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)

原文《以太坊常见问题和错误》中的:
http://cw.hubwiz.com/card/c/ethereum-FAQ/1/1/20/

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