rfc1186.txt

著名的RFC文档,其中有一些文档是已经翻译成中文的的.

Network Working Group                                         R. Rivest
Request for Comments: 1186          MIT Laboratory for Computer Science
                                                           October 1990


                    The MD4 Message Digest Algorithm

Status of this Memo

   This RFC is the specification of the MD4 Digest Algorithm.  If you
   are going to implement MD4, it is suggested you do it this way.  This
   memo is for informational use and does not constitute a standard.
   Distribution of this memo is unlimited.

Table of Contents

   1.  Abstract ....................................................    1
   2.  Terminology and Notation ....................................    2
   3.  MD4 Algorithm Description ...................................    2
   4.  Extensions ..................................................    6
   5.  Summary .....................................................    7
   6.  Acknowledgements ............................................    7
   APPENDIX - Reference Implementation .............................    7
   Security Considerations..........................................   18
   Author's Address.................................................   18

1. Abstract

   This note describes the MD4 message digest algorithm.  The algorithm
   takes as input an input message of arbitrary length and produces as
   output a 128-bit "fingerprint" or "message digest" of the input.  It
   is conjectured that it is computationally infeasible to produce two
   messages having the same message digest, or to produce any message
   having a given prespecified target message digest.  The MD4 algorithm
   is thus ideal for digital signature applications, where a large file
   must be "compressed" in a secure manner before being signed with the
   RSA public-key cryptosystem.

   The MD4 algorithm is designed to be quite fast on 32-bit machines.
   On a SUN Sparc station, MD4 runs at 1,450,000 bytes/second.  On a DEC
   MicroVax II, MD4 runs at approximately 70,000 bytes/second.  On a
   20MHz 80286, MD4 runs at approximately 32,000 bytes/second.  In
   addition, the MD4 algorithm does not require any large substitution
   tables; the algorithm can be coded quite compactly.

   The MD4 algorithm is being placed in the public domain for review and
   possible adoption as a standard.




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RFC 1186              MD4 Message Digest Algorithm          October 1990


   (Note: The document supersedes an earlier draft.  The algorithm
   described here is a slight modification of the one described in the
   draft.)

2.  Terminology and Notation

   In this note a "word" is a 32-bit quantity and a byte is an 8-bit
   quantity.  A sequence of bits can be interpreted in a natural manner
   as a sequence of bytes, where each consecutive group of 8 bits is
   interpreted as a byte with the high-order (most significant) bit of
   each byte listed first.  Similarly, a sequence of bytes can be
   interpreted as a sequence of 32-bit words, where each consecutive
   group of 4 bytes is interpreted as a word with the low-order (least
   significant) byte given first.

   Let x_i denote "x sub i".  If the subscript is an expression, we
   surround it in braces, as in x_{i+1}.  Similarly, we use ^ for
   superscripts (exponentiation), so that x^i denotes x to the i-th
   power.

   Let the symbol "+" denote addition of words (i.e., modulo- 2^32
   addition). Let X <<< s denote the 32-bit value obtained by circularly
   shifting (rotating) X left by s bit positions.  Let not(X) denote the
   bit-wise complement of X, and let X v Y denote the bit-wise OR of X
   and Y.  Let X xor Y denote the bit-wise XOR of X and Y, and let XY
   denote the bit-wise AND of X and Y.

3.  MD4 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 8,
   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.

      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 (in
         which case 512 bits of padding are added).



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         Padding is performed as follows: a single "1" bit is appended
         to the message, and then enough zero bits are appended so that
         the length in bits of the padded message becomes congruent to
         448, modulo 512.

      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.

      Step 3. Initialize MD buffer

         A 4-word buffer (A,B,C,D) is used to compute the message
         digest.  Here each of A,B,C,D are 32-bit registers.  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

      Step 4. Process message in 16-word blocks

         We first define three 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)  =  XY v XZ v YZ
            h(X,Y,Z)  =  X xor Y xor 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.)  In each bit position g acts as a majority function:
         if at least two of x, y, z are on, then g has a one in that bit
         position, else g has a zero. It is interesting to note that if



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         the bits of X, Y, and Z are independent and unbiased, the each
         bit of f(X,Y,Z) will be independent and unbiased, and similarly
         each bit of g(X,Y,Z) will be independent and unbiased.  The
         function h is the bit-wise "xor" or "parity" function; it has
         properties similar to those of f and g.

