非对称加密RSA C#加密源码

陽陽陽

RSA C#加密源码，不知道写的对不对，请各位指正，只是略微搞懂个原理。还有就是里面肯定有更简洁的方式找公匙私匙，也欢迎大佬补充。
注意：使用RSA加密时密匙必须大于加密内容，否则输出错误信息。

[C#] 纯文本查看 复制代码

using System;
using System.Collections.Generic;
using System.Numerics;
using System.Security.Cryptography;

public class HelloWorld
{
    public static void Main(string[] args)
    {
        Console.WriteLine("STARTED");
        for (int i = 0; i < 1; i++)
        {
            var primes = GenerateLargePrimes(4096);
            CalcKey(primes.Item1, primes.Item2);
        }
    }

    private static (BigInteger, BigInteger) GenerateLargePrimes(int bitLength)
    {
        BigInteger firstPrime = _GenerateLargePrime(bitLength);
        BigInteger secondPrime = _GenerateLargePrime(bitLength);
        return (firstPrime, secondPrime);
    }

    private static BigInteger _GenerateLargePrime(int bitLength)
    {
        using (var rng = new RNGCryptoServiceProvider())
        {
            BigInteger prime;
            byte[] bytes = new byte[bitLength / 8];
            do
            {
                rng.GetBytes(bytes);
                prime = new BigInteger(bytes);
                prime = BigInteger.Abs(prime);
                prime |= BigInteger.One; // 确保是奇数
            } while (!IsProbablyPrime(prime, 10)); // 使用 Miller-Rabin 测试

            return prime;
        }
    }

    private static bool IsProbablyPrime(BigInteger source, int certainty)
    {
        if (source == 2 || source == 3)
            return true;
        if (source < 2 || source % 2 == 0)
            return false;

        BigInteger d = source - 1;
        int s = 0;

        while (d % 2 == 0)
        {
            d /= 2;
            s += 1;
        }

        for (int i = 0; i < certainty; i++)
        {
            BigInteger a = RandomIntegerBelow(source - 2) + 1;
            BigInteger temp = d;
            BigInteger mod = BigInteger.ModPow(a, temp, source);
            if (mod == 1 || mod == source - 1)
                continue;

            for (int j = 0; j < s - 1; j++)
            {
                mod = BigInteger.ModPow(mod, 2, source);
                if (mod == 1)
                    return false;
                if (mod == source - 1)
                    break;
            }

            if (mod != source - 1)
                return false;
        }

        return true;
    }

    private static BigInteger RandomIntegerBelow(BigInteger n)
    {
        using (var rng = new RNGCryptoServiceProvider())
        {
            byte[] bytes = n.ToByteArray();
            BigInteger r;

            do
            {
                rng.GetBytes(bytes);
                r = new BigInteger(bytes);
            } while (r >= n || r <= 0);

            return r;
        }
    }

    public static void CalcKey(BigInteger p, BigInteger q)
    {
        BigInteger n = p * q;
        BigInteger phi = (p - 1) * (q - 1);

        BigInteger e = FindCoprime(phi);
        BigInteger d = ModInverse(e, phi);

        Console.WriteLine("Public key (e, n): (" + e + ", " + n + ")");
        Console.WriteLine("Private key (d, n): (" + d + ", " + n + ")");

        BigInteger message = BigInteger.Parse("9999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999");
        BigInteger encrypted = Encrypt(message, e, n);

        Console.WriteLine("Encrypted: " + encrypted);

        BigInteger decrypted = Decrypt(encrypted, d, n);
        Console.WriteLine("Decrypted: " + decrypted);
    }

    public static BigInteger GCD(BigInteger a, BigInteger b)
    {
        if (b == 0)
            return a;
        return GCD(b, a % b);
    }

    public static BigInteger FindCoprime(BigInteger r)
    {
        BigInteger e = 2;
        while (e < r)
        {
            if (GCD(e, r) == 1)
                return e;
            e++;
        }
        return 1;
    }

    public static BigInteger ModInverse(BigInteger e, BigInteger r)
    {
        BigInteger x, y;
        BigInteger gcd = ExtendedGCD(e, r, out x, out y);
        if (gcd != 1)
        {
            throw new Exception("Inverse doesn't exist.");
        }
        else
        {
            return (x % r + r) % r;
        }
    }

    public static BigInteger ExtendedGCD(BigInteger a, BigInteger b, out BigInteger x, out BigInteger y)
    {
        if (a == 0)
        {
            x = 0;
            y = 1;
            return b;
        }
        BigInteger x1, y1;
        BigInteger gcd = ExtendedGCD(b % a, a, out x1, out y1);
        x = y1 - (b / a) * x1;
        y = x1;
        return gcd;
    }

    public static BigInteger Encrypt(BigInteger m, BigInteger e, BigInteger N)
    {
        return BigInteger.ModPow(m, e, N);
    }

    public static BigInteger Decrypt(BigInteger c, BigInteger d, BigInteger N)
    {
        return BigInteger.ModPow(c, d, N);
    }
}

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