使用密钥的可逆洗牌算法

Question

如何在 C# 中编写可逆的随机播放算法，该算法使用密钥进行随机播放并且可以反转到原始状态？

例如，我有一个字符串：“Hello world”，我怎样才能将它打乱，以便稍后我可以将打乱的字符串反转回“Hello world”。

Answer 1

查看Fisher-Yates shuffle 以了解基于键置换字符串的方法。将密钥作为种子输入到 PRNG 中，使用它来生成 shuffle 使用的随机数。

现在，如何逆转这个过程？ Fisher-Yates 通过交换某些元素对来工作。因此，要反转该过程，您可以将相同的密钥提供给相同的 PRNG，然后运行 ​​Fisher-Yates 算法就好像您正在改组一个字符串大小的数组。但实际上你并没有移动任何东西，只是记录了每个阶段要交换的元素的索引。

完成此操作后，逆向遍历你的交换列表，将它们应用到你的洗牌字符串。结果是原始字符串。

例如，假设我们使用以下交换对字符串“hello”进行了洗牌（我在这里没有使用 PRNG，我掷骰子，但关于 PRNG 的重点是它为您提供相同的数字序列给定相同的种子）：

(4,0): "hello" -> "oellh"
(3,3): "oellh" -> "oellh"
(2,1): "oellh" -> "olelh"
(1,0): "olelh" -> "loelh"

所以，洗牌后的字符串是“loelh”。

为了去洗牌，我生成了相同系列的“随机”数字，0、3、1、0。然后以相反的顺序应用交换：

(1,0): "loelh" -> "olelh"
(2,1): "olelh" -> "oellh"
(3,3): "oellh" -> "oellh"
(4,0): "oellh" -> "hello"

成功了！

当然，这样做的缺点是它使用大量内存进行洗牌：索引数组与原始字符数组一样长。因此，对于真正巨大的数组，您可能想要选择一个 PRNG（或者无论如何是序列生成函数），它可以向前或向后步进，而无需存储所有输出。这排除了基于哈希的加密安全 PRNG，但 LFSR 是可逆的。

顺便说一句，你为什么要这样做？

Answer 2

这是您需要的一个简单实现（如果我做得好的话）：

public static class ShuffleExtensions
{
    public static int[] GetShuffleExchanges(int size, int key)
    {
        int[] exchanges = new int[size - 1];
        var rand = new Random(key);
        for (int i = size - 1; i > 0; i--)
        {
            int n = rand.Next(i + 1);
            exchanges[size - 1 - i] = n;
        }
        return exchanges;
    }

    public static string Shuffle(this string toShuffle, int key)
    {
        int size = toShuffle.Length;
        char[] chars = toShuffle.ToArray();
        var exchanges = GetShuffleExchanges(size, key);
        for (int i = size - 1; i > 0; i--)
        {
            int n = exchanges[size - 1 - i];
            char tmp = chars[i];
            chars[i] = chars[n];
            chars[n] = tmp;
        }
        return new string(chars);
    }

    public static string DeShuffle(this string shuffled, int key)
    {
        int size = shuffled.Length;
        char[] chars = shuffled.ToArray();
        var exchanges = GetShuffleExchanges(size, key);
        for (int i = 1; i < size; i++)
        {
            int n = exchanges[size - i - 1];
            char tmp = chars[i];
            chars[i] = chars[n];
            chars[n] = tmp;
        }
        return new string(chars);
    }
}

用法：

var originalString = "Hello world";
var shuffled = originalString.Shuffle(123);
var deShuffled = shuffled.DeShuffle(123);

// shuffled = "lelooH rwld";
// deShuffled = "Hello world";

密钥必须是整数，如果需要使用字符串作为密码，只需调用GetHashCode()即可：

var shuffled = originalString.Shuffle(myStringKey.GetHashCode());

