Network Working Group B. Kaliski Request for Comments: 1319 RSA Laboratories Updates: RFC 1115 April 1992
The MD2 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
The description of MD2 is based on material prepared by John Linn and Ron Rivest. Their permission to incorporate that material is greatly appreciated.
This document describes the MD2 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 MD2 algorithm is intended for digital signature applications, where a large file must be "compressed" in a secure manner before being signed with a private (secret) key under a public-key cryptosystem such as RSA.
License to use MD2 is granted for non-commerical Internet Privacy- Enhanced Mail [1-3].
This document is an update to the August 1989 RFC 1115 [3], which also gives a reference implementation of MD2. The main differences
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are that a textual description of MD2 is included, and that the reference implementation of MD2 is more portable.
For OSI-based applications, MD2's object identifier is
In the X.509 type AlgorithmIdentifier [4], the parameters for MD2 should have type NULL.
2. Terminology and Notation
In this document, a "byte" is an eight-bit quantity.
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 X xor Y denote the bit-wise XOR of X and Y.
3. MD2 Algorithm Description
We begin by supposing that we have a b-byte message as input, and that we wish to find its message digest. Here b is an arbitrary nonnegative integer; b may be zero, and it may be arbitrarily large. We imagine the bytes 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 Bytes
The message is "padded" (extended) so that its length (in bytes) is congruent to 0, modulo 16. That is, the message is extended so that it is a multiple of 16 bytes long. Padding is always performed, even if the length of the message is already congruent to 0, modulo 16.
Padding is performed as follows: "i" bytes of value "i" are appended to the message so that the length in bytes of the padded message becomes congruent to 0, modulo 16. At least one byte and at most 16 16 bytes are appended.
At this point the resulting message (after padding with bytes) has a length that is an exact multiple of 16 bytes. Let M[0 ... N-1] denote
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the bytes of the resulting message, where N is a multiple of 16.
3.2 Step 2. Append Checksum
A 16-byte checksum of the message is appended to the result of the previous step.
This step uses a 256-byte "random" permutation constructed from the digits of pi. Let S[i] denote the i-th element of this table. The table is given in the appendix.
Do the following:
/* Clear checksum. */ For i = 0 to 15 do: Set C[i] to 0. end /* of loop on i */
Set L to 0.
/* Process each 16-word block. */ For i = 0 to N/16-1 do
/* Checksum block i. */ For j = 0 to 15 do Set c to M[i*16+j]. Set C[j] to S[c xor L]. Set L to C[j]. end /* of loop on j */ end /* of loop on i */
The 16-byte checksum C[0 ... 15] is appended to the message. Let M[0 with checksum), where N' = N + 16.
3.3 Step 3. Initialize MD Buffer
A 48-byte buffer X is used to compute the message digest. The buffer is initialized to zero.
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3.4 Step 4. Process Message in 16-Byte Blocks
This step uses the same 256-byte permutation S as step 2 does.
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[16+j] to M[i*16+j]. Set X[32+j] to (X[16+j] xor X[j]). end /* of loop on j */
Set t to 0.
/* Do 18 rounds. */ For j = 0 to 17 do
/* Round j. */ For k = 0 to 47 do Set t and X[k] to (X[k] xor S[t]). end /* of loop on k */
Set t to (t+j) modulo 256. end /* of loop on j */
end /* of loop on i */
3.5 Step 5. Output
The message digest produced as output is X[0 ... 15]. That is, we begin with X[0], and end with X[15].
This completes the description of MD2. A reference implementation in C is given in the appendix.
4. Summary
The MD2 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 MD2 algorithm has been carefully scrutinized for weaknesses. It is, however, a relatively new algorithm and further security analysis is of course
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justified, as is the case with any new proposal of this sort.
References
[1] Linn, J., "Privacy Enhancement for Internet Electronic Mail: Part I -- Message Encipherment and Authentication Procedures", RFC 1113, DEC, IAB Privacy Task Force, August 1989.
