/
Signature.class.php
415 lines (333 loc) · 11.5 KB
/
Signature.class.php
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<?php
/*
* Crypto Currency Message Signing and Verification
* For Bitcoin/Zetacoin compatable Crypto Currency utilizing the secp256k1 curve
* @author Daniel Morante
* Some parts may contain work based on Jan Moritz Lindemann, Matyas Danter, and Joey Hewitt
*/
class Signature {
/***
* Sign a hash with the private key that was set and returns signatures as an array (R,S)
*
* @param $hash
* @param $k
* @param null $nonce
* @throws \Exception
* @return Array
*/
public static function getSignatureHashPoints($hash, $k, $nonce = null)
{
$secp256k1 = new SECp256k1();
$a = $secp256k1->a;
$b = $secp256k1->b;
$G = $secp256k1->G;
$n = $secp256k1->n;
$p = $secp256k1->p;
if(empty($k))
{
throw new \Exception('No Private Key was defined');
}
if(null == $nonce)
{
$random = openssl_random_pseudo_bytes(256, $cStrong);
$random = $random . microtime(true).rand(100000000000, 1000000000000);
$nonce = gmp_strval(gmp_mod(gmp_init(hash('sha256',$random), 16), $n), 16);
}
//first part of the signature (R).
$rPt = PointMathGMP::mulPoint($nonce, $G, $a, $b, $p);
$R = gmp_strval($rPt ['x'], 16);
while(strlen($R) < 64)
{
$R = '0' . $R;
}
//second part of the signature (S).
//S = nonce^-1 (hash + privKey * R) mod p
$S = gmp_strval(
gmp_mod(
gmp_mul(
gmp_invert(
gmp_init($nonce, 16),
$n
),
gmp_add(
gmp_init($hash, 16),
gmp_mul(
gmp_init($k, 16),
gmp_init($R, 16)
)
)
),
$n
),
16
);
if(strlen($S)%2)
{
$S = '0' . $S;
}
if(strlen($R)%2)
{
$R = '0' . $R;
}
return array('R' => $R, 'S' => $S);
}
/***
* Sign a hash with the private key that was set and returns a DER encoded signature
*
* @param $hash
* @param null $nonce
* @return string
*/
public static function signHash($hash, $k, $nonce = null)
{
$points = self::getSignatureHashPoints($hash, $k, $nonce);
$signature = '02' . dechex(strlen(hex2bin($points['R']))) . $points['R'] . '02' . dechex(strlen(hex2bin($points['S']))) . $points['S'];
$signature = '30' . dechex(strlen(hex2bin($signature))) . $signature;
return $signature;
}
/***
* extract the public key from the signature and using the recovery flag.
* see http://crypto.stackexchange.com/a/18106/10927
* based on https://github.com/brainwallet/brainwallet.github.io/blob/master/js/bitcoinsig.js
* possible public keys are r−1(sR−zG) and r−1(sR′−zG)
* Recovery flag rules are :
* binary number between 28 and 35 inclusive
* if the flag is > 30 then the address is compressed.
*
* @param $flag (INT)
* @param $R (HEX String)
* @param $S (HEX String)
* @param $hash (HEX String)
* @return array
*/
public static function getPubKeyWithRS($flag, $R, $S, $hash)
{
$secp256k1 = new SECp256k1();
$a = $secp256k1->a;
$b = $secp256k1->b;
$G = $secp256k1->G;
$n = $secp256k1->n;
$p = $secp256k1->p;
$isCompressed = false;
if ($flag < 27 || $flag >= 35) {
return false;
}
if($flag >= 31) //if address is compressed
{
$isCompressed = true;
$flag -= 4;
}
$recid = $flag - 27;
//step 1.1
$x = null;
$x = gmp_add(
gmp_init($R, 16),
gmp_mul(
$n,
gmp_div_q( //check if j is equal to 0 or to 1.
gmp_init($recid, 10),
gmp_init(2, 10)
)
)
);
//step 1.3
$y = null;
if(1 == $flag % 2) //check if y is even.
