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

1. Executive Summary

   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.

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;

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 *));

A.3 md2c.c

/* MD2C.C - RSA Data Security, Inc., MD2 message-digest algorithm
 */

/* 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.
 */

#include "global.h"
#include "md2.h"

static void MD2Transform PROTO_LIST
  ((unsigned char [16], unsigned char [16], unsigned char [16]));
static void MD2_memcpy PROTO_LIST ((POINTER, POINTER, unsigned int));
static void MD2_memset PROTO_LIST ((POINTER, int, unsigned int));

/* Permutation of 0..255 constructed from the digits of pi. It gives a
   "random" nonlinear byte substitution operation.
 */
static unsigned char PI_SUBST[256] = {
  41, 46, 67, 201, 162, 216, 124, 1, 61, 54, 84, 161, 236, 240, 6,



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  19, 98, 167, 5, 243, 192, 199, 115, 140, 152, 147, 43, 217, 188,
  76, 130, 202, 30, 155, 87, 60, 253, 212, 224, 22, 103, 66, 111, 24,
  138, 23, 229, 18, 190, 78, 196, 214, 218, 158, 222, 73, 160, 251,
  245, 142, 187, 47, 238, 122, 169, 104, 121, 145, 21, 178, 7, 63,
  148, 194, 16, 137, 11, 34, 95, 33, 128, 127, 93, 154, 90, 144, 50,
  39, 53, 62, 204, 231, 191, 247, 151, 3, 255, 25, 48, 179, 72, 165,
  181, 209, 215, 94, 146, 42, 172, 86, 170, 198, 79, 184, 56, 210,
  150, 164, 125, 182, 118, 252, 107, 226, 156, 116, 4, 241, 69, 157,
  112, 89, 100, 113, 135, 32, 134, 91, 207, 101, 230, 45, 168, 2, 27,
  96, 37, 173, 174, 176, 185, 246, 28, 70, 97, 105, 52, 64, 126, 15,
  85, 71, 163, 35, 221, 81, 175, 58, 195, 92, 249, 206, 186, 197,
  234, 38, 44, 83, 13, 110, 133, 40, 132, 9, 211, 223, 205, 244, 65,
  129, 77, 82, 106, 220, 55, 200, 108, 193, 171, 250, 36, 225, 123,
  8, 12, 189, 177, 74, 120, 136, 149, 139, 227, 99, 232, 109, 233,
  203, 213, 254, 59, 0, 29, 57, 242, 239, 183, 14, 102, 88, 208, 228,
  166, 119, 114, 248, 235, 117, 75, 10, 49, 68, 80, 180, 143, 237,
  31, 26, 219, 153, 141, 51, 159, 17, 131, 20
};

static unsigned char *PADDING[] = {
  (unsigned char *)"",
  (unsigned char *)"\001",
  (unsigned char *)"\002\002",
  (unsigned char *)"\003\003\003",
  (unsigned char *)"\004\004\004\004",
  (unsigned char *)"\005\005\005\005\005",
  (unsigned char *)"\006\006\006\006\006\006",
  (unsigned char *)"\007\007\007\007\007\007\007",
  (unsigned char *)"\010\010\010\010\010\010\010\010",
  (unsigned char *)"\011\011\011\011\011\011\011\011\011",
  (unsigned char *)"\012\012\012\012\012\012\012\012\012\012",
  (unsigned char *)"\013\013\013\013\013\013\013\013\013\013\013",
  (unsigned char *)"\014\014\014\014\014\014\014\014\014\014\014\014",
  (unsigned char *)
    "\015\015\015\015\015\015\015\015\015\015\015\015\015",
  (unsigned char *)
    "\016\016\016\016\016\016\016\016\016\016\016\016\016\016",
  (unsigned char *)
    "\017\017\017\017\017\017\017\017\017\017\017\017\017\017\017",
  (unsigned char *)
    "\020\020\020\020\020\020\020\020\020\020\020\020\020\020\020\020"
};

/* MD2 initialization. Begins an MD2 operation, writing a new context.
 */
void MD2Init (context)
MD2_CTX *context;                                        /* context */
{



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  context->count = 0;
  MD2_memset ((POINTER)context->state, 0, sizeof (context->state));
  MD2_memset
    ((POINTER)context->checksum, 0, sizeof (context->checksum));
}

/* 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.
    */