处理 BigInteger 问题

Question

假设以下 Diffie-Hellman 信息也可以在 page 上找到

1)P

string givenp = "00e655cc9e04f3bebae76ecca77143ef5c4451876615a9f8b4f712b8f3bdf47ee7f717c09bb5b2b66450831367d9dcf85f9f0528bcd5318fb1dab2f23ce77c48b6b7381eed13e80a14cca6b30b5e37ffe53db15e2d6b727a2efcee51893678d50e9a89166a359e574c4c3ca5e59fae79924fe6f186b36a2ebde9bf09fe4de50453";
        BigInteger p = new BigInteger(HexToBytesv2(givenp));

2)G

BigInteger g = new BigInteger(2);

3)商户私钥

string merchantPrivateKeyHEX = "48887dfd090d175e33beea29e7b38334299289069f9ab492b67807905faa98d96d22d79205bef03f14af093f1797b904734132c34a388fdc79e20497bfa1465fec2aac4fabdf3bb0c9be8685d20f7bfe0346a9abdf7fa89838c3fa9ca6abdb70bea66795ab6699cc154db59490e4159f142f7bddff603c1d3d6c4fff8177e11d";
        BigInteger a = new BigInteger(HexToBytesv2(merchantPrivateKeyHEX));

使用公式publickey = g ^ a mod p 我应该得到初始链接中提供的公钥，但在执行时

BigInteger A = BigInteger.ModPow(g, a, p);
ToHex(A.ToByteArray())

我得到的结果是

00f85c41e84446ecfe43c9911df31d3cf60d83642afd496b741363290139badf75f8b8c5c010dda2446dd483dc553b6c2698c16c9d082391677785f81d54bc9c7c45f8b6d5bdb3e49fec7f5522b880c8c753fb7d3ff2c81e47dcb27d52842def40a812dc95cc679575baf237a955ee9944bd0797326f2a0a58c6c087f9b0b9e82c

而不是

00d9abd78c93dfddeb920d57d6513126d8f1118c9237a45101408dbffe6cfd95b011a016e4e0ab8aef0601e836a452b8bb88be7ca71e4f22f97aa65f8358ee69348d1227d65db6e53641d1a6542aa4be4b4adc75fac816af79a8e3f5097f8313e7b725df37eadc8c774e2033dfa99c95ccef333bf402b066198c30481e2a83875c

有什么想法吗？我一定错过了很明显的东西，但我不确定那可能是什么。

附：添加正在使用的函数：

 public static byte[] HexToBytesv2(this string hex)
    {
        if (hex.Length % 2 == 1)
            hex = '0' + hex;

        byte[] ret = new byte[hex.Length / 2];

        for (int i = 0; i < ret.Length; i++)
            ret[i] = Convert.ToByte(hex.Substring(i * 2, 2), 16);

        return ret;

    }

  public static string ToHex(byte[] ba)
    {
        StringBuilder hex = new StringBuilder(ba.Length * 2);
        foreach (byte b in ba)
            hex.AppendFormat("{0:x2}", b);
        return hex.ToString();

    }

Answer 1

这是一个字节序问题。

我已经调整了你的编码和解码，现在得到了你正在寻找的答案：

public static byte[] HexToBytesv2(string hex)
{
    if (hex.Length % 2 == 1)
        hex = '0' + hex;

    byte[] ret = new byte[hex.Length / 2];

    for (int i = 0; i < ret.Length; i++)
        ret[i] = Convert.ToByte(hex.Substring(hex.Length - (i+1) * 2, 2), 16);

    return ret;

}

public static string ToHex( byte[] bytes)
{
    var sb = new StringBuilder();
    foreach (var b in bytes.Reverse())
    {
        sb.AppendFormat("{0:x2}", b);
    }
    return sb.ToString();
}

