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<p><b>New page</b></p><div>[[Image:Ron Rivest.jpg|thumbnail|right|MD5 was designed by [[Ronald Rivest]] (one of the inventors of the [[RSA]] algorithm) in 1991.]]<br />
In [[cryptography]], '''MD5''' ('''Message-Digest algorithm 5''') is a widely-used [[cryptographic hash function]] with a 128-bit hash value. As an Internet standard (RFC 1321), MD5 has been employed in a wide variety of security applications, and is also commonly used to check the integrity of files.<br />
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MD5 was designed by [[Ronald Rivest]] in [[1991]] to replace an earlier hash function, [[MD4]]. In [[1996]], a flaw was found with the design of MD5; while it was not a clearly fatal weakness, cryptographers began to recommend using other algorithms, such as [[SHA-1]] (recent claims suggest that SHA-1 has been broken, however). In [[2004]], more serious flaws were discovered making further use of the algorithm for security purposes questionable.<br />
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==History and cryptanalysis==<br />
MD5 is one of a series of message digest algorithms designed by Professor [[Ronald Rivest]] of [[Massachusetts Institute of Technology|MIT]] (Rivest, 1994). When analytic work indicated that MD5's predecessor &mdash; [[MD4]] &mdash; was likely to be insecure, MD5 was designed in [[1991]] to be a secure replacement (weaknesses were indeed subsequently found in MD4 by [[Hans Dobbertin]]).<br />
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In 1993, den Boer and Bosselaers gave an early, although limited, result of finding a "pseudo-collision" of the MD5 compression function; that is, two different [[initialisation vector]]s <math>I</math> and <math>J</math> with 4-bit difference between them, such that:<br />
:<math>MD5compress(I,X) = MD5compress(J,X)</math><br />
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In 1996, Dobbertin announced a collision of the compression function of MD5 (Dobbertin, 1996). While this was not an attack on the full MD5 hash function, it was close enough for cryptographers to recommend switching to a replacement, such as [[WHIRLPOOL]], [[SHA-1]] or [[RIPEMD-160]].<br />
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The size of the hash &mdash; 128 bits &mdash; is small enough to contemplate a [[brute force attack|brute force]] [[birthday attack]]. [[MD5CRK]] was a [[distributed computing|distributed project]] started in March [[2004]] with the aim of demonstrating that MD5 is practically insecure by finding a collision using a brute force attack.<br />
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However, MD5CRK ended shortly after [[17 August]], [[2004]], when [[hash collision|collision]]s for the full MD5 were announced by Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu [http://eprint.iacr.org/2004/199] [http://eprint.iacr.org/2004/264]. Their analytical attack was reported to take only one hour on an [[IBM p690]] cluster.<br />
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On [[1 March]] [[2005]], Arjen Lenstra, Xiaoyun Wang, and Benne de Weger demonstrated [http://eprint.iacr.org/2005/067] construction of two X.509 certificates with different public keys and the same MD5 hash, a demonstrably practical collision. The construction included private keys for both public keys. And a few days later, Vlastimil Klima described [http://eprint.iacr.org/2005/075] an improved algorithm, able to construct MD5 collisions in a few hours on a single notebook computer. Given this, MD5 is definitely not practically collision-free.<br />
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Because MD5 makes only one pass over the data, if two prefixes with the same hash can be constructed, a common suffix can be added to both to make the collision more reasonable. And because the current collision-finding techniques allow the preceding hash state to be specified arbitrarily, a collision can be found for any desired prefix. All that is required to generate two colliding files is a template file, with a 128-byte block of data aligned on a 64-byte boundary, that can be changed freely by the collision-finding algorithm.<br />
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==Integrity checking==<br />
MD5 digests have been widely used in the software world to provide some assurance that a downloaded file has not been altered. A user can compare a published MD5 sum with the [[checksum]] of a downloaded file. <br />
Now that it is easy to generate MD5 collisions, though, it is possible for the person who creates the file to create a second file with the same checksum, so this technique cannot protect against some forms of malicious tampering.<br />
It is also often the case that the checksum cannot be trusted (for example, it was obtained over the same channel as the downloaded file), in which case MD5 can only provide error-checking functionality: it will recognize a corrupt or incomplete download - Ever more common as larger files are being downloaded. Indeed, now, when downloading 1Gb+ files, the chance of one being corrupt is exceedingly likely.<br />
