md5算法描述

原文

http://www.ietf.org/rfc/rfc1321.txt

3. MD5 Algorithm Description

 

   We begin by supposing that we have a b-bit message as input, and that

   we wish to find its message digest. Here b is an arbitrary

   nonnegative integer; b may be zero, it need not be a multiple of

   eight, and it may be arbitrarily large. We imagine the bits of the

   message written down as follows:

          m_0 m_1 ... m_{b-1}

   The following five steps are performed to compute the message digest

   of the message.

 

3.1 Step 1. Append Padding Bits

   The message is "padded" (extended) so that its length (in bits) is

   congruent to 448, modulo 512. That is, the message is extended so

   that it is just 64 bits shy of being a multiple of 512 bits long.

   Padding is always performed, even if the length of the message is

   already congruent to 448, modulo 512.

 

   Padding is performed as follows: a single "1" bit is appended to the

   message, and then "0" bits are appended so that the length in bits of

   the padded message becomes congruent to 448, modulo 512. In all, at

   least one bit and at most 512 bits are appended.

 

3.2 Step 2. Append Length

   A 64-bit representation of b (the length of the message before the

   padding bits were added) is appended to the result of the previous

   step. In the unlikely event that b is greater than 2^64, then only

   the low-order 64 bits of b are used. (These bits are appended as two

   32-bit words and appended low-order word first in accordance with the

   previous conventions.)

 

   At this point the resulting message (after padding with bits and with

   b) has a length that is an exact multiple of 512 bits. Equivalently,

   this message has a length that is an exact multiple of 16 (32-bit)

   words. Let M[0 ... N-1] denote the words of the resulting message,

   where N is a multiple of 16.

 

3.3 Step 3. Initialize MD Buffer

   A four-word buffer (A,B,C,D) is used to compute the message digest.

   Here each of A, B, C, D is a 32-bit register. These registers are

   initialized to the following values in hexadecimal, low-order bytes

   first):

         word A: 01 23 45 67

          word B: 89 ab cd ef

          word C: fe dc ba 98

          word D: 76 54 32 10

 

3.4 Step 4. Process Message in 16-Word Blocks

   We first define four auxiliary functions that each take as input

   three 32-bit words and produce as output one 32-bit word.

 

          F(X,Y,Z) = XY v not(X) Z

          G(X,Y,Z) = XZ v Y not(Z)

          H(X,Y,Z) = X xor Y xor Z

          I(X,Y,Z) = Y xor (X v not(Z))

 

   In each bit position F acts as a conditional: if X then Y else Z.

   The function F could have been defined using + instead of v since XY

   and not(X)Z will never have 1's in the same bit position.) It is

   interesting to note that if the bits of X, Y, and Z are independent

   and unbiased, the each bit of F(X,Y,Z) will be independent and

   unbiased.

 

   The functions G, H, and I are similar to the function F, in that they

   act in "bitwise parallel" to produce their output from the bits of X,

   Y, and Z, in such a manner that if the corresponding bits of X, Y,

   and Z are independent and unbiased, then each bit of G(X,Y,Z),

   H(X,Y,Z), and I(X,Y,Z) will be independent and unbiased. Note that

   the function H is the bit-wise "xor" or "parity" function of its

   inputs.

 

   This step uses a 64-element table T[1 ... 64] constructed from the

   sine function. Let T[i] denote the i-th element of the table, which

   is equal to the integer part of 4294967296 times abs(sin(i)), where i

   is in radians. The elements of the table are given in the appendix.

