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Network Working Group R. Rivest
Request for Comments: 1321 MIT Laboratory for Computer Science
and RSA Data Security, Inc.
April 1992
The MD5 Message-Digest Algorithm
Status of this 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,
David Chaum, and Noam Nisan for numerous helpful comments and
suggestions.
Table of Contents
1. Executive Summary 1
2. Terminology and Notation 2
3. MD5 Algorithm Description 3
4. Summary 6
5. Differences Between MD4 and MD5 6
References 7
APPENDIX A - Reference Implementation 7
Security Considerations 21
Author's Address 21
1. Executive Summary
This document describes the MD5 message-digest algorithm. 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 MD5
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.
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RFC 1321 MD5 Message-Digest Algorithm April 1992
The MD5 algorithm is designed to be quite fast on 32-bit machines. In
addition, the MD5 algorithm does not require any large substitution
tables; the algorithm can be coded quite compactly.
The MD5 algorithm is an extension of the MD4 message-digest algorithm
1,2]. MD5 is slightly slower than MD4, but is more "conservative" in
design. MD5 was designed because it was felt that MD4 was perhaps
being adopted for use more quickly than justified by the existing
critical review; because MD4 was designed to be exceptionally fast,
it is "at the edge" in terms of risking successful cryptanalytic
attack. MD5 backs off a bit, giving up a little in speed for a much
greater likelihood of ultimate security. It incorporates some
suggestions made by various reviewers, and contains additional
optimizations. The MD5 algorithm is being placed in the public domain
for review and possible adoption as a standard.
For OSI-based applications, MD5's object identifier is
md5 OBJECT IDENTIFIER ::=
iso(1) member-body(2) US(840) rsadsi(113549) digestAlgorithm(2) 5}
In the X.509 type AlgorithmIdentifier [3], the parameters for MD5
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.
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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):
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RFC 1321 MD5 Message-Digest Algorithm April 1992
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
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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 */
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RFC 1321 MD5 Message-Digest Algorithm April 1992
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.
4. Summary
The MD5 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 MD5 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.
5. Differences Between MD4 and MD5
The following are the differences between MD4 and MD5:
1. A fourth round has been added.
2. Each step now has a unique additive constant.
3. The function g in round 2 was changed from (XY v XZ v YZ) to
(XZ v Y not(Z)) to make g less symmetric.
4. Each step now adds in the result of the previous step. This
promotes a faster "avalanche effect".
5. The order in which input words are accessed in rounds 2 and
3 is changed, to make these patterns less like each other.
6. The shift amounts in each round have been approximately
optimized, to yield a faster "avalanche effect." The shifts in
different rounds are distinct.
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RFC 1321 MD5 Message-Digest Algorithm April 1992
References
[1] Rivest, R., "The MD4 Message Digest Algorithm", RFC 1320, MIT and
RSA Data Security, Inc., April 1992.
[2] 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.
[3] CCITT Recommendation X.509 (1988), "The Directory -
Authentication Framework."
APPENDIX A - Reference Implementation
This appendix contains the following files taken from RSAREF: A
Cryptographic Toolkit for Privacy-Enhanced Mail:
global.h -- global header file
md5.h -- header file for MD5
md5c.c -- source code for MD5
For more information on RSAREF, send email to <rsaref@rsa.com>.
The appendix also includes the following file:
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 MD5Transform can be replaced with
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
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RFC 1321 MD5 Message-Digest Algorithm April 1992
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) ()
#endif
A.2 md5.h
/* MD5.H - header file for MD5C.C
*/
/* Copyright (C) 1991-2, RSA Data Security, Inc. Created 1991. All
rights reserved.
License to copy and use this software is granted provided that it
is identified as the "RSA Data Security, Inc. MD5 Message-Digest
Algorithm" in all material mentioning or referencing this software
or this function.
License is also granted to make and use derivative works provided
that such works are identified as "derived from the RSA Data
Security, Inc. MD5 Message-Digest Algorithm" in all material
mentioning or referencing the derived work.
RSA Data Security, Inc. makes no representations concerning either
the merchantability of this software or the suitability of this
software for any particular purpose. It is provided "as is"
without express or implied warranty of any kind.
