MD5算法详解

前面一篇,带大家对加密算法进行了鸟瞰,本篇主要谈md5算法的实现。

MD5:Message-Digest Algorithm 5(信息摘要5),确保信息的完整性。其算法是1992年公开的,那时我才几岁,鉴于大家对md5都很熟悉,且程序中经常应用,我就不再介绍了。我简单的介绍下设计者。其人是罗纳德·李维斯特,美国密码学家,后来发明了非对称秘钥RSA算法,因这个算法的在信息安全中的突破与重要性而获得了2002年的图灵奖。

好了,接下来一起看算法步骤以及源代码:

1、填充

在MD5算法中,首先需要对信息进行填充,使其位长对512求余的结果等于448,并且填充必须进行,使其位长对512求余的结果等于448。因此,信息的位长(Bits Length)将被扩展至N*512+448,N为一个非负整数,N可以是零。

理解:位长,就是位数。比如一个“wbq”,字符串是三个字节存储,一个字节8bit,所以位长就是24。

用数学语言可能更简洁:设M为位长,当且仅当  M%512==448时,才可以处理。换另一种表示方式,M=N*512+448 ,N>=0

填充的方法如下:

1) 在信息的后面填充一个1和无数个0,直到满足上面的条件时才停止用0对信息的填充。

2) 在这个结果后面附加一个以64位二进制表示的填充前信息长度(单位为Bit),如果二进制表示的填充前信息长度超过64位,则取低64位。

经过这两步的处理,M=N*512+448+64=(N+1)*512,即长度恰好是512的整数倍。这样做的原因是为满足后面处理中对信息长度的要求。

经过两步处理后,信息变成了这样,如下图所示:

 

 

64位,8个字节,用来表示原始信息的位长。

 1         private static UInt32[] MD5_Append(byte[] input)
 2         {
 3             int zeros = 0;
 4             int ones = 1;
 5             int size = 0;
 6             int n = input.Length;
 7             int m = n % 64;
 8             if (m < 56)
 9             {
10                 zeros = 55 - m;
11                 size = n - m + 64;
12             }
13             else if (m == 56)
14             {
15                 zeros = 0;
16                 ones = 0;
17                 size = n + 8;
18             }
19             else
20             {
21                 zeros = 63 - m + 56;
22                 size = n + 64 - m + 64;
23             }
24 
25             ArrayList bs = new ArrayList(input);
26             if (ones == 1)
27             {
28                 bs.Add((byte)0x80); // 0x80 = $10000000
29             }
30             for (int i = 0; i < zeros; i++)
31             {
32                 bs.Add((byte)0);
33             }
34 
35             UInt64 N = (UInt64)n * 8;
36             byte h1 = (byte)(N & 0xFF);
37             byte h2 = (byte)((N >> 8) & 0xFF);
38 
39             byte h3 = (byte)((N >> 16) & 0xFF);
40             byte h4 = (byte)((N >> 24) & 0xFF);
41             byte h5 = (byte)((N >> 32) & 0xFF);
42             byte h6 = (byte)((N >> 40) & 0xFF);
43             byte h7 = (byte)((N >> 48) & 0xFF);
44             byte h8 = (byte)(N >> 56);
45             bs.Add(h1);
46             bs.Add(h2);
47             bs.Add(h3);
48             bs.Add(h4);
49             bs.Add(h5);
50             bs.Add(h6);
51             bs.Add(h7);
52             bs.Add(h8);
53             byte[] ts = (byte[])bs.ToArray(typeof(byte));
54 
55             /* Decodes input (byte[]) into output (UInt32[]). Assumes len is
56              * a multiple of 4.
57              */
58             UInt32[] output = new UInt32[size / 4];
59             for (Int64 i = 0, j = 0; i < size; j++, i += 4)
60             {
61                 output[j] = (UInt32)(ts[i] | ts[i + 1] << 8 | ts[i + 2] << 16 | ts[i + 3] << 24);
62             }
63             return output;
64         }

说明,补多少0,如何补?第7行,求余。第10行,为什么是55-m,而不是56-m?此时m<56,56-m表示,还需要补多少。因为需要补1个1,所以补0,就是56-m-1=55-m。那么变更后的长度size如何计算?应该是新长度=原始长度+补1的长度+补0的长度+最后64位的长度,第11行  size = n - m + 64,推导如下:

size=n+1+55-m+8=n-m+64

注意:这里的计算都是字节数的计算

其余两个分支,可以以此类推。从35-44行,把原始信息的位长转为字节,追加到数组后面。58行以后,是把信息划分了4组。分组是UInt32,无符号32位,即4个字节。61行的操作,就是把四个字节转为一个UInt32。

2、初始化变量

      private static void MD5_Init()
        {
            A = 0x67452301;  //in memory, this is 0x01234567
            B = 0xefcdab89;  //in memory, this is 0x89abcdef
            C = 0x98badcfe;  //in memory, this is 0xfedcba98
            D = 0x10325476;  //in memory, this is 0x76543210
        }

注意:这里用的是小端模式,什么是大端和小端模式?