         Do the following:

         For i = 0 to N/16-1 do  /* process each 16-word block */
                 For j = 0 to 15 do: /* copy block i into X */
                   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.

                 [Round 1]
                   Let [A B C D i s] denote the operation
                         A = (A + f(B,C,D) + X[i]) <<< s  .
                   Do the following 16 operations:
                         [A B C D 0 3]
                         [D A B C 1 7]
                         [C D A B 2 11]
                         [B C D A 3 19]
                         [A B C D 4 3]
                         [D A B C 5 7]
                         [C D A B 6 11]
                         [B C D A 7 19]
                         [A B C D 8 3]
                         [D A B C 9 7]
                         [C D A B 10 11]
                         [B C D A 11 19]
                         [A B C D 12 3]
                         [D A B C 13 7]
                         [C D A B 14 11]
                         [B C D A 15 19]

                 [Round 2]
                   Let [A B C D i s] denote the operation
                         A = (A + g(B,C,D) + X[i] + 5A827999) <<< s .
                   (The value 5A..99 is a hexadecimal 32-bit
                   constant, written with the high-order digit
                   first. This constant represents the square
                   root of 2.  The octal value of this constant
                   is 013240474631.  See Knuth, The Art of
                   Programming, Volume 2 (Seminumerical
                   Algorithms), Second Edition (1981),
                   Addison-Wesley.  Table 2, page 660.)
                   Do the following 16 operations:
                         [A B C D 0  3]



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                         [D A B C 4  5]
                         [C D A B 8  9]
                         [B C D A 12 13]
                         [A B C D 1  3]
                         [D A B C 5  5]
                         [C D A B 9  9]
                         [B C D A 13 13]
                         [A B C D 2  3]
                         [D A B C 6  5]
                         [C D A B 10 9]
                         [B C D A 14 13]
                         [A B C D 3  3]
                         [D A B C 7  5]
                         [C D A B 11 9]
                         [B C D A 15 13]

                 [Round 3]
                   Let [A B C D i s] denote the operation
                         A = (A + h(B,C,D) + X[i] + 6ED9EBA1) <<< s .
                   (The value 6E..A1 is a hexadecimal 32-bit
                   constant, written with the high-order digit
                   first.  This constant represents the square
                   root of 3.  The octal value of this constant
                   is 015666365641.  See Knuth, The Art of
                   Programming, Volume 2 (Seminumerical
                   Algorithms), Second Edition (1981),
                   Addison-Wesley.  Table 2, page 660.)
                   Do the following 16 operations:
                         [A B C D 0  3]
                         [D A B C 8  9]
                         [C D A B 4  11]
                         [B C D A 12 15]
                         [A B C D 2  3]
                         [D A B C 10 9]
                         [C D A B 6  11]
                         [B C D A 14 15]
                         [A B C D 1  3]
                         [D A B C 9  9]
                         [C D A B 5  11]
                         [B C D A 13 15]
                         [A B C D 3  3]
                         [D A B C 11 9]
                         [C D A B 7  11]
                         [B C D A 15 15]

         Then perform the following additions:
                         A = A + AA
                         B = B + BB



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RFC 1186              MD4 Message Digest Algorithm          October 1990


                         C = C + CC
                         D = D + DD
         (That is, each of the four registers is incremented by
         the value it had before this block was started.)

         end /* of loop on i */

      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 MD4.  A reference
         implementation in C is given in the Appendix.

4.  Extensions

   If more than 128 bits of output are required, then the following
   procedure is recommended to obtain a 256-bit output.  (There is no
   provision made for obtaining more than 256 bits.)

   Two copies of MD4 are run in parallel over the input.  The first copy
   is standard as described above.  The second copy is modified as
   follows.

   The initial state of the second copy is:
                    word A:    00 11 22 33
                    word B:    44 55 66 77
                    word C:    88 99 aa bb
                    word D:    cc dd ee ff

   The magic constants in rounds 2 and 3 for the second copy of MD4 are
   changed from sqrt(2) and sqrt(3) to cuberoot(2) and cuberoot(3):

                                    Octal           Hex
            Round 2 constant        012050505746    50a28be6
            Round 3 constant        013423350444    5c4dd124

   Finally, after every 16-word block is processed (including the last
   block), the values of the A registers in the two copies are
   exchanged.

   The final message digest is obtaining by appending the result of the
   second copy of MD4 to the end of the result of the first copy of MD4.