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.
加拿大文化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 "compresd" in a cure manner before being
encrypted with a private (cret) 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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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-bad 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 quence of bits can be interpreted in a
natural manner as a quence of bytes, where each concutive group
of eight bits is interpreted as a byte with the high-order (most
significant) bit of each byte listed first. Similarly, a quence of bytes can be interpreted as a quence of 32-bit words, where each
concutive 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 u ^ 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-wi complement of X, and let X v Y denote the bit-wi OR of X
and Y. Let X xor Y denote the bit-wi XOR of X and Y, and let XY
denote the bit-wi 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 reprentation 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 ud. (The bits are appended as two 32-bit words and appended l
ow-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
职业打假公司A four-word buffer (A,B,C,D) is ud to compute the message digest.
株的词语Here each of A, B, C, D is a 32-bit register. The 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 el 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, el G has a "0" bit. It is interesting to note that if the bits of X, Y, and Z are independent and unbiad, the each bit of f(X,Y,Z) will be
independent and unbiad, and similarly each bit of g(X,Y,Z) will be independent and unbiad. The function H is the bit-wi XOR or纪律委员职责
祝天下所有的情侣都是失散多年的兄妹parity" function; it has properties similar to tho 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 reprents 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 reprents 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
jerrycof 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,国庆趣事作文
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 weakness. It is, however, a
relatively new algorithm and further curity analysis is of cour
justified, as is the ca 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
补办电话卡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 exerci left to the reader. For example, on "little-endian" platforms where the lowest-addresd 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 Rivest [Page 6]