{
$gmpY = PointMathGMP::calculateYWithX(gmp_strval($x, 16), $a, $b, $p, '02');
if(null != $gmpY)
$y = gmp_init($gmpY, 16);
}
else
{
$gmpY = PointMathGMP::calculateYWithX(gmp_strval($x, 16), $a, $b, $p, '03');
if(null != $gmpY)
$y = gmp_init($gmpY, 16);
}
if(null == $y)
return null;
$Rpt = array('x' => $x, 'y' => $y);
//step 1.6.1
//calculate r^-1 (S*Rpt - eG)
$eG = PointMathGMP::mulPoint($hash, $G, $a, $b, $p);
$Rinv = gmp_strval(gmp_invert(gmp_init($R, 16), $n), 16);
// Possible issue
$eG['y'] = gmp_mod(gmp_neg($eG['y']), $p);
// Possible Fix
//$eG['y'] = gmp_neg($eG['y']);
$SR = PointMathGMP::mulPoint($S, $Rpt, $a, $b, $p);
$sR_plus_eGNeg = PointMathGMP::addPoints($SR, $eG, $a, $p);
$pubKey = PointMathGMP::mulPoint(
$Rinv,
$sR_plus_eGNeg,
$a,
$b,
$p
);
$pubKey['x'] = gmp_strval($pubKey['x'], 16);
$pubKey['y'] = gmp_strval($pubKey['y'], 16);
while(strlen($pubKey['x']) < 64)
$pubKey['x'] = '0' . $pubKey['x'];
while(strlen($pubKey['y']) < 64)
$pubKey['y'] = '0' . $pubKey['y'];
if($isCompressed){
$derPubKey = AddressCodec::Compress($pubKey);
}
else{
$derPubKey = AddressCodec::Hex($pubKey);
}
if(self::checkSignaturePoints($derPubKey, $R, $S, $hash)){
return $derPubKey;
}
else{
return false;
}
}
// Same as Below but accepts HEX strings
public static function recoverPublicKey_HEX($flag, $R, $S, $hash){
return self::recoverPublicKey(gmp_init($R,16), gmp_init($S,16), gmp_init($hash,16), $flag);
}
// $R, $S, and $hash are GMP
// $recoveryFlags is INT
public static function recoverPublicKey($R, $S, $hash, $recoveryFlags){
$secp256k1 = new SECp256k1();
$a = $secp256k1->a;
$b = $secp256k1->b;
$G = $secp256k1->G;
$n = $secp256k1->n;
$p = $secp256k1->p;
$isYEven = ($recoveryFlags & 1) != 0;
$isSecondKey = ($recoveryFlags & 2) != 0;
// PointMathGMP::mulPoint wants HEX String
$e = gmp_strval($hash, 16);
$s = gmp_strval($S, 16);
// Precalculate (p + 1) / 4 where p is the field order
// $p_over_four is GMP
static $p_over_four; // XXX just assuming only one curve/prime will be used
if (!$p_over_four) {
$p_over_four = gmp_div(gmp_add($p, 1), 4);
}
// 1.1 Compute x
// $x is GMP
if (!$isSecondKey) {
$x = $R;
} else {
$x = gmp_add($R, $n);
}
// 1.3 Convert x to point
// $alpha is GMP
$alpha = gmp_mod(gmp_add(gmp_add(gmp_pow($x, 3), gmp_mul($a, $x)), $b), $p);
// $beta is DEC String (INT)
$beta = gmp_strval(gmp_powm($alpha, $p_over_four, $p));
// If beta is even, but y isn't or vice versa, then convert it,
// otherwise we're done and y == beta.
