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@(#)README.md5 10.1 3/25/94 08:04:18 Landon Curt Noll chongo@toad.com /\../\ This is an implementation of the RSA Data Security, Inc. MD5 Message-Digest Algorithm The digests produced from strings (-s string), files or stdin are identical to the RSA's original md5 program. The command line and output interface are upward compatible as well. Users of the original shs program may replace it with this version has their existing use and digests will be preserved. See md5drvr.c for version information. See the man page md5.1 for other details. -- Landon Curt Noll chongo@toad.com =-= Network Working Group R. Rivest INTERNET-DRAFT MIT Laboratory for Computer Science S. Dusse RSA Data Security, Inc. 10 July 1991 The MD5 Message-Digest Algorithm STATUS OF THIS MEMO This draft document will be submitted to the RFC editor as a protocol specification. Comments should be sent to <pem-dev@tis.com> or to the authors. Distribution of this memo is unlimited. ACKNOWLEDGEMENT 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 7 5. Summary of Differences Between MD4 and MD5 7 6. Security Considerations 7 References 8 Authors' Addresses 8 APPENDIX - Reference Implementation 9 1. Executive Summary This document describes the MD5 message-digest algorithm. The algorithm takes as input an input 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. 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. A version of this document including the C source code in the appendix is available by FTP from RSA.COM in the file "pub/md5.doc". This document may be referred to, unofficially, as Internet draft [MD5-A]. 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. 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 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 Bits 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 (in which case 512 bits of padding are added). Padding is performed as follows: a single "1" bit is appended to the message, and then enough zero bits are appended so that the length in bits of the padded message becomes congruent to 448, modulo 512. 3.2 Step 2. Append Length 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. 3.3 Step 3. Initialize MD Buffer 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 3.4 Step 4. Process Message in 16-Word Blocks We first define four 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) = XZ v Y not(Z) H(X,Y,Z) = X xor Y xor Z I(X,Y,Z) = Y xor (X v not(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's in the same bit position.) 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. The functions G, H, and I are similar to the function F, in that they act in "bitwise parallel" to produce their output from the bits of X, Y, and Z, in such a manner that if the corresponding bits of X, Y, and Z are independent and unbiased, then each bit of G(X,Y,Z), H(X,Y,Z), and I(X,Y,Z) will be independent and unbiased. Note that the function H is the bit-wise "xor" or "parity" function of its inputs. 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 FF(a,b,c,d,X[k],s,t) denote the operation a = b + ((a + F(b,c,d) + X[k] + t) <<< s). */ /* Here the additive constants t are chosen as follows: In step i, the additive constant is the integer part of 4294967296 times abs(sin(i)), where i is in radians. */ /* Let S11 = 7, S12 = 12, S13 = 17, and S14 = 22. */ /* Do the following 16 operations. */ FF (a, b, c, d, X[ 0], S11, 3614090360); /* Step 1 */ FF (d, a, b, c, X[ 1], S12, 3905402710); /* 2 */ FF (c, d, a, b, X[ 2], S13, 606105819); /* 3 */ FF (b, c, d, a, X[ 3], S14, 3250441966); /* 4 */ FF (a, b, c, d, X[ 4], S11, 4118548399); /* 5 */ FF (d, a, b, c, X[ 5], S12, 1200080426); /* 6 */ FF (c, d, a, b, X[ 6], S13, 2821735955); /* 7 */ FF (b, c, d, a, X[ 7], S14, 4249261313); /* 8 */ FF (a, b, c, d, X[ 8], S11, 1770035416); /* 9 */ FF (d, a, b, c, X[ 9], S12, 2336552879); /* 10 */ FF (c, d, a, b, X[10], S13, 4294925233); /* 11 */ FF (b, c, d, a, X[11], S14, 2304563134); /* 12 */ FF (a, b, c, d, X[12], S11, 1804603682); /* 13 */ FF (d, a, b, c, X[13], S12, 4254626195); /* 14 */ FF (c, d, a, b, X[14], S13, 2792965006); /* 15 */ FF (b, c, d, a, X[15], S14, 1236535329); /* 16 */ /* Round 2. */ /* Let GG(a,b,c,d,X[k],s,t) denote the operation a = b + ((a + G(b,c,d) + X[k] + t) <<< s). */ /* Let S21 = 5, S22 = 9, S23 = 14, and S24 = 20. */ /* Do the following 16 operations. */ GG (a, b, c, d, X[ 1], S21, 4129170786); /* 17 */ GG (d, a, b, c, X[ 6], S22, 3225465664); /* 18 */ GG (c, d, a, b, X[11], S23, 643717713); /* 19 */ GG (b, c, d, a, X[ 0], S24, 3921069994); /* 20 */ GG (a, b, c, d, X[ 5], S21, 3593408605); /* 21 */ GG (d, a, b, c, X[10], S22, 38016083); /* 22 */ GG (c, d, a, b, X[15], S23, 3634488961); /* 23 */ GG (b, c, d, a, X[ 4], S24, 3889429448); /* 24 */ GG (a, b, c, d, X[ 9], S21, 568446438); /* 25 */ GG (d, a, b, c, X[14], S22, 3275163606); /* 26 */ GG (c, d, a, b, X[ 3], S23, 4107603335); /* 27 */ GG (b, c, d, a, X[ 