Question

我正在使用EC曲线P-256。我生成一个密钥对。然后，形成私钥，然后计算公钥。

由于某些原因，两个公钥值不对应。

请参阅附带的函数代码以生成密钥对：

public static AsymmetricCipherKeyPair  Generate_EC_P256_Key_Pair(SecureRandom random)
    {
        // Select the curve P-256 //
        string curveName = "P-256";
        X9ECParameters ecP = NistNamedCurves.GetByName(curveName);
        ECDomainParameters dom_parameters = new ECDomainParameters(ecP.Curve, ecP.G, ecP.N);

        // Generate EC Key Pair //
        ECKeyPairGenerator pGen = new ECKeyPairGenerator();
        ECKeyGenerationParameters genParam = new ECKeyGenerationParameters(dom_parameters, random);
        pGen.Init(genParam);
        AsymmetricCipherKeyPair keypair = pGen.GenerateKeyPair();

        AsymmetricKeyParameter Priv_key = keypair.Private;
        AsymmetricKeyParameter Pub_key = keypair.Public;

        ECPrivateKeyParameters private_key = (ECPrivateKeyParameters)keypair.Private;
        ECPublicKeyParameters public_key = (ECPublicKeyParameters)keypair.Public;

        BigInteger priv_key_exp = private_key.D;
        BigInteger test2 = public_key.Q.XCoord.ToBigInteger();
        BigInteger test3 = public_key.Q.YCoord.ToBigInteger();

        ECPoint pub_key_1 = dom_parameters.G.Multiply(priv_key_exp);
        BigInteger test4 = pub_key_1.XCoord.ToBigInteger();
        BigInteger test5 = pub_key_1.YCoord.ToBigInteger();

        Console.WriteLine("Exponent: " + priv_key_exp.ToString(16));
        Console.WriteLine("X-Coord: " + test2.ToString(16));
        Console.WriteLine("X-Coord: " + test4.ToString(16));
        Console.WriteLine("\n");
        Console.WriteLine("Y-Coord: " + test3.ToString(16));
        Console.WriteLine("Y-Coord: " + test5.ToString(16));

        return keypair;
    }

如果比较生成的公共密钥和计算的公共密钥的（X，Y）坐标。您将获得不同的价值。我期望相同的价值！怎么了？

Answer 1

James K Polk向我指出了正确的方向。在获取坐标之前，我必须先对点进行归一化（“ pub_key_1 = pub_key_1.Normalize（）”）。我相应地更改了代码，现在它给了我正确的结果。

谢谢！

public static AsymmetricCipherKeyPair  Generate_EC_P256_Key_Pair(SecureRandom random)
    {
        // Select the curve P-256 //
        string curveName = "P-256";
        X9ECParameters ecP = NistNamedCurves.GetByName(curveName);
        ECDomainParameters dom_parameters = new ECDomainParameters(ecP.Curve, ecP.G, ecP.N);

        // Generate EC Key Pair //
        ECKeyPairGenerator pGen = new ECKeyPairGenerator();
        ECKeyGenerationParameters genParam = new ECKeyGenerationParameters(dom_parameters, random);
        pGen.Init(genParam);
        AsymmetricCipherKeyPair keypair = pGen.GenerateKeyPair();


        ECPrivateKeyParameters private_key = (ECPrivateKeyParameters)keypair.Private;
        ECPublicKeyParameters public_key = (ECPublicKeyParameters)keypair.Public;

        BigInteger priv_key_exp = private_key.D;

        BigInteger genx = public_key.Q.XCoord.ToBigInteger();
        BigInteger geny = public_key.Q.YCoord.ToBigInteger();
        BigInteger genx_aff = public_key.Q.AffineXCoord.ToBigInteger();
        BigInteger geny_aff = public_key.Q.AffineYCoord.ToBigInteger();

        ECPoint pub_key_1 = dom_parameters.G.Multiply(priv_key_exp);

        pub_key_1 =pub_key_1.Normalize();

        BigInteger calcx = pub_key_1.XCoord.ToBigInteger();
        BigInteger calcy = pub_key_1.YCoord.ToBigInteger();

        Console.WriteLine("Exponent: " + priv_key_exp.ToString(16));
        Console.WriteLine("Generated X-Coord        : " + genx.ToString(16));
        Console.WriteLine("Generated X-Coord Affine : " + genx_aff.ToString(16));
        Console.WriteLine("Calculated X-Coord Affine: " + calcx.ToString(16));
        Console.WriteLine("\n");
        Console.WriteLine("Generated Y-Coord        : " + geny.ToString(16));
        Console.WriteLine("Generated Y-Coord Affine : " + geny_aff.ToString(16));
        Console.WriteLine("Calculated Y-Coord Affine: " + calcy.ToString(16));


        return keypair;
    }

Answer 2

您得到的X和Y坐标错误。在内部，点被存储在涉及投影坐标的替代表示形式（X，Y，Z）中。您需要仿射坐标。通过属性AffineXCoord和AffineYCoord检索等效的（X，Y）仿射坐标。

从私钥计算公钥不正确

2 个答案: