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.
Table of Contents
1. Executive Summary 1
2. Terminology and Notation 2
3. MD2 Algorithm Description 2
4. Summary 4
References 5
APPENDIX A - Reference Implementation 5
Security Considerations 17
Author's Address 17
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
md2 OBJECT IDENTIFIER ::=
iso(1) member-body(2) US(840) rsadsi(113549) digestAlgorithm(2) 2}
In the X.509 type AlgorithmIdentifier [4], the parameters for MD2
should have type NULL.
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.
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.
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.
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.
A 48-byte buffer X is used to compute the message digest. The buffer
is initialized to zero.
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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 */
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.
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.
/* 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
/* 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;
void MD2Init PROTO_LIST ((MD2_CTX *));
void MD2Update PROTO_LIST
((MD2_CTX *, unsigned char *, unsigned int));
void MD2Final PROTO_LIST ((unsigned char [16], MD2_CTX *));
The MD2 test suite (driver option "-x") should print the following
results:
MD2 test suite:
MD2 ("") = 8350e5a3e24c153df2275c9f80692773
MD2 ("a") = 32ec01ec4a6dac72c0ab96fb34c0b5d1
MD2 ("abc") = da853b0d3f88d99b30283a69e6ded6bb
MD2 ("message digest") = ab4f496bfb2a530b219ff33031fe06b0
MD2 ("abcdefghijklmnopqrstuvwxyz") = 4e8ddff3650292ab5a4108c3aa47940b
MD2 ("ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789") =
da33def2a42df13975352846c30338cd
MD2 ("123456789012345678901234567890123456789012345678901234567890123456
78901234567890") = d5976f79d83d3a0dc9806c3c66f3efd8
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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
Phone: (415) 595-8782
FAX: (415) 595-4126
EMail: burt@rsa.com
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