Network Working Group R. Rivest Request for Comments: 1320 MIT Laboratory for Computer Science Obsoletes: RFC 1186 and RSA Data Security, Inc. April 1992
This memo provides information for the Internet community. It does not specify an Internet standard. Distribution of this memo is unlimited.
We would like to thank Don Coppersmith, Burt Kaliski, Ralph Merkle, and Noam Nisan for numerous helpful comments and suggestions.
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
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.
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.
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.
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.
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.
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.
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
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. */
/* 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.
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.
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.
[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.
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
a typecast.
*/
*/
*/
*/
License to copy and use this software is granted provided that it is identified as the "RSA Data Security, Inc. MD4 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. MD4 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.
*/
UINT4 state[4]; /* state (ABCD) */ UINT4 count[2]; /* number of bits, modulo 2^64 (lsb first) */ unsigned char buffer[64]; /* input buffer */
*/
License to copy and use this software is granted provided that it is identified as the "RSA Data Security, Inc. MD4 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. MD4 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.
*/
*/
*/
*/
*/
/* Load magic initialization constants. */ context->state[0] = 0x67452301; context->state[1] = 0xefcdab89; context->state[2] = 0x98badcfe; context->state[3] = 0x10325476;
*/
/* Compute number of bytes mod 64 */ index = (unsigned int)((context->count[0] >> 3) & 0x3F); /* Update number of bits */ if ((context->count[0] += ((UINT4)inputLen << 3)) < ((UINT4)inputLen << 3)) context->count[1]++; context->count[1] += ((UINT4)inputLen >> 29);
partLen = 64 - index;
/* Transform as many times as possible. */ if (inputLen >= partLen) { MD4_memcpy ((POINTER)&context->buffer[index], (POINTER)input, partLen); MD4Transform (context->state, context->buffer);
for (i = partLen; i + 63 < inputLen; i += 64)
MD4Transform (context->state, &input[i]);
index = 0;
}
else
i = 0;
/* Buffer remaining input */ MD4_memcpy ((POINTER)&context->buffer[index], (POINTER)&input[i], inputLen-i);
*/
/* Save number of bits */ Encode (bits, context->count, 8); /* Pad out to 56 mod 64. */ index = (unsigned int)((context->count[0] >> 3) & 0x3f); padLen = (index < 56) ? (56 - index) : (120 - index); MD4Update (context, PADDING, padLen); /* Append length (before padding) */ MD4Update (context, bits, 8); /* Store state in digest */ Encode (digest, context->state, 16); /* Zeroize sensitive information. */ MD4_memset ((POINTER)context, 0, sizeof (*context));
*/
Decode (x, block, 64);
/* Round 1 */ FF (a, b, c, d, x[ 0], S11); /* 1 */ FF (d, a, b, c, x[ 1], S12); /* 2 */ FF (c, d, a, b, x[ 2], S13); /* 3 */ FF (b, c, d, a, x[ 3], S14); /* 4 */ FF (a, b, c, d, x[ 4], S11); /* 5 */ FF (d, a, b, c, x[ 5], S12); /* 6 */ FF (c, d, a, b, x[ 6], S13); /* 7 */ FF (b, c, d, a, x[ 7], S14); /* 8 */ FF (a, b, c, d, x[ 8], S11); /* 9 */ FF (d, a, b, c, x[ 9], S12); /* 10 */ FF (c, d, a, b, x[10], S13); /* 11 */ FF (b, c, d, a, x[11], S14); /* 12 */ FF (a, b, c, d, x[12], S11); /* 13 */ FF (d, a, b, c, x[13], S12); /* 14 */ FF (c, d, a, b, x[14], S13); /* 15 */ FF (b, c, d, a, x[15], S14); /* 16 */ /* Round 2 */ GG (a, b, c, d, x[ 0], S21); /* 17 */ GG (d, a, b, c, x[ 4], S22); /* 18 */ GG (c, d, a, b, x[ 8], S23); /* 19 */ GG (b, c, d, a, x[12], S24); /* 20 */ GG (a, b, c, d, x[ 1], S21); /* 21 */ GG (d, a, b, c, x[ 5], S22); /* 22 */ GG (c, d, a, b, x[ 9], S23); /* 23 */ GG (b, c, d, a, x[13], S24); /* 24 */ GG (a, b, c, d, x[ 2], S21); /* 25 */ GG (d, a, b, c, x[ 6], S22); /* 26 */ GG (c, d, a, b, x[10], S23); /* 27 */ GG (b, c, d, a, x[14], S24); /* 28 */ GG (a, b, c, d, x[ 3], S21); /* 29 */ GG (d, a, b, c, x[ 7], S22); /* 30 */ GG (c, d, a, b, x[11], S23); /* 31 */ GG (b, c, d, a, x[15], S24); /* 32 */
