPoint + parentPubkeyPoint
$decompressed = BitcoinLib::decompress_public_key($public_key);
// Can return FALSE. Throw exception?
$curve = \SECcurve::curve_secp256k1();
// Prepare offset, by multiplying Il by g, and adding this to the previous public key point.
// Create a new point by adding the two.
$new_point = \Point::add(\Point::mul(gmp_init($I_l, 16), $g), $decompressed['point']);
$new_x = str_pad(gmp_strval($new_point->getX(), 16), 64, '0', STR_PAD_LEFT);
$new_y = str_pad(gmp_strval($new_point->getY(), 16), 64, '0', STR_PAD_LEFT);
$key = BitcoinLib::compress_public_key('04' . $new_x . $new_y);
}
}
if (!isset($key)) {
return FALSE;
}
$data = array('network' => $previous['network'], 'testnet' => $previous['testnet'], 'magic_bytes' => $previous['magic_bytes'], 'type' => $previous['type'], 'depth' => $previous['depth'] + 1, 'fingerprint' => $fingerprint, 'i' => $i, 'address_number' => self::get_address_number($i), 'chain_code' => $I_r, 'key' => $key);
return count($address_definition) > 0 ? self::CKD(self::encode($data), $address_definition, $generated) : array(self::encode($data), implode('/', $generated));
}
