rfc1320.txt

A console-based hah calculators

Network Working Group                                          R. Rivest
Request for Comments: 1320           MIT Laboratory for Computer Science
Obsoletes: RFC 1186                          and RSA Data Security, Inc.
                                                              April 1992


                    The MD4 Message-Digest Algorithm

Status of thie Memo

   This memo provides information for the Internet community.  It does
   not specify an Internet standard.  Distribution of this memo is
   unlimited.

Acknowlegements

   We would like to thank Don Coppersmith, Burt Kaliski, Ralph Merkle,
   and Noam Nisan for numerous helpful comments and suggestions.

Table of Contents

   1. Executive Summary                                                1
   2. Terminology and Notation                                         2
   3. MD4 Algorithm Description                                        2
   4. Summary                                                          6
   References                                                          6
   APPENDIX A - Reference Implementation                               6
   Security Considerations                                            20
   Author's Address                                                   20

1. Executive Summary

   This document describes the MD4 message-digest algorithm [1]. The
   algorithm takes as input a 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 intended for digital signature applications, where a
   large file must be "compressed" in a secure manner before being
   encrypted with a private (secret) key under a public-key cryptosystem
   such as RSA.

   The MD4 algorithm is designed to be quite fast on 32-bit machines. In
   addition, the MD4 algorithm does not require any large substitution
   tables; the algorithm can be coded quite compactly.





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RFC 1320              MD4 Message-Digest Algorithm            April 1992


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

   This document replaces the October 1990 RFC 1186 [2].  The main
   difference is that the reference implementation of MD4 in the
   appendix is more portable.

   For OSI-based applications, MD4's object identifier is

   md4 OBJECT IDENTIFIER ::=
     {iso(1) member-body(2) US(840) rsadsi(113549) digestAlgorithm(2) 4}

   In the X.509 type AlgorithmIdentifier [3], the parameters for MD4
   should have type NULL.

2. Terminology and Notation

   In this document a "word" is a 32-bit quantity and a "byte" is an
   eight-bit quantity. A sequence of bits can be interpreted in a
   natural manner as a sequence of bytes, where each consecutive group
   of eight 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 four 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
   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}




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   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









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3.4 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" bits 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 "1" bit in that bit position, else G has
   a "0" bit. 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, 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:

      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] denote the operation
             a = (a + F(b,c,d) + X[k]) <<< s. */
        /* Do the following 16 operations. */
        [ABCD  0  3]  [DABC  1  7]  [CDAB  2 11]  [BCDA  3 19]
        [ABCD  4  3]  [DABC  5  7]  [CDAB  6 11]  [BCDA  7 19]
        [ABCD  8  3]  [DABC  9  7]  [CDAB 10 11]  [BCDA 11 19]
        [ABCD 12  3]  [DABC 13  7]  [CDAB 14 11]  [BCDA 15 19]

        /* Round 2. */
        /* Let [abcd k s] denote the operation
             a = (a + G(b,c,d) + X[k] + 5A827999) <<< s. */



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        /* Do the following 16 operations. */
        [ABCD  0  3]  [DABC  4  5]  [CDAB  8  9]  [BCDA 12 13]
        [ABCD  1  3]  [DABC  5  5]  [CDAB  9  9]  [BCDA 13 13]
        [ABCD  2  3]  [DABC  6  5]  [CDAB 10  9]  [BCDA 14 13]
        [ABCD  3  3]  [DABC  7  5]  [CDAB 11  9]  [BCDA 15 13]

        /* Round 3. */
        /* Let [abcd k s] denote the operation
             a = (a + H(b,c,d) + X[k] + 6ED9EBA1) <<< s. */
        /* Do the following 16 operations. */
        [ABCD  0  3]  [DABC  8  9]  [CDAB  4 11]  [BCDA 12 15]
        [ABCD  2  3]  [DABC 10  9]  [CDAB  6 11]  [BCDA 14 15]
        [ABCD  1  3]  [DABC  9  9]  [CDAB  5 11]  [BCDA 13 15]
        [ABCD  3  3]  [DABC 11  9]  [CDAB  7 11]  [BCDA 15 15]

        /* 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 */

   Note. 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.

   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.

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






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4. Summary

   The MD4 message-digest algorithm is simple to implement, and provides
   a "fingerprint" or message digest of a message of arbitrary length.
   It is conjectured that the difficulty of coming up with two messages
   having the same message digest is on the order of 2^64 operations,
   and that the difficulty of coming up with any message having a given
   message digest is on the order of 2^128 operations. The MD4 algorithm
   has been carefully scrutinized for weaknesses. It is, however, a
   relatively new algorithm and further security analysis is of course
   justified, as is the case with any new proposal of this sort.

References

   [1] Rivest, R., "The MD4 message digest algorithm", in A.J.  Menezes
       and S.A. Vanstone, editors, Advances in Cryptology - CRYPTO '90
       Proceedings, pages 303-311, Springer-Verlag, 1991.

   [2] Rivest, R., "The MD4 Message Digest Algorithm", RFC 1186, MIT,
       October 1990.

   [3] CCITT Recommendation X.509 (1988), "The Directory -
       Authentication Framework".

   [4] Rivest, R., "The MD5 Message-Digest Algorithm", RFC 1321, MIT and
       RSA Data Security, Inc, April 1992.

APPENDIX A - Reference Implementation

   This appendix contains the following files:

        global.h -- global header file

        md4.h -- header file for MD4

        md4c.c -- source code for MD4

        mddriver.c -- test driver for MD2, MD4 and MD5

   The driver compiles for MD5 by default but can compile for MD2 or MD4
   if the symbol MD is defined on the C compiler command line as 2 or 4.

   The implementation is portable and should work on many different
   plaforms. However, it is not difficult to optimize the implementation
   on particular platforms, an exercise left to the reader. For example,
   on "little-endian" platforms where the lowest-addressed byte in a 32-
   bit word is the least significant and there are no alignment
   restrictions, the call to Decode in MD4Transform can be replaced with



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   a typecast.

A.1 global.h

/* GLOBAL.H - RSAREF types and constants
 */

/* PROTOTYPES should be set to one if and only if the compiler supports
     function argument prototyping.
   The following makes PROTOTYPES default to 0 if it has not already
     been defined with C compiler flags.
 */
#ifndef PROTOTYPES
#define PROTOTYPES 0
#endif

/* POINTER defines a generic pointer type */
typedef unsigned char *POINTER;

/* UINT2 defines a two byte word */
typedef unsigned short int UINT2;

/* UINT4 defines a four byte word */
typedef unsigned long int UINT4;

/* PROTO_LIST is defined depending on how PROTOTYPES is defined above.
   If using PROTOTYPES, then PROTO_LIST returns the list, otherwise it
     returns an empty list.
 */

#if PROTOTYPES
#define PROTO_LIST(list) list
#else
#define PROTO_LIST(list) ()