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==Algorithm==<br />
[[Image:MD5.png|right|thumbnail|300px|Figure 1. One MD5 operation &mdash; MD5 consists of 64 of these operations, grouped in four rounds of 16 operations. ''F'' is a nonlinear function; one function is used in each round. ''M<sub>i</sub>'' denotes a 32-bit block of the message input, and ''K<sub>i</sub>'' denotes a 32-bit constant, different for each operation.]] <br />
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[[Image:lll.png|left shift]]<sub>''s''</sub> denotes a left bit rotation by ''s'' places; ''s'' varies for each operation. [[Image:Boxplus.png|Addition]] denotes addition modulo 2<sup>32</sup>.<br />
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MD5 processes a variable length message into a fixed-length output of 128 bits. The input message is broken up into chunks of 512-bit blocks; the message is [[padding (cryptography)|padded]] so that its length is divisible by 512. The padding works as follows: first a single bit, 1, is appended to the end of the message. This is followed by as many zeros as are required to bring the length of the message up to 64 bits fewer than a multiple of 512. The remaining bits are filled up with a 64-bit integer representing the length of the original message. <br />
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The main MD5 algorithm operates on a 128-bit state, divided into four 32-bit words, denoted ''A'', ''B'', ''C'' and ''D''. These are initialised to certain fixed constants. The main algorithm then operates on each 512-bit message block in turn, each block modifying the state. The processing of a message block consists of four similar stages, termed ''rounds''; each round is composed of 16 similar operations based on a non-linear function ''F'', modular addition, and left rotation. Figure 1 illustrates one operation within a round. There are four possible functions ''F'', a different one is used in each round:<br />
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:<math>F(X,Y,Z) = (X\wedge{Y}) \vee (\neg{X} \wedge{Z})</math><br />
:<math>G(X,Y,Z) = (X\wedge{Z}) \vee (Y \wedge \neg{Z})</math><br />
:<math>H(X,Y,Z) = X \oplus Y \oplus Z</math><br />
:<math>I(X,Y,Z) = Y \oplus (X \vee \neg{Z})</math><br />
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<math>\oplus, \wedge, \vee, \neg</math> denote the XOR, AND, OR and NOT operations respectively.<br />
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==Pseudocode==<br />
[[Pseudocode]] for the MD5 algorithm follows.<br />
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//''Note: All variables are unsigned 32 bits and wrap modulo 2^32 when calculating''<br />
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//''Define r as the following''<br />
'''var''' ''int''[64] r, k<br />
r[ 0..15] := {7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22}<br />
r[16..31] := {5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20}<br />
r[32..47] := {4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23}<br />
r[48..63] := {6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21}<br />
<br />
//''Use binary fractional part of the sines of integers as constants:''<br />
'''for''' i '''from''' 0 '''to''' 63<br />
k[i] := floor(abs(sin(i + 1)) &times; 2^32)<br />
<br />
//''Initialize variables:''<br />
'''var''' ''int'' h0 := 0x67452301<br />
'''var''' ''int'' h1 := 0xEFCDAB89<br />
'''var''' ''int'' h2 := 0x98BADCFE<br />
'''var''' ''int'' h3 := 0x10325476<br />
<br />
//''Pre-processing:''<br />
'''append''' "1" bit '''to''' message<br />
'''append''' "0" bits '''until''' message length in bits &#8801; 448 (mod 512)<br />
'''append''' bit length of message '''as''' ''64-bit little-endian integer'' '''to''' message<br />
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//''Process the message in successive 512-bit chunks:''<br />
'''for each''' ''512-bit'' chunk '''of''' message<br />
break chunk into sixteen 32-bit little-endian words w(i), 0 &le; i &le; 15<br />
<br />
//''Initialize hash value for this chunk:''<br />
'''var''' ''int'' a := h0<br />
'''var''' ''int'' b := h1<br />
'''var''' ''int'' c := h2<br />
'''var''' ''int'' d := h3<br />
<br />
//''Main loop:''<br />
'''for''' i '''from''' 0 '''to''' 63<br />
'''if''' 0 &le; i &le; 15 '''then'''<br />
f := (b '''and''' c) '''or''' (('''not''' b) '''and''' d)<br />
g := i<br />
'''else if''' 16 &le; i &le; 31<br />
f := (d '''and''' b) '''or''' (('''not''' d) '''and''' c)<br />
g := (5&times;i + 1) '''mod''' 16<br />
'''else if''' 32 &le; i &le; 47<br />
f := b '''xor''' c '''xor''' d<br />
g := (3&times;i + 5) '''mod''' 16<br />
'''else if''' 48 &le; i &le; 63<br />
f := c '''xor''' (b '''or''' ('''not''' d))<br />
g := (7&times;i) '''mod''' 16<br />
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temp := d<br />
d := c<br />
c := b<br />
b := ((a + f + k(i) + w(g)) '''leftrotate''' r(i)) + b<br />
a := temp<br />
<br />
//''Add this chunk's hash to result so far:''<br />
h0 := h0 + a<br />
h1 := h1 + b <br />
h2 := h2 + c<br />
h3 := h3 + d<br />
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'''var''' ''int'' digest := h0 '''append''' h1 '''append''' h2 '''append''' h3 //''(expressed as little-endian)''<br />