 

   Do the following:

 

   /* Process each 16-word block. */

   For i = 0 to N/16-1 do

 

     /* Copy block i into X. */

     For j = 0 to 15 do

       Set X[j] to M[i*16+j].

     end /* of loop on j */

 

     /* Save A as AA, B as BB, C as CC, and D as DD. */

     AA = A

     BB = B  CC = C

     DD = D

 

     /* Round 1. */

     /* Let [abcd k s i] denote the operation

          a = b + ((a + F(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  0  7  1]  [DABC  1 12  2]  [CDAB  2 17  3]  [BCDA  3 22  4]

     [ABCD  4  7  5]  [DABC  5 12  6]  [CDAB  6 17  7]  [BCDA  7 22  8]

     [ABCD  8  7  9]  [DABC  9 12 10]  [CDAB 10 17 11]  [BCDA 11 22 12]

     [ABCD 12  7 13]  [DABC 13 12 14]  [CDAB 14 17 15]  [BCDA 15 22 16]

 

     /* Round 2. */

     /* Let [abcd k s i] denote the operation

          a = b + ((a + G(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  1  5 17]  [DABC  6  9 18]  [CDAB 11 14 19]  [BCDA  0 20 20]

     [ABCD  5  5 21]  [DABC 10  9 22]  [CDAB 15 14 23]  [BCDA  4 20 24]

     [ABCD  9  5 25]  [DABC 14  9 26]  [CDAB  3 14 27]  [BCDA  8 20 28]

     [ABCD 13  5 29]  [DABC  2  9 30]  [CDAB  7 14 31]  [BCDA 12 20 32]

 

     /* Round 3. */

     /* Let [abcd k s t] denote the operation

          a = b + ((a + H(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  5  4 33]  [DABC  8 11 34]  [CDAB 11 16 35]  [BCDA 14 23 36]

     [ABCD  1  4 37]  [DABC  4 11 38]  [CDAB  7 16 39]  [BCDA 10 23 40]

     [ABCD 13  4 41]  [DABC  0 11 42]  [CDAB  3 16 43]  [BCDA  6 23 44]

     [ABCD  9  4 45]  [DABC 12 11 46]  [CDAB 15 16 47]  [BCDA  2 23 48]

 

     /* Round 4. */

     /* Let [abcd k s t] denote the operation

          a = b + ((a + I(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  0  6 49]  [DABC  7 10 50]  [CDAB 14 15 51]  [BCDA  5 21 52]

     [ABCD 12  6 53]  [DABC  3 10 54]  [CDAB 10 15 55]  [BCDA  1 21 56]

     [ABCD  8  6 57]  [DABC 15 10 58]  [CDAB  6 15 59]  [BCDA 13 21 60]

     [ABCD  4  6 61]  [DABC 11 10 62]  [CDAB  2 15 63]  [BCDA  9 21 64]

 

     /* Then perform the following additions. (That is increment each

        of the four registers by the value it had before this block

        was started.) */

     A = A + AA

     B = B + BB

     C = C + CC

     D = D + DD

 

   end /* of loop on i */

3.5 Step 5. Output

   The message digest produced as output is A, B, C, D. That is, we

   begin with the low-order byte of A, and end with the high-order byte

   of D.

 

   This completes the description of MD5. A reference implementation in

   C is given in the appendix.

译文：

摘要：

MD5算法的实现有5个步骤：

一 补位

二 补数据长度

三 初始化MD5参数

四 用16块来处理消息

五 输出结果

 

3 MD5算法描述

We begin by supposing that we have a b-bit message as input, and that

   we wish to find its message digest. Here b is an arbitrary

   nonnegative integer; b may be zero, it need not be a multiple of

   eight, and it may be arbitrarily large. We imagine the bits of the

   message written down as follows:

          m_0 m_1 ... m_{b-1}

   The following five steps are performed to compute the message digest

   of the message.