举一个例子,比如数字0x12 34 56 78在内存中的表示形式。

1)大端模式:Big-Endian就是高位字节排放在内存的低地址端,低位字节排放在内存的高地址端。(其实大端模式比较直观)

低地址 --------------------> 高地址
0x12  |  0x34  |  0x56  |  0x78

2)小端模式:Little-Endian就是低位字节排放在内存的低地址端,高位字节排放在内存的高地址端。

低地址 --------------------> 高地址
0x78  |  0x56  |  0x34  |  0x12

3. 处理分组数据

        private static UInt32[] MD5_Trasform(UInt32[] x)
        {
            UInt32 a, b, c, d;

            for (int k = 0; k < x.Length; k += 16)
            {
                a = A;
                b = B;
                c = C;
                d = D;

                /* Round 1 */
                FF(ref a, b, c, d, x[k + 0], S11, 0xd76aa478); /* 1 */
                FF(ref d, a, b, c, x[k + 1], S12, 0xe8c7b756); /* 2 */
                FF(ref c, d, a, b, x[k + 2], S13, 0x242070db); /* 3 */
                FF(ref b, c, d, a, x[k + 3], S14, 0xc1bdceee); /* 4 */
                FF(ref a, b, c, d, x[k + 4], S11, 0xf57c0faf); /* 5 */
                FF(ref d, a, b, c, x[k + 5], S12, 0x4787c62a); /* 6 */
                FF(ref c, d, a, b, x[k + 6], S13, 0xa8304613); /* 7 */
                FF(ref b, c, d, a, x[k + 7], S14, 0xfd469501); /* 8 */
                FF(ref a, b, c, d, x[k + 8], S11, 0x698098d8); /* 9 */
                FF(ref d, a, b, c, x[k + 9], S12, 0x8b44f7af); /* 10 */
                FF(ref c, d, a, b, x[k + 10], S13, 0xffff5bb1); /* 11 */
                FF(ref b, c, d, a, x[k + 11], S14, 0x895cd7be); /* 12 */
                FF(ref a, b, c, d, x[k + 12], S11, 0x6b901122); /* 13 */
                FF(ref d, a, b, c, x[k + 13], S12, 0xfd987193); /* 14 */
                FF(ref c, d, a, b, x[k + 14], S13, 0xa679438e); /* 15 */
                FF(ref b, c, d, a, x[k + 15], S14, 0x49b40821); /* 16 */

                /* Round 2 */
                GG(ref a, b, c, d, x[k + 1], S21, 0xf61e2562); /* 17 */
                GG(ref d, a, b, c, x[k + 6], S22, 0xc040b340); /* 18 */
                GG(ref c, d, a, b, x[k + 11], S23, 0x265e5a51); /* 19 */
                GG(ref b, c, d, a, x[k + 0], S24, 0xe9b6c7aa); /* 20 */
                GG(ref a, b, c, d, x[k + 5], S21, 0xd62f105d); /* 21 */
                GG(ref d, a, b, c, x[k + 10], S22, 0x2441453); /* 22 */
                GG(ref c, d, a, b, x[k + 15], S23, 0xd8a1e681); /* 23 */
                GG(ref b, c, d, a, x[k + 4], S24, 0xe7d3fbc8); /* 24 */
                GG(ref a, b, c, d, x[k + 9], S21, 0x21e1cde6); /* 25 */
                GG(ref d, a, b, c, x[k + 14], S22, 0xc33707d6); /* 26 */
                GG(ref c, d, a, b, x[k + 3], S23, 0xf4d50d87); /* 27 */
                GG(ref b, c, d, a, x[k + 8], S24, 0x455a14ed); /* 28 */
                GG(ref a, b, c, d, x[k + 13], S21, 0xa9e3e905); /* 29 */
                GG(ref d, a, b, c, x[k + 2], S22, 0xfcefa3f8); /* 30 */
                GG(ref c, d, a, b, x[k + 7], S23, 0x676f02d9); /* 31 */
                GG(ref b, c, d, a, x[k + 12], S24, 0x8d2a4c8a); /* 32 */