8], S24, 1163531501); /* 28 */ GG (a, b, c, d, X[13], S21, 2850285829); /* 29 */ GG (d, a, b, c, X[ 2], S22, 4243563512); /* 30 */ GG (c, d, a, b, X[ 7], S23, 1735328473); /* 31 */ GG (b, c, d, a, X[12], S24, 2368359562); /* 32 */ /* Round 3. */ /* Let HH(a,b,c,d,X[k],s,t) denote the operation a = b + ((a + H(b,c,d) + X[k] + t) <<< s). */ /* Let S31 = 4, S32 = 11, S33 = 16, and S34 = 23. */ /* Do the following 16 operations. */ HH (a, b, c, d, X[ 5], S31, 4294588738); /* 33 */ HH (d, a, b, c, X[ 8], S32, 2272392833); /* 34 */ HH (c, d, a, b, X[11], S33, 1839030562); /* 35 */ HH (b, c, d, a, X[14], S34, 4259657740); /* 36 */ HH (a, b, c, d, X[ 1], S31, 2763975236); /* 37 */ HH (d, a, b, c, X[ 4], S32, 1272893353); /* 38 */ HH (c, d, a, b, X[ 7], S33, 4139469664); /* 39 */ HH (b, c, d, a, X[10], S34, 3200236656); /* 40 */ HH (a, b, c, d, X[13], S31, 681279174); /* 41 */ HH (d, a, b, c, X[ 0], S32, 3936430074); /* 42 */ HH (c, d, a, b, X[ 3], S33, 3572445317); /* 43 */ HH (b, c, d, a, X[ 6], S34, 76029189); /* 44 */ HH (a, b, c, d, X[ 9], S31, 3654602809); /* 45 */ HH (d, a, b, c, X[12], S32, 3873151461); /* 46 */ HH (c, d, a, b, X[15], S33, 530742520); /* 47 */ HH (b, c, d, a, X[ 2], S34, 3299628645); /* 48 */ /* Round 4. */ /* Let II(a,b,c,d,X[k],s,t) denote the operation a = b + ((a + I(b,c,d) + X[k] + t) <<< s). */ /* Let S41 = 6, S42 = 10, S43 = 15, and S44 = 21. */ /* Do the following 16 operations. */ II (a, b, c, d, X[ 0], S41, 4096336452); /* 49 */ II (d, a, b, c, X[ 7], S42, 1126891415); /* 50 */ II (c, d, a, b, X[14], S43, 2878612391); /* 51 */ II (b, c, d, a, X[ 5], S44, 4237533241); /* 52 */ II (a, b, c, d, X[12], S41, 1700485571); /* 53 */ II (d, a, b, c, X[ 3], S42, 2399980690); /* 54 */ II (c, d, a, b, X[10], S43, 4293915773); /* 55 */ II (b, c, d, a, X[ 1], S44, 2240044497); /* 56 */ II (a, b, c, d, X[ 8], S41, 1873313359); /* 57 */ II (d, a, b, c, X[15], S42, 4264355552); /* 58 */ II (c, d, a, b, X[ 6], S43, 2734768916); /* 59 */ II (b, c, d, a, X[13], S44, 1309151649); /* 60 */ II (a, b, c, d, X[ 4], S41, 4149444226); /* 61 */ II (d, a, b, c, X[11], S42, 3174756917); /* 62 */ II (c, d, a, b, X[ 2], S43, 718787259); /* 63 */ II (b, c, d, a, X[ 9], S44, 3951481745); /* 64 */ /* 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 */ 3.5 Step 5. Output 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 MD5. A reference implementation in C is given in the Appendix. 4. Summary The MD5 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 MD5 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. 5. Summary of Differences Between MD4 and MD5 The following are the differences between MD4 and MD5: -- A fourth round has been added. -- Each step now has a unique additive constant. -- The function g in round 2 was changed from (XY v XZ v YZ) to (XZ v Y not(Z)) to make g less symmetric. -- Each step now adds in the result of the previous step. This promotes a faster "avalanche effect". -- The order in which input words are accessed in rounds 2 and 3 is changed, to make these patterns less like each other. -- The shift amounts in each round have been approximately optimized, to yield a faster "avalanche effect". The shifts in different rounds are distinct. 6. 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 MD5 and a public-key cryptosystem. References [1] Rivest, R.L., The MD4 Message Digest Algorithm (RFC 1186), October 1990. [2] Rivest, R.L., The MD4 message digest algorithm, presented at CRYPTO '90 (Santa Barbara, CA, August 11-15, 1990). [3] CCITT, The Directory---Authentication Framework (Recommendation X.509), 1988. Authors' Addresses 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 Steve Dusse RSA Data Security, Inc. 10 Twin Dolphin Drive Redwood City, CA 94065 Phone: (415) 595-8782 EMail: dusse@rsa.com APPENDIX - Reference Implementation This appendix contains the following files: md5.h -- header file for implementation of MD5 md5.c -- the source code for MD5 routines md5driver.c -- sample test routines session -- sample results of running md5driver It is not difficult to improve this implementation on particular platforms, an exercise left to the reader. Following are some suggestions: 1. Change MD5Update so that the context is not used at all if it is empty (mdi == 0) and 64 or more bytes remain (inLen >= 64). In other words, call Transform with inBuf in this case. (This requires that byte ordering is correct in inBuf.) 2. Implement a procedure MD5UpdateLong modeled after MD5Update where inBuf is UINT4 * instead of unsigned char *. MD5UpdateLong would call Transform directly with 16- word blocks from inBuf. Call this instead of MD5Update in general. This works well if you have an I/O procedure that can read long words from a file. 3. On "little-endian" platforms where the lowest-address byte in a long word is the least significant (and there are no alignment restrictions), change MD5Update to call Transform directly with 64-byte blocks from inBuf (typecast to a UINT4 *).