if (PointMathGMP::isEvenNumber($beta) == $isYEven) {
// gmp_sub function will convert the DEC String "$beta" into a GMP
// $y is a GMP
$y = gmp_sub($p, $beta);
} else {
// $y is a GMP
$y = gmp_init($beta);
}
// 1.4 Check that nR is at infinity (implicitly done in construtor) -- Not reallly
// $Rpt is Array(GMP, GMP)
$Rpt = array('x' => $x, 'y' => $y);
// 1.6.1 Compute a candidate public key Q = r^-1 (sR - eG)
// $rInv is a HEX String
$rInv = gmp_strval(gmp_invert($R, $n), 16);
// $eGNeg is Array (GMP, GMP)
$eGNeg = PointMathGMP::negatePoint(PointMathGMP::mulPoint($e, $G, $a, $b, $p));
$sR = PointMathGMP::mulPoint($s, $Rpt, $a, $b, $p);
$sR_plus_eGNeg = PointMathGMP::addPoints($sR, $eGNeg, $a, $p);
// $Q is Array (GMP, GMP)
$Q = PointMathGMP::mulPoint($rInv, $sR_plus_eGNeg, $a, $b, $p);
// Q is the derrived public key
// $pubkey is Array (HEX String, HEX String)
// Ensure it's always 64 HEX Charaters
$pubKey['x'] = str_pad(gmp_strval($Q['x'], 16), 64, 0, STR_PAD_LEFT);
$pubKey['y'] = str_pad(gmp_strval($Q['y'], 16), 64, 0, STR_PAD_LEFT);
return $pubKey;
}
/***
* Check signature with public key R & S values of the signature and the message hash.
*
* @param $pubKey
* @param $R
* @param $S
* @param $hash
* @return bool
*/
public static function checkSignaturePoints($pubKey, $R, $S, $hash)
{
$secp256k1 = new SECp256k1();
$a = $secp256k1->a;
$b = $secp256k1->b;
$G = $secp256k1->G;
$n = $secp256k1->n;
$p = $secp256k1->p;
$pubKeyPts = AddressCodec::Decompress($pubKey);
// S^-1* hash * G + S^-1 * R * Qa
// S^-1* hash
$exp1 = gmp_strval(
gmp_mul(
gmp_invert(
gmp_init($S, 16),
$n
),
gmp_init($hash, 16)
),
16
);
// S^-1* hash * G
$exp1Pt = PointMathGMP::mulPoint($exp1, $G, $a, $b, $p);
// S^-1 * R
$exp2 = gmp_strval(
gmp_mul(
gmp_invert(
gmp_init($S, 16),
$n
),
gmp_init($R, 16)
),
16
);
// S^-1 * R * Qa
$pubKeyPts['x'] = gmp_init($pubKeyPts['x'], 16);
$pubKeyPts['y'] = gmp_init($pubKeyPts['y'], 16);
$exp2Pt = PointMathGMP::mulPoint($exp2, $pubKeyPts, $a, $b, $p);
$resultingPt = PointMathGMP::addPoints($exp1Pt, $exp2Pt, $a, $p);
$xRes = gmp_strval($resultingPt['x'], 16);
while(strlen($xRes) < 64)
$xRes = '0' . $xRes;
if($xRes == $R)
return true;
else
return false;
}
/***
* checkSignaturePoints wrapper for DER signatures
*
* @param $pubKey
* @param $signature
* @param $hash
* @return bool
*/
public static function checkDerSignature($pubKey, $signature, $hash)
{
$signature = hex2bin($signature);
if('30' != bin2hex(substr($signature, 0, 1)))
return false;
$RLength = hexdec(bin2hex(substr($signature, 3, 1)));
$R = bin2hex(substr($signature, 4, $RLength));
$SLength = hexdec(bin2hex(substr($signature, $RLength + 5, 1)));
$S = bin2hex(substr($signature, $RLength + 6, $SLength));
//echo "\n\nsignature:\n";
//print_r(bin2hex($signature));
//echo "\n\nR:\n";
//print_r($R);
//echo "\n\nS:\n";
//print_r($S);
return self::checkSignaturePoints($pubKey, $R, $S, $hash);
}
}
?>