                /* Round 3 */
                HH(ref a, b, c, d, x[k + 5], S31, 0xfffa3942); /* 33 */
                HH(ref d, a, b, c, x[k + 8], S32, 0x8771f681); /* 34 */
                HH(ref c, d, a, b, x[k + 11], S33, 0x6d9d6122); /* 35 */
                HH(ref b, c, d, a, x[k + 14], S34, 0xfde5380c); /* 36 */
                HH(ref a, b, c, d, x[k + 1], S31, 0xa4beea44); /* 37 */
                HH(ref d, a, b, c, x[k + 4], S32, 0x4bdecfa9); /* 38 */
                HH(ref c, d, a, b, x[k + 7], S33, 0xf6bb4b60); /* 39 */
                HH(ref b, c, d, a, x[k + 10], S34, 0xbebfbc70); /* 40 */
                HH(ref a, b, c, d, x[k + 13], S31, 0x289b7ec6); /* 41 */
                HH(ref d, a, b, c, x[k + 0], S32, 0xeaa127fa); /* 42 */
                HH(ref c, d, a, b, x[k + 3], S33, 0xd4ef3085); /* 43 */
                HH(ref b, c, d, a, x[k + 6], S34, 0x4881d05); /* 44 */
                HH(ref a, b, c, d, x[k + 9], S31, 0xd9d4d039); /* 45 */
                HH(ref d, a, b, c, x[k + 12], S32, 0xe6db99e5); /* 46 */
                HH(ref c, d, a, b, x[k + 15], S33, 0x1fa27cf8); /* 47 */
                HH(ref b, c, d, a, x[k + 2], S34, 0xc4ac5665); /* 48 */

                /* Round 4 */
                II(ref a, b, c, d, x[k + 0], S41, 0xf4292244); /* 49 */
                II(ref d, a, b, c, x[k + 7], S42, 0x432aff97); /* 50 */
                II(ref c, d, a, b, x[k + 14], S43, 0xab9423a7); /* 51 */
                II(ref b, c, d, a, x[k + 5], S44, 0xfc93a039); /* 52 */
                II(ref a, b, c, d, x[k + 12], S41, 0x655b59c3); /* 53 */
                II(ref d, a, b, c, x[k + 3], S42, 0x8f0ccc92); /* 54 */
                II(ref c, d, a, b, x[k + 10], S43, 0xffeff47d); /* 55 */
                II(ref b, c, d, a, x[k + 1], S44, 0x85845dd1); /* 56 */
                II(ref a, b, c, d, x[k + 8], S41, 0x6fa87e4f); /* 57 */
                II(ref d, a, b, c, x[k + 15], S42, 0xfe2ce6e0); /* 58 */
                II(ref c, d, a, b, x[k + 6], S43, 0xa3014314); /* 59 */
                II(ref b, c, d, a, x[k + 13], S44, 0x4e0811a1); /* 60 */
                II(ref a, b, c, d, x[k + 4], S41, 0xf7537e82); /* 61 */
                II(ref d, a, b, c, x[k + 11], S42, 0xbd3af235); /* 62 */
                II(ref c, d, a, b, x[k + 2], S43, 0x2ad7d2bb); /* 63 */
                II(ref b, c, d, a, x[k + 9], S44, 0xeb86d391); /* 64 */

                A += a;
                B += b;
                C += c;
                D += d;
            }
            return new UInt32[] { A, B, C, D };
        }

每一个分组经过64轮处理,FF、GG、HH、II为处理函数。从上面程序,可以看出,每16个数字为一组。以上是算法的核心处理方法,下面是程序主方法:

        public static byte[] MD5Array(byte[] input)
        {
            MD5_Init();
            UInt32[] block = MD5_Append(input);
            UInt32[] bits = MD5_Trasform(block);

            /* Encodes bits (UInt32[]) into output (byte[]). Assumes len is
             * a multiple of 4.
                 */
            byte[] output = new byte[bits.Length * 4];
            for (int i = 0, j = 0; i < bits.Length; i++, j += 4)
            {
                output[j] = (byte)(bits[i] & 0xff);
                output[j + 1] = (byte)((bits[i] >> 8) & 0xff);
                output[j + 2] = (byte)((bits[i] >> 16) & 0xff);
                output[j + 3] = (byte)((bits[i] >> 24) & 0xff);
            }
            return output;
        }