3.1 补位

MD5算法先对输入的数据进行补位，使得数据位长度LEN对512求余的结果是448。即数据扩展至K*512+448位。即K*64+56个字节，K为整数。

具体补位操作：补一个1，然后补0至满足上述要求。

 

3.2 补数据长度

用一个64位的数字表示数据的原始长度B，把B用两个32位数表示。这时，数

据就被填补成长度为512位的倍数。

 

3.3 初始化MD5参数

四个32位整数 (A,B,C,D) 用来计算信息摘要，初始化使用的是十六进制表示的数字。

       word A: 01 23 45 67

       word B: 89 ab cd ef

       word C: fe dc ba 98

       word D: 76 54 32 10

 

3.2用16块来处理消息

       首先定义3个32位整数(X，Y，Z)作为4个非线性函数的输出参数。

          F(X,Y,Z) = XY v not(X) Z

          G(X,Y,Z) = XZ v Y not(Z)

          H(X,Y,Z) = X xor Y xor Z

          I(X,Y,Z) = Y xor (X v not(Z))

 

//////////函数变换过程，暂略描述///////////////////

 

具体过程如下：

   /* Process each 16-word block. */

   For i = 0 to N/16-1 do

 

     /* Copy block i into X. */

     For j = 0 to 15 do

       Set X[j] to M[i*16+j].

     end /* of loop on j */

 

     /* Save A as AA, B as BB, C as CC, and D as DD. */

     AA = A

     BB = B

     CC = C

     DD = D

 

     /* 第1轮. */

     /* Let [abcd k s i] denote the operation

          a = b + ((a + F(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  0  7  1]  [DABC  1 12  2]  [CDAB  2 17  3]  [BCDA  3 22  4]

     [ABCD  4  7  5]  [DABC  5 12  6]  [CDAB  6 17  7]  [BCDA  7 22  8]

     [ABCD  8  7  9]  [DABC  9 12 10]  [CDAB 10 17 11]  [BCDA 11 22 12]

     [ABCD 12  7 13]  [DABC 13 12 14]  [CDAB 14 17 15]  [BCDA 15 22 16]

 

     /* 第 2轮. */

     /* Let [abcd k s i] denote the operation

          a = b + ((a + G(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  1  5 17]  [DABC  6  9 18]  [CDAB 11 14 19]  [BCDA  0 20 20]

     [ABCD  5  5 21]  [DABC 10  9 22]  [CDAB 15 14 23]  [BCDA  4 20 24]

     [ABCD  9  5 25]  [DABC 14  9 26]  [CDAB  3 14 27]  [BCDA  8 20 28]

     [ABCD 13  5 29]  [DABC  2  9 30]  [CDAB  7 14 31]  [BCDA 12 20 32]

 

     /* 第 3轮. */

     /* Let [abcd k s t] denote the operation

          a = b + ((a + H(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  5  4 33]  [DABC  8 11 34]  [CDAB 11 16 35]  [BCDA 14 23 36]

     [ABCD  1  4 37]  [DABC  4 11 38]  [CDAB  7 16 39]  [BCDA 10 23 40]

     [ABCD 13  4 41]  [DABC  0 11 42]  [CDAB  3 16 43]  [BCDA  6 23 44]

     [ABCD  9  4 45]  [DABC 12 11 46]  [CDAB 15 16 47]  [BCDA  2 23 48]

 

     /* 第 4轮. */

     /* Let [abcd k s t] denote the operation

          a = b + ((a + I(b,c,d) + X[k] + T[i]) <<< s). */

     /* Do the following 16 operations. */

     [ABCD  0  6 49]  [DABC  7 10 50]  [CDAB 14 15 51]  [BCDA  5 21 52]

     [ABCD 12  6 53]  [DABC  3 10 54]  [CDAB 10 15 55]  [BCDA  1 21 56]

     [ABCD  8  6 57]  [DABC 15 10 58]  [CDAB  6 15 59]  [BCDA 13 21 60]

     [ABCD  4  6 61]  [DABC 11 10 62]  [CDAB  2 15 63]  [BCDA  9 21 64]

 

     /* Then perform the following additions. (That is increment each

        of the four registers by the value it had before this block

        was started.) */

     A = A + AA

     B = B + BB

     C = C + CC

     D = D + DD

 

   end /* of loop on i */

 

3.5 输出结果

       消息摘要的输出结果是A，B，C，D，以A为开始的低字节，以D为结束的高字节。

上面完成了MD5的算法描述，一个C的相关实现已在附录中给出。