从私钥计算公钥不正确答案

【问题标题】：calculate public key from private key is not correct从私钥计算公钥不正确
【发布时间】：2019-10-10 22:17:51
【问题描述】：

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

由于某种原因，两个公钥值不对应。

查看包含的代码以及生成密钥对的函数：

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;
    }

如果您比较生成的公钥和计算的公钥的 (X,Y) 坐标。你会得到不同的价值。我期望相同的价值！怎么了？

【问题讨论】：

标签： c# bouncycastle private-key public-key elliptic-curve

【解决方案1】：

James K Polk 为我指明了正确的方向。在获得坐标之前，我必须先规范化该点（“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;
    }

【讨论】：

【解决方案2】：

您得到了错误的 X 和 Y 坐标。在内部，点存储在另一个表示（X，Y，Z）中，涉及称为投影坐标的东西。你想要仿射坐标。通过属性 AffineXCoord 和 AffineYCoord 检索等效的 (X, Y) 仿射坐标。

【讨论】：