[2] Kent, S., and J. Linn, "Privacy Enhancement for Internet Electronic Mail: Part II -- Certificate-Based Key Management", RFC 1114, BBNCC, DEC, IAB Privacy Task Force, August 1989.
[3] Linn, J., "Privacy Enhancement for Internet Electronic Mail: Part III -- Algorithms, Modes, and Identifiers", RFC 1115 DEC, IAB Privacy Task Force, August 1989.
[4] 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
md2.h -- header file for MD2
md2c.c -- source code for MD2
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.
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.
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*/ #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 md2.h
/* MD2.H - header file for MD2C.C */
/* Copyright (C) 1990-2, RSA Data Security, Inc. Created 1990. All rights reserved.
License to copy and use this software is granted for non-commercial Internet Privacy-Enhanced Mail provided that it is identified as the "RSA Data Security, Inc. MD2 Message Digest Algorithm" in all material mentioning or referencing this software or this function.
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. */
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typedef struct { unsigned char state[16]; /* state */ unsigned char checksum[16]; /* checksum */ unsigned int count; /* number of bytes, modulo 16 */ unsigned char buffer[16]; /* input buffer */ } MD2_CTX;
/* Copyright (C) 1990-2, RSA Data Security, Inc. Created 1990. All rights reserved.
License to copy and use this software is granted for non-commercial Internet Privacy-Enhanced Mail provided that it is identified as the "RSA Data Security, Inc. MD2 Message Digest Algorithm" in all material mentioning or referencing this software or this function.
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. */
/* MD2 block update operation. Continues an MD2 message-digest operation, processing another message block, and updating the context. */ void MD2Update (context, input, inputLen) MD2_CTX *context; /* context */ unsigned char *input; /* input block */ unsigned int inputLen; /* length of input block */ { unsigned int i, index, partLen;
/* Update number of bytes mod 16 */ index = context->count; context->count = (index + inputLen) & 0xf;
partLen = 16 - index;
/* Transform as many times as possible. */ if (inputLen >= partLen) { MD2_memcpy ((POINTER)&context->buffer[index], (POINTER)input, partLen); MD2Transform (context->state, context->checksum, context->buffer);
for (i = partLen; i + 15 < inputLen; i += 16) MD2Transform (context->state, context->checksum, &input[i]);
/* Note: Replace "for loop" with standard memcpy if possible. */ static void MD2_memcpy (output, input, len) POINTER output; POINTER input; unsigned int len; { unsigned int i;
for (i = 0; i < len; i++) output[i] = input[i]; }
/* Note: Replace "for loop" with standard memset if possible. */ static void MD2_memset (output, value, len) POINTER output; int value; unsigned int len; { unsigned int i;
for (i = 0; i < len; i++) ((char *)output)[i] = (char)value; }
A.4 mddriver.c
/* MDDRIVER.C - test driver for MD2, MD4 and MD5 */
/* Copyright (C) 1990-2, RSA Data Security, Inc. Created 1990. All rights reserved.
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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. */
/* The following makes MD default to MD5 if it has not already been defined with C compiler flags. */ #ifndef MD #define MD MD5 #endif
Arguments (may be any combination): -sstring - digests string -t - runs time trial -x - runs test script filename - digests file (none) - digests standard input */ int main (argc, argv) int argc; char *argv[]; { int i;
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); }
/* Digests a string and prints the result. */ static void MDString (string) char *string;
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{ MD_CTX context; unsigned char digest[16]; unsigned int len = strlen (string);
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printf ("Speed = %ld bytes/second\n", (long)TEST_BLOCK_LEN * (long)TEST_BLOCK_COUNT/(endTime-startTime)); } /* Digests a reference suite of strings and prints the results. */ static void MDTestSuite () { printf ("MD%d test suite:\n", MD);
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Security Considerations
The level of security discussed in this memo is considered to be sufficient for implementing very high security hybrid digital signature schemes based on MD2 and a public-key cryptosystem.
Author's Address
Burton S. Kaliski Jr. RSA Laboratories (a division of RSA Data Security, Inc.) 10 Twin Dolphin Drive Redwood City, CA 94065