把output连接起来,就是md5值,output传入到下面方法:

      public static string ArrayToHexString(byte[] array, bool uppercase)
        {
            string hexString = "";
            string format = "x2";
            if (uppercase)
            {
                format = "X2";
            }
            foreach (byte b in array)
            {
                hexString += b.ToString(format);
            }
            return hexString;
        }

附录:常量和基础函数:

       //static state variables
        private static UInt32 A;
        private static UInt32 B;
        private static UInt32 C;
        private static UInt32 D;

        #region 常量

        //number of bits to rotate in tranforming
        private const int S11 = 7;
        private const int S12 = 12;
        private const int S13 = 17;
        private const int S14 = 22;
        private const int S21 = 5;
        private const int S22 = 9;
        private const int S23 = 14;
        private const int S24 = 20;
        private const int S31 = 4;
        private const int S32 = 11;
        private const int S33 = 16;
        private const int S34 = 23;
        private const int S41 = 6;
        private const int S42 = 10;
        private const int S43 = 15;
        private const int S44 = 21;

        #endregion

        #region 基础函数

        /* F, G, H and I are basic MD5 functions.
         * 四个非线性函数:
         * 
         * F(X,Y,Z) =(X&Y)|((~X)&Z)
         * G(X,Y,Z) =(X&Z)|(Y&(~Z))
         * H(X,Y,Z) =X^Y^Z
         * I(X,Y,Z)=Y^(X|(~Z))
         * 
         * (&与,|或,~非,^异或)
         */
        private static uint F(UInt32 x, UInt32 y, UInt32 z)
        {
            return (x & y) | ((~x) & z);
        }
        private static uint G(UInt32 x, UInt32 y, UInt32 z)
        {
            return (x & z) | (y & (~z));
        }
        private static uint H(UInt32 x, UInt32 y, UInt32 z)
        {
            return x ^ y ^ z;   
        }
        private static uint I(UInt32 x, UInt32 y, UInt32 z)
        {
            return y ^ (x | (~z));
        }

        /* FF, GG, HH, and II transformations for rounds 1, 2, 3, and 4.
         * Rotation is separate from addition to prevent recomputation.
         */
        private static void FF(ref UInt32 a, UInt32 b, UInt32 c, UInt32 d, UInt32 mj, int s, UInt32 ti)
        {
            a = a + F(b, c, d) + mj + ti;
            a = a << s | a >> (32 - s);
            a += b;
        }
        private static void GG(ref UInt32 a, UInt32 b, UInt32 c, UInt32 d, UInt32 mj, int s, UInt32 ti)
        {
            a = a + G(b, c, d) + mj + ti;
            a = a << s | a >> (32 - s);
            a += b;
        }
        private static void HH(ref UInt32 a, UInt32 b, UInt32 c, UInt32 d, UInt32 mj, int s, UInt32 ti)
        {
            a = a + H(b, c, d) + mj + ti;
            a = a << s | a >> (32 - s);
            a += b;
        }
        private static void II(ref UInt32 a, UInt32 b, UInt32 c, UInt32 d, UInt32 mj, int s, UInt32 ti)
        {
            a = a + I(b, c, d) + mj + ti;
            a = a << s | a >> (32 - s);
            a += b;
        }

        #endregion

 

说明:

假设Mj表示消息的第j个子分组(从0到15),常数ti是4294967296*abs( sin(i) )的整数部分,i 取值从1到64,单位是弧度。(4294967296=2的32次方)

现定义:

FF(a ,b ,c ,d ,Mj ,s ,ti ) 操作为 a = b + ( (a + F(b,c,d) + Mj + ti) << s)

GG(a ,b ,c ,d ,Mj ,s ,ti ) 操作为 a = b + ( (a + G(b,c,d) + Mj + ti) << s)

HH(a ,b ,c ,d ,Mj ,s ,ti) 操作为 a = b + ( (a + H(b,c,d) + Mj + ti) << s)

II(a ,b ,c ,d ,Mj ,s ,ti) 操作为 a = b + ( (a + I(b,c,d) + Mj + ti) << s)

注意:此处“<<”表示循环左移位,不是左移位。函数内部有循环左移位的处理,符号本身表示左移位。FF函数的第二行代码如下:

 a = a << s | a >> (32 - s);

它先左移,然后右移,两者与操作。左移,右边补0。右移,左边补0。所以实现了循环左移。可以想象把一直线,首尾相连,然后移动点,最后从某处切开,变成了新的首尾。

小结:关于MD5的算法,还算是比较简单的算法,相比其它的加密算法而言。每一个算法都值得去推敲和学习。

 

posted @ 2021-06-28 19:21  micDavid  阅读(2716)  评论(0编辑  收藏  举报