从非对称密钥参数的私有和公共获取 X、Y 坐标

问题描述

public class EccGenerator
{
    public asymmetricCipherKeyPair GenerateKeyPairs(int keySize)
    {
        ECKeyPairGenerator gen = new ECKeyPairGenerator("ECDSA");
        KeyGenerationParameters keyGenParam = new KeyGenerationParameters(new SecureRandom(),keySize);
        gen.Init(keyGenParam);
        asymmetricCipherKeyPair keyPair = gen.GenerateKeyPair();
        return keyPair;
    }

    public static void  PrintPublicX_Y(asymmetricKeyParameter publicKey)
    {
        EcpublicKeyParameters key = (EcpublicKeyParameters)publicKey;
        string X = Encoding.ASCII.GetString(UrlBase64.Encode(key.Q.XCoord.ToBigInteger().ToByteArrayUnsigned()));
        string Y = Encoding.ASCII.GetString(UrlBase64.Encode(key.Q.YCoord.ToBigInteger().ToByteArrayUnsigned()));
        Console.WriteLine(X + "--" + Y);
    }

    public static void PrintPrivateX_Y(asymmetricKeyParameter privateKey)
    {
        ECPrivateKeyParameters key = (ECPrivateKeyParameters)privateKey;
        string D = Encoding.ASCII.GetString(UrlBase64.Encode(key.D.ToByteArrayUnsigned()));
        string X = Encoding.ASCII.GetString(UrlBase64.Encode(key.Parameters.G.XCoord.ToBigInteger().ToByteArrayUnsigned()));
        string Y = Encoding.ASCII.GetString(UrlBase64.Encode(key.Parameters.G.YCoord.ToBigInteger().ToByteArrayUnsigned()));
        Console.WriteLine(X + "--" + Y);
    }

    public static void Main(string[] args)
    {
        EccGenerator ecc = new EccGenerator();
        asymmetricCipherKeyPair pair = ecc.GenerateKeyPairs(256);
        PrintPublicX_Y(pair.Public);
        PrintPrivateX_Y(pair.Private);
    }
}

这里的问题是 public 和 private 中的 X 不相同，与 Y 相同，我如何才能为私有获得正确的 x 和 y 和 D

我正在使用 Bouncy Castle C#

解决方法

公钥是通过将基点 G 与私钥 D 相乘获得的。结果通常必须归一化（后者负责将出于性能原因使用的射影坐标转换为仿射坐标坐标，有关详细信息，请参见例如 here）。

因此，在 PrintPrivateX_Y() 中，表达式 key.Parameters.G 必须替换为 key.Parameters.G.Multiply(key.D).Normalize()。

以下替代代码：

using Org.BouncyCastle.Crypto;
using Org.BouncyCastle.Crypto.Generators;
using Org.BouncyCastle.Crypto.Parameters;
using Org.BouncyCastle.Math.EC;
using Org.BouncyCastle.Security;
using Org.BouncyCastle.Utilities.Encoders;
using System;
...
AsymmetricCipherKeyPair pair = GenerateKeyPairs(256);

ECPublicKeyParameters publicKeyParams = (ECPublicKeyParameters)pair.Public;
ECPoint publicKey = publicKeyParams.Q;
PrintKey(publicKey);

ECPrivateKeyParameters privateKeyParams = (ECPrivateKeyParameters)pair.Private;
ECPoint publicKeyViaPrivate = privateKeyParams.Parameters.G.Multiply(privateKeyParams.D).Normalize();
PrintKey(publicKeyViaPrivate);

与

public static void PrintKey(ECPoint ecPoint)
{
    string X = Hex.ToHexString(ecPoint.XCoord.ToBigInteger().ToByteArrayUnsigned());
    string Y = Hex.ToHexString(ecPoint.YCoord.ToBigInteger().ToByteArrayUnsigned());
    Console.WriteLine(X + " -- " + Y);
}

和问题中发布的（静态）GenerateKeyPairs(int keySize) 使用十六进制表示显示，两个公钥与预期相同。

bouncycastle elliptic-curve