为什么我对签名消息的签名验证在PHP代码中未工作？
我正在尝试验证PHP中的签名消息。
我不希望与JSON-RPC或任何外部服务有接口，我知道这两个服务都是可以成功地验证了我提供的示例签名消息。
另外，我很清楚message prefix和消息长度问题。
这个问题似乎源于我正在使用的Signature类或对R和S值的GMP转换，在签名本身中起的作用。
在我的代码中使用的唯一外部库是https://github.com/0xbb/php-sha3/blob/master/src/Sha3.php，它需要对第334行进行修改，将0x06更改为0x01，用于keccak兼容，这是以太坊所使用的。这里的改变应该说是一个正确的改变，因为在用web3库hash同一条消息时，当哈希原始消息时，将其保持为0x01会产生不同的结果。
下面是我的代码。如果有人能告诉我哪里出了问题，我将不胜感激。
<?php
use bb\Sha3\Sha3;
require_once('./Sha3.php');
$message = 'This is an example of a signed message.';
$signerAddress = '0xd4e01f608982ff53022e8c3ff43e145a192a9c4a';
$signedMessage = '0x6a65ed07a44715169177223ce508a2257f8167db452df0b2e37966b39350a61940e370616b3a0ea0f20adfa4661a7db10eeb583ca5a58ec8468e726eff4131a11c';
$signedMessageStrip = '6a65ed07a44715169177223ce508a2257f8167db452df0b2e37966b39350a61940e370616b3a0ea0f20adfa4661a7db10eeb583ca5a58ec8468e726eff4131a11c';
$prefix = "\x19Ethereum Signed Message:\n".strlen($message);
$stringToSign = $prefix.$message;
//\x19Ethereum Signed Message:\n39This is an example of a signed message.
$messageHex = Sha3::hash($stringToSign, 256); //this matches web3.sha() output for the given message and prefix.
$messageGmp = gmp_init("0x".$messageHex);
$r = substr($signedMessageStrip, 0,64);
$s = substr($signedMessageStrip, 64,64);
$v = substr($signedMessageStrip, 128,2);
$vChecksum = hexdec($v) - 27;
if($vChecksum !== 0 && $vChecksum !== 1) { echo "Invalid checksum.\n"; exit; }
$rGmp = gmp_init("0x".$r);
$sGmp = gmp_init("0x".$s);
$publicKey = Signature::recoverPublicKey($rGmp, $sGmp, $messageGmp, $vChecksum);
//the below line is where things are going wrong. The output hash of Sha3::hash($publicKey['x'].$publicKey['y'], 256) is not correct, according to stepping through similar processes using the web3 library, which generates different results, despite an earlier check that publicKey *is* correct. I cannot figure out what's going wrong.
$recovered = "0x".substr(Sha3::hash($publicKey['x'].$publicKey['y'], 256),24)."\n"; //convert to public address format
//$recovered = 0xf2517bd73c56d6d5a5409c4a1ee29c8f2d5438ff
if (strtolower($recovered) == strtolower($signerAddress)) { echo "Address recovered successfully.\n"; }
else { echo "Address NOT recovered successfully.\n"; }
?>
<?php
class SECp256k1 {
public $a;
public $b;
public $p;
public $n;
public $G;
public function __construct(){
$this->a = gmp_init('0', 10);
$this->b = gmp_init('7', 10);
$this->p = gmp_init('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F', 16);
$this->n = gmp_init('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141', 16);
$this->G = array('x' => gmp_init('55066263022277343669578718895168534326250603453777594175500187360389116729240'),
'y' => gmp_init('32670510020758816978083085130507043184471273380659243275938904335757337482424'));
}
}
class Signature {
public static function recoverPublicKey($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;
}
}
class PointMathGMP {
/***
* Computes the result of a point addition and returns the resulting point as an Array.
*
* @param Array $pt
* @return Array Point
* @throws \Exception
*/
public static function doublePoint(Array $pt, $a, $p)
{
$gcd = gmp_strval(gmp_gcd(gmp_mod(gmp_mul(gmp_init(2, 10), $pt['y']), $p),$p));
if($gcd != '1')
{
throw new \Exception('This library doesn\'t yet supports point at infinity. See https://github.com/BitcoinPHP/BitcoinECDSA.php/issues/9');
}
// SLOPE = (3 * ptX^2 + a )/( 2*ptY )
// Equals (3 * ptX^2 + a ) * ( 2*ptY )^-1
$slope = gmp_mod(
gmp_mul(
gmp_invert(
gmp_mod(
gmp_mul(
gmp_init(2, 10),
$pt['y']
),
$p
),
$p
),
gmp_add(
gmp_mul(
gmp_init(3, 10),
gmp_pow($pt['x'], 2)
),
$a
)
),
$p
);
// nPtX = slope^2 - 2 * ptX
// Equals slope^2 - ptX - ptX
$nPt = array();
$nPt['x'] = gmp_mod(
gmp_sub(
gmp_sub(
gmp_pow($slope, 2),
$pt['x']
),
$pt['x']
),
$p
);
// nPtY = slope * (ptX - nPtx) - ptY
$nPt['y'] = gmp_mod(
gmp_sub(
gmp_mul(
$slope,
gmp_sub(
$pt['x'],
$nPt['x']
)
),
$pt['y']
),
$p
);
return $nPt;
}
/***
* Computes the result of a point addition and returns the resulting point as an Array.