仅供参考，我使用的是 LinqPad，主要方法是问题中的代码（经过调整），并检查数据在途中是否丢失任何内容：

void Main()
{
    string givenp = "00e655cc9e04f3bebae76ecca77143ef5c4451876615a9f8b4f712b8f3bdf47ee7f717c09bb5b2b66450831367d9dcf85f9f0528bcd5318fb1dab2f23ce77c48b6b7381eed13e80a14cca6b30b5e37ffe53db15e2d6b727a2efcee51893678d50e9a89166a359e574c4c3ca5e59fae79924fe6f186b36a2ebde9bf09fe4de50453";
    BigInteger p = new BigInteger(HexToBytesv2(givenp));
    (ToHex(p.ToByteArray()) == "00e655cc9e04f3bebae76ecca77143ef5c4451876615a9f8b4f712b8f3bdf47ee7f717c09bb5b2b66450831367d9dcf85f9f0528bcd5318fb1dab2f23ce77c48b6b7381eed13e80a14cca6b30b5e37ffe53db15e2d6b727a2efcee51893678d50e9a89166a359e574c4c3ca5e59fae79924fe6f186b36a2ebde9bf09fe4de50453").Dump();
    BigInteger g = new BigInteger(2);
    string merchantPrivateKeyHEX = "48887dfd090d175e33beea29e7b38334299289069f9ab492b67807905faa98d96d22d79205bef03f14af093f1797b904734132c34a388fdc79e20497bfa1465fec2aac4fabdf3bb0c9be8685d20f7bfe0346a9abdf7fa89838c3fa9ca6abdb70bea66795ab6699cc154db59490e4159f142f7bddff603c1d3d6c4fff8177e11d";
    BigInteger a = new BigInteger(HexToBytesv2(merchantPrivateKeyHEX));
    (ToHex(a.ToByteArray()) == "48887dfd090d175e33beea29e7b38334299289069f9ab492b67807905faa98d96d22d79205bef03f14af093f1797b904734132c34a388fdc79e20497bfa1465fec2aac4fabdf3bb0c9be8685d20f7bfe0346a9abdf7fa89838c3fa9ca6abdb70bea66795ab6699cc154db59490e4159f142f7bddff603c1d3d6c4fff8177e11d").Dump();
    BigInteger A = BigInteger.ModPow(g, a, p);
    (ToHex(A.ToByteArray()) == "00f85c41e84446ecfe43c9911df31d3cf60d83642afd496b741363290139badf75f8b8c5c010dda2446dd483dc553b6c2698c16c9d082391677785f81d54bc9c7c45f8b6d5bdb3e49fec7f5522b880c8c753fb7d3ff2c81e47dcb27d52842def40a812dc95cc679575baf237a955ee9944bd0797326f2a0a58c6c087f9b0b9e82c").Dump();
    (ToHex(A.ToByteArray()) == "00d9abd78c93dfddeb920d57d6513126d8f1118c9237a45101408dbffe6cfd95b011a016e4e0ab8aef0601e836a452b8bb88be7ca71e4f22f97aa65f8358ee69348d1227d65db6e53641d1a6542aa4be4b4adc75fac816af79a8e3f5097f8313e7b725df37eadc8c774e2033dfa99c95ccef333bf402b066198c30481e2a83875c").Dump();
}

在我交换顺序并包含您原始问题中的 .Concat(new byte[] { 0 }).ToArray() 之前，输出为：

True
True
True
False

现在是：

True
True
False
True

您看到的另一个问题是BigInteger.Parse 和Byte[] 构造函数总是期望第一个半字节或最后一个字节的最高位分别是符号位。所以你需要分别包含额外的0 字符或字节以避免这种情况。

Answer 2

您正在进行许多不必要的转换，并且它们在某处引入了错误。

如果您删除损坏的string-byte[]-BigInteger-byte[]-string 步骤并让BigInteger 自己为您完成工作，那么您将生成预期的结果：

string givenp = "00e655cc9e04f3bebae76ecca77143ef5c4451876615a9f8b4f712b8f3bdf47ee7f717c09bb5b2b66450831367d9dcf85f9f0528bcd5318fb1dab2f23ce77c48b6b7381eed13e80a14cca6b30b5e37ffe53db15e2d6b727a2efcee51893678d50e9a89166a359e574c4c3ca5e59fae79924fe6f186b36a2ebde9bf09fe4de50453";
var p = BigInteger.Parse(givenp, NumberStyles.HexNumber);

var g = new BigInteger(2);

var merchantPrivateKeyHEX = "48887dfd090d175e33beea29e7b38334299289069f9ab492b67807905faa98d96d22d79205bef03f14af093f1797b904734132c34a388fdc79e20497bfa1465fec2aac4fabdf3bb0c9be8685d20f7bfe0346a9abdf7fa89838c3fa9ca6abdb70bea66795ab6699cc154db59490e4159f142f7bddff603c1d3d6c4fff8177e11d";
var a = BigInteger.Parse(merchantPrivateKeyHEX, NumberStyles.HexNumber);

var publicKey = BigInteger.ModPow(g, a, p);
Console.WriteLine(publicKey.ToString("x"));  // displays 0d9abd7...