编辑：

现在正是 Fisher-Yates shuffle 算法的实现。 感谢 Jeff the code

Answer 3

您可以查看以下问题及其答案。 Encrypt/Decrypt string in .NET

Answer 4

一个java问题也重定向到这里，所以这里是完整的加密强度java实现：

import java.security.*;
import java.util.*;

/** Cryptographic strength reversible random shuffle. To be truly secure, the passKey arguments should be 20 chars or more and (obviously) not guessable. */
public class SecureShuffle
{
    public static int[] getShuffleExchanges(int size, String passKey)
    {
        int[] exchanges = new int[size - 1];
        SecureRandom rand = new SecureRandom(passKey.getBytes());
        for (int i = size - 1; i > 0; i--)
        {
            int n = rand.nextInt(i + 1);
            exchanges[size - 1 - i] = n;
        }
        return exchanges;
    }

    public static void shuffle(byte[] toShuffle, String passKey)
    {
        int size = toShuffle.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = size - 1; i > 0; i--)
        {
            int n = exchanges[size - 1 - i];
            byte tmp = toShuffle[i];
            toShuffle[i] = toShuffle[n];
            toShuffle[n] = tmp;
        }
    }

    public static void deshuffle(byte[] shuffled, String passKey)
    {
        int size = shuffled.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = 1; i < size; i++)
        {
            int n = exchanges[size - i - 1];
            byte tmp = shuffled[i];
            shuffled[i] = shuffled[n];
            shuffled[n] = tmp;
        }
    }

    public static void shuffle(char[] toShuffle, String passKey)
    {
        int size = toShuffle.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = size - 1; i > 0; i--)
        {
            int n = exchanges[size - 1 - i];
            char tmp = toShuffle[i];
            toShuffle[i] = toShuffle[n];
            toShuffle[n] = tmp;
        }
    }

    public static void deshuffle(char[] shuffled, String passKey)
    {
        int size = shuffled.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = 1; i < size; i++)
        {
            int n = exchanges[size - i - 1];
            char tmp = shuffled[i];
            shuffled[i] = shuffled[n];
            shuffled[n] = tmp;
        }
    }

    public static void shuffle(int[] toShuffle, String passKey)
    {
        int size = toShuffle.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = size - 1; i > 0; i--)
        {
            int n = exchanges[size - 1 - i];
            int tmp = toShuffle[i];
            toShuffle[i] = toShuffle[n];
            toShuffle[n] = tmp;
        }
    }

    public static void deshuffle(int[] shuffled, String passKey)
    {
        int size = shuffled.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = 1; i < size; i++)
        {
            int n = exchanges[size - i - 1];
            int tmp = shuffled[i];
            shuffled[i] = shuffled[n];
            shuffled[n] = tmp;
        }
    }

    public static void shuffle(long[] toShuffle, String passKey)
    {
        int size = toShuffle.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = size - 1; i > 0; i--)
        {
            int n = exchanges[size - 1 - i];
            long tmp = toShuffle[i];
            toShuffle[i] = toShuffle[n];
            toShuffle[n] = tmp;
        }
    }

    public static void deshuffle(long[] shuffled, String passKey)
    {
        int size = shuffled.length;
        int[] exchanges = getShuffleExchanges(size, passKey);
        for (int i = 1; i < size; i++)
        {
            int n = exchanges[size - i - 1];
            long tmp = shuffled[i];
            shuffled[i] = shuffled[n];
            shuffled[n] = tmp;
        }
    }

    public static void main(String[] args)
    {
        String passphrase = "passphrase";
        String text = "The rain in Spain stays mainly on the plain";

        char[] chars = text.toCharArray();
        shuffle(chars, passphrase);
        System.out.println(new String(chars));

        deshuffle(chars, passphrase);
        System.out.println(new String(chars));

        byte[] bytes = new byte[] {0, 1, 2, 3, 4, 5, 6, 7};
        shuffle(bytes, passphrase);
        System.out.println(Arrays.toString(bytes));

        deshuffle(bytes, passphrase);
        System.out.println(Arrays.toString(bytes));
    }

}