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''Note: Instead of the formulation from the original RFC 1321 shown, the following may be used for improved efficiency:''<br />
(0 &le; i &le; 15): f := d '''xor''' (b '''and''' (c '''xor''' d))<br />
(16 &le; i &le; 31): f := c '''xor''' (d '''and''' (b '''xor''' c))<br />
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==MD5 hashes==<br />
The 128-bit (16-byte) MD5 hashes (also termed ''message digests'') are typically represented as 32-digit [[hexadecimal]] numbers. The following demonstrates a 43-byte [[ASCII]] input and the corresponding MD5 hash:<br />
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MD5("The quick brown fox jumps over the lazy dog") = 9e107d9d372bb6826bd81d3542a419d6<br />
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Even a small change in the message will (with overwhelming probability) result in a completely different hash, e.g. changing <tt>d</tt> to <tt>c</tt>:<br />
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MD5("The quick brown fox jumps over the lazy cog") = 1055d3e698d289f2af8663725127bd4b<br />
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The hash of the zero-length string is:<br />
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MD5("") = d41d8cd98f00b204e9800998ecf8427e<br />
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==See also== <br />
*[[MD2]]<br />
*[[MD4]]<br />
*[[SHA hash functions|SHA]]<br />
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==References==<br />
* Thomas A. Berson, Differential Cryptanalysis Mod 2<sup>32</sup> with Applications to MD5, EUROCRYPT 1992, pp71&ndash;80.<br />
* Bert den Boer and Antoon Bosselaers, Collisions for the Compression Function of MD5, EUROCRYPT 1993, pp293&ndash;304.<br />
* Hans Dobbertin, Cryptanalysis of MD5 compress. Announcement on Internet, May 1996 [http://citeseer.ist.psu.edu/dobbertin96cryptanalysis.html].<br />
* Hans Dobbertin, The Status of MD5 After a Recent Attack, in CryptoBytes 2(2), 1996 [http://www.rsasecurity.com/rsalabs/node.asp?id=2149].<br />
* Xiaoyun Wang and Hongbo Yu, How to Break MD5 and Other Hash Functions, EUROCRYPT 2005 [http://www.infosec.sdu.edu.cn/paper/md5-attack.pdf].<br />
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==Implementations==<br />
* [http://block111.servehttp.com/hash Calculate MD5 or SHA1 hash of any text] &mdash; Javascript implementation of MD5 and [[SHA1]] by Pavel Pavlov. Free for any use.<br />
* [http://userpages.umbc.edu/~mabzug1/cs/md5/md5.html MD5 Unofficial homepage] &mdash; contains links to implementations in various programming languages.<br />
* [http://pajhome.org.uk/crypt/md5/ Paj's Home: Cryptography] &mdash; by Paj in [[JavaScript]]. Also supports [[MD4]] and [[SHA-1]]. Released under the [[BSD License]]. Contains links to several other implementations.<br />
* [http://www.cs.eku.edu/faculty/styer/460/Encrypt/JS-MD5.html Javascript MD5 calculator] &mdash; by Eugene Styer in [[JavaScript]]. Shows intermediate values in the calculation.<br />
* [http://discodia.org/en/md5 Calculate MD5 hashes from strings and files online] &mdash; The hashes are calculated server-side; no JavaScript required.<br />
* [[Jacksum]] &mdash; by Dipl.-Inf. (FH) Johann N. LĂ¶fflmann in [[Java programming language|Java]]. Various message verification functions. Released under the [[GPL]].<br />
* [[wxChecksums]] &mdash; by Julien Couot in [[C plus plus|C++]]. Also supports [[SFV]]. Released under the [[GPL]].<br />
* [http://www.md5summer.org/ Windows MD5 Sum generator] &mdash; by Luke Pascoe in [[Pascal]]. Released under the [[GPL]].<br />
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== External links ==<br />
===MD5 information===<br />
* RFC 1321 &mdash; ''The MD5 Message-Digest Algorithm''<br />
* [http://groups.google.com/groups?selm=fgrieu-AE7D15.18300202042004%40news.fu-berlin.de Annotated bibliography of MD5 cryptanalysis] <!-- we should work these into this article at some point --><br />
* [http://www.cryptography.com/cnews/hash.html Hash Collision Q&A]<br />
* [http://www.phpbbsupport.co.uk/md5.php MD5 Hash Example/Generator]<br />
* [http://www.md5sums.com MD5 Checksums for Linux and BSD Distributions]<br />
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===Web based MD5 Crackers===<br />
* [http://passcracking.com/ MD5 crack] - 47.6G of [[rainbow tables]] and database, waiting list (Closed)<br />
* [http://passcracking.ru/ MD5 online RTcrack] - 47.6G of [[rainbow tables]] and database, waiting list (Doing well)<br />
* [http://md5.rednoize.com MD5 Reverse Lookup] - First site that introduced the DB based reverse md5 lookup<br />
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===Collisions===<br />
* [http://cryptography.hyperlink.cz/MD5_collisions.html Faster collisions finding by V. Klima]<br />
* [http://www.cits.rub.de/MD5Collisions/ Two colliding Postscript files with the same size]<br />
* [http://www.shmoo.com/md5-collision.html MD5 Collision, Visualised]<br />
* [http://www.codeproject.com/useritems/HackingMd5.asp Exploiting MD5 collisions, in C#]<br />
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