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RFC 1321 MD5 Message-Digest Algorithm April 1992
These notices must be retained in any copies of any part of this
documentation and/or software.
*/
/* MD5 context. */
typedef struct {
UINT4 state[4]; /* state (ABCD) */
UINT4 count[2]; /* number of bits, modulo 2^64 (lsb first) */
unsigned char buffer[64]; /* input buffer */
} MD5_CTX;
void MD5Init PROTO_LIST ((MD5_CTX *));
void MD5Update PROTO_LIST
((MD5_CTX *, unsigned char *, unsigned int));
void MD5Final PROTO_LIST ((unsigned char [16], MD5_CTX *));
A.3 md5c.c
/* MD5C.C - RSA Data Security, Inc., MD5 message-digest algorithm
*/
/* Copyright (C) 1991-2, RSA Data Security, Inc. Created 1991. All
rights reserved.
License to copy and use this software is granted provided that it
is identified as the "RSA Data Security, Inc. MD5 Message-Digest
Algorithm" in all material mentioning or referencing this software
or this function.
License is also granted to make and use derivative works provided
that such works are identified as "derived from the RSA Data
Security, Inc. MD5 Message-Digest Algorithm" in all material
mentioning or referencing the derived work.
RSA Data Security, Inc. makes no representations concerning either
the merchantability of this software or the suitability of this
software for any particular purpose. It is provided "as is"
without express or implied warranty of any kind.
These notices must be retained in any copies of any part of this
documentation and/or software.
*/
#include "global.h"
#include "md5.h"
/* Constants for MD5Transform routine.
*/
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#define S11 7
#define S12 12
#define S13 17
#define S14 22
#define S21 5
#define S22 9
#define S23 14
#define S24 20
#define S31 4
#define S32 11
#define S33 16
#define S34 23
#define S41 6
#define S42 10
#define S43 15
#define S44 21
static void MD5Transform PROTO_LIST ((UINT4 [4], unsigned char [64]));
static void Encode PROTO_LIST
((unsigned char *, UINT4 *, unsigned int));
static void Decode PROTO_LIST
((UINT4 *, unsigned char *, unsigned int));
static void MD5_memcpy PROTO_LIST ((POINTER, POINTER, unsigned int));
static void MD5_memset PROTO_LIST ((POINTER, int, unsigned int));
static unsigned char PADDING[64] = {
0x80, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
};
/* F, G, H and I are basic MD5 functions.
*/
#define F(x, y, z) (((x) & (y)) | ((~x) & (z)))
#define G(x, y, z) (((x) & (z)) | ((y) & (~z)))
#define H(x, y, z) ((x) ^ (y) ^ (z))
#define I(x, y, z) ((y) ^ ((x) | (~z)))
/* ROTATE_LEFT rotates x left n bits.
*/
#define ROTATE_LEFT(x, n) (((x) << (n)) | ((x) >> (32-(n))))
/* FF, GG, HH, and II transformations for rounds 1, 2, 3, and 4.
Rotation is separate from addition to prevent recomputation.
*/
#define FF(a, b, c, d, x, s, ac) { \
(a) += F ((b), (c), (d)) + (x) + (UINT4)(ac); \
(a) = ROTATE_LEFT ((a), (s)); \
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RFC 1321 MD5 Message-Digest Algorithm April 1992
(a) += (b); \
}
#define GG(a, b, c, d, x, s, ac) { \
(a) += G ((b), (c), (d)) + (x) + (UINT4)(ac); \
(a) = ROTATE_LEFT ((a), (s)); \
(a) += (b); \
}
#define HH(a, b, c, d, x, s, ac) { \
(a) += H ((b), (c), (d)) + (x) + (UINT4)(ac); \
(a) = ROTATE_LEFT ((a), (s)); \
(a) += (b); \
}
#define II(a, b, c, d, x, s, ac) { \
(a) += I ((b), (c), (d)) + (x) + (UINT4)(ac); \
(a) = ROTATE_LEFT ((a), (s)); \
(a) += (b); \
}
/* MD5 initialization. Begins an MD5 operation, writing a new context.
*/
void MD5Init (context)
MD5_CTX *context; /* context */
{
context->count[0] = context->count[1] = 0;
/* Load magic initialization constants.