The MD5 Message-Digest Algorithm
RFC 1321

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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.

Rivest                                                          [Page 1]
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.

Rivest                                                          [Page 2]
RFC 1321              MD5 Message-Digest Algorithm            April 1992

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