MD5
From Academic Kids

In cryptography, MