从公钥字节数组重新创建椭圆曲线的 X 和 Y

Question

我对加密技术非常陌生，但是我的目标是从公钥的字节数组表示中获取X和Y坐标。我正在使用secp256r1曲线。

// get curve
X9ECParameters x9 = ECNamedCurveTable.GetByName("secp256r1");
ECCurve curve = x9.Curve;

// get coordinates from ASN.1 encoded public key point
var asn1 = (Asn1Sequence)Asn1Object.FromByteArray(publicKeyBytes);
var at1 = (DerBitString)asn1[1];
var bytes = at1.GetBytes();
var x = bytes.Skip(1).Take(32).Reverse().ToArray();
var y = bytes.Skip(33).Take(32).Reverse().ToArray();

// get affine X and Y using point on curve from X and Y
var ecPoint = curve.CreatePoint(new Org.BouncyCastle.Math.BigInteger(1, x), new Org.BouncyCastle.Math.BigInteger(1, y));
ECDomainParameters dParams = new ECDomainParameters(curve, ecPoint, x9.N);
ECPublicKeyParameters pubKey = new ECPublicKeyParameters(ecPoint, dParams);
var affineX = pubKey.Q.AffineXCoord.ToBigInteger().ToByteArrayUnsigned();
var affineY = pubKey.Q.AffineYCoord.ToBigInteger().ToByteArrayUnsigned();

// return a tuple of the coordinates
return (affineX, affineY);

我收到了X和Y坐标，但它们可能不正确。我做错了什么？谢谢。

- Ivan

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你所拥有的X和Y坐标有什么问题？ - President James K. Polk

Answer 1

好的，代码有一些问题。这是可以运行的版本，希望对某些人有所帮助。

internal static (string x, string y) GetCertificateCoordinates(byte[] publicKeyBytes)
{
    // parse based on asn1 format the content of the certificate
    var asn1 = (Asn1Sequence)Asn1Object.FromByteArray(publicKeyBytes);
    var at1 = (DerBitString)asn1[1];
    var xyBytes = at1.GetBytes();

    //retrieve preddefined parameters for P256 curve
    X9ECParameters x9 = ECNamedCurveTable.GetByName("P-256");
    //establish domain we will be looking for the x and y
    ECDomainParameters domainParams = new ECDomainParameters(x9.Curve, x9.G, x9.N, x9.H, x9.GetSeed());
    ECPublicKeyParameters publicKeyParams = new ECPublicKeyParameters(x9.Curve.DecodePoint(xyBytes), domainParams);
    //get the affine x and y coordinates
    var affineX = EncodeCordinate(publicKeyParams.Q.AffineXCoord.ToBigInteger());
    var affineY = EncodeCordinate(publicKeyParams.Q.AffineYCoord.ToBigInteger());

    return (affineX, affineY);
}

public static string EncodeCordinate(Org.BouncyCastle.Math.BigInteger integer)
{
    var notPadded = integer.ToByteArray();
    int bytesToOutput = (256 + 7) / 8;
    if (notPadded.Length >= bytesToOutput)
        return Jose.Base64Url.Encode(notPadded);
    var padded = new byte[bytesToOutput];
    Array.Copy(notPadded, 0, padded, bytesToOutput - notPadded.Length, notPadded.Length);
    return Jose.Base64Url.Encode(padded);
}

我在安卓中使用这段代码，通过将X和Y作为头部中的jwk提供给服务器来提供JWT。

- Ivan