*
* @param Array $pt1
* @param Array $pt2
* @return Array Point
* @throws \Exception
*/
public static function addPoints(Array $pt1, Array $pt2, $a, $p)
{
if(gmp_cmp($pt1['x'], $pt2['x']) == 0 && gmp_cmp($pt1['y'], $pt2['y']) == 0) //if identical
{
return self::doublePoint($pt1, $a, $p);
}
$gcd = gmp_strval(gmp_gcd(gmp_sub($pt1['x'], $pt2['x']), $p));
if($gcd != '1')
{
throw new \Exception('This library doesn\'t yet support points at infinity. See https://github.com/BitcoinPHP/BitcoinECDSA.php/issues/9');
}
// SLOPE = (pt1Y - pt2Y)/( pt1X - pt2X )
// Equals (pt1Y - pt2Y) * ( pt1X - pt2X )^-1
$slope = gmp_mod(
gmp_mul(
gmp_sub(
$pt1['y'],
$pt2['y']
),
gmp_invert(
gmp_sub(
$pt1['x'],
$pt2['x']
),
$p
)
),
$p
);
// nPtX = slope^2 - ptX1 - ptX2
$nPt = array();
$nPt['x'] = gmp_mod(
gmp_sub(
gmp_sub(
gmp_pow($slope, 2),
$pt1['x']
),
$pt2['x']
),
$p
);
// nPtX = slope * (ptX1 - nPtX) - ptY1
$nPt['y'] = gmp_mod(
gmp_sub(
gmp_mul(
$slope,
gmp_sub(
$pt1['x'],
$nPt['x']
)
),
$pt1['y']
),
$p
);
return $nPt;
}
/***
* Computes the result of a point multiplication and returns the resulting point as an Array.
*
* @param String Hex $k
* @param Array $pG (GMP, GMP)
* @param $base (INT)
* @throws \Exception
* @return Array Point (GMP, GMP)
*/
public static function mulPoint($k, Array $pG, $a, $b, $p, $base = null)
{
//in order to calculate k*G
if($base == 16 || $base == null || is_resource($base))
$k = gmp_init($k, 16);
if($base == 10)
$k = gmp_init($k, 10);
$kBin = gmp_strval($k, 2);
$lastPoint = $pG;
for($i = 1; $i < strlen($kBin); $i++)
{
if(substr($kBin, $i, 1) == 1 )
{
$dPt = self::doublePoint($lastPoint, $a, $p);
$lastPoint = self::addPoints($dPt, $pG, $a, $p);
}
else
{
$lastPoint = self::doublePoint($lastPoint, $a, $p);
}
}
if(!self::validatePoint(gmp_strval($lastPoint['x'], 16), gmp_strval($lastPoint['y'], 16), $a, $b, $p)){
throw new \Exception('The resulting point is not on the curve.');
}
return $lastPoint;
}
/***
* Returns true if the point is on the curve and false if it isn't.
*
* @param $x
* @param $y
* @return bool
*/
public static function validatePoint($x, $y, $a, $b, $p)
{
$x = gmp_init($x, 16);
$y2 = gmp_mod(
gmp_add(
gmp_add(
gmp_powm($x, gmp_init(3, 10), $p),
gmp_mul($a, $x)
),
$b
),
$p
);
$y = gmp_mod(gmp_pow(gmp_init($y, 16), 2), $p);
if(gmp_cmp($y2, $y) == 0)
return true;
else
return false;
}
/***
* Returns Negated Point (Y).
*
* @param $point Array(GMP, GMP)
* @return Array(GMP, GMP)
*/
public static function negatePoint($point) {
return array('x' => $point['x'], 'y' => gmp_neg($point['y']));
}
// Checks is the given number (DEC String) is even
public static function isEvenNumber($number) {
return (((int)$number[strlen($number)-1]) & 1) == 0;
}
}
?>
问题解答
将问题与所产生的公钥的hash分开，事实证明，必须将公钥的字节，而不是十六进制hash本身传递给keccak哈希算法。
$recovered = "0x".substr(Sha3::hash(hex2bin($publicKey['x'].$publicKey['y']), 256),24)