/* Round 3 */ HH (a, b, c, d, x[ 0], S31); /* 33 */ HH (d, a, b, c, x[ 8], S32); /* 34 */ HH (c, d, a, b, x[ 4], S33); /* 35 */ HH (b, c, d, a, x[12], S34); /* 36 */ HH (a, b, c, d, x[ 2], S31); /* 37 */ HH (d, a, b, c, x[10], S32); /* 38 */ HH (c, d, a, b, x[ 6], S33); /* 39 */ HH (b, c, d, a, x[14], S34); /* 40 */ HH (a, b, c, d, x[ 1], S31); /* 41 */ HH (d, a, b, c, x[ 9], S32); /* 42 */ HH (c, d, a, b, x[ 5], S33); /* 43 */ HH (b, c, d, a, x[13], S34); /* 44 */ HH (a, b, c, d, x[ 3], S31); /* 45 */ HH (d, a, b, c, x[11], S32); /* 46 */ HH (c, d, a, b, x[ 7], S33); /* 47 */ HH (b, c, d, a, x[15], S34); /* 48 */
state[0] += a;
state[1] += b;
state[2] += c;
state[3] += d;
/* Zeroize sensitive information. */ MD4_memset ((POINTER)x, 0, sizeof (x));
*/
for (i = 0, j = 0; j < len; i++, j += 4) {
output[j] = (unsigned char)(input[i] & 0xff);
output[j+1] = (unsigned char)((input[i] >> 8) & 0xff);
output[j+2] = (unsigned char)((input[i] >> 16) & 0xff);
output[j+3] = (unsigned char)((input[i] >> 24) & 0xff);
}
*/
for (i = 0, j = 0; j < len; i++, j += 4)
output[i] = ((UINT4)input[j]) | (((UINT4)input[j+1]) << 8) |
(((UINT4)input[j+2]) << 16) | (((UINT4)input[j+3]) << 24);
*/
for (i = 0; i < len; i++)
output[i] = input[i];
*/
for (i = 0; i < len; i++)
((char *)output)[i] = (char)value;
*/
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.
*/
*/
*/
Arguments (may be any combination):
-sstring - digests string -t - runs time trial -x - runs test script filename - digests file (none) - digests standard input */
if (argc > 1)
for (i = 1; i < argc; i++)
if (argv[i][0] == '-' && argv[i][1] == 's')
MDString (argv[i] + 2);
else if (strcmp (argv[i], "-t") == 0)
MDTimeTrial ();
else if (strcmp (argv[i], "-x") == 0)
MDTestSuite ();
else
MDFile (argv[i]);
else
MDFilter ();
return (0);
*/
MDInit (&context);
MDUpdate (&context, string, len);
MDFinal (digest, &context);
printf ("MD%d (\"%s\") = ", MD, string);
MDPrint (digest);
printf ("\n");
*/
printf
("MD%d time trial. Digesting %d %d-byte blocks ...", MD,
TEST_BLOCK_LEN, TEST_BLOCK_COUNT);
/* Initialize block */ for (i = 0; i < TEST_BLOCK_LEN; i++) block[i] = (unsigned char)(i & 0xff); /* Start timer */ time (&startTime); /* Digest blocks */ MDInit (&context); for (i = 0; i < TEST_BLOCK_COUNT; i++) MDUpdate (&context, block, TEST_BLOCK_LEN); MDFinal (digest, &context); /* Stop timer */ time (&endTime);
printf (" done\n");
printf ("Digest = ");
MDPrint (digest);
printf ("\nTime = %ld seconds\n", (long)(endTime-startTime));
printf
("Speed = %ld bytes/second\n",
(long)TEST_BLOCK_LEN * (long)TEST_BLOCK_COUNT/(endTime-startTime));
*/
MDString ("");
MDString ("a");
MDString ("abc");
MDString ("message digest");
MDString ("abcdefghijklmnopqrstuvwxyz");
MDString
("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789");
MDString
("1234567890123456789012345678901234567890\
*/
if ((file = fopen (filename, "rb")) == NULL)
printf ("%s can't be opened\n", filename);
else {
MDInit (&context);
while (len = fread (buffer, 1, 1024, file))
MDUpdate (&context, buffer, len);
MDFinal (digest, &context);
fclose (file);
printf ("MD%d (%s) = ", MD, filename);
MDPrint (digest);
printf ("\n");
}
*/
MDInit (&context);
while (len = fread (buffer, 1, 16, stdin))
MDUpdate (&context, buffer, len);
MDFinal (digest, &context);
MDPrint (digest);
printf ("\n");
*/
for (i = 0; i < 16; i++)
printf ("%02x", digest[i]);
The MD4 test suite (driver option "-x") should print the following results:
The level of security discussed in this memo is considered to be sufficient for implementing moderate security hybrid digital- signature schemes based on MD4 and a public-key cryptosystem. We do not know of any reason that MD4 would not be sufficient for implementing very high security digital-signature schemes, but because MD4 was designed to be exceptionally fast, it is "at the edge" in terms of risking successful cryptanalytic attack. After further critical review, it may be appropriate to consider MD4 for very high security applications. For very high security applications before the completion of that review, the MD5 algorithm [4] is recommended.
Ronald L. Rivest
Massachusetts Institute of Technology
Laboratory for Computer Science
NE43-324
545 Technology Square
Cambridge, MA 02139-1986
Phone: (617) 253-5880
EMail: rivest@theory.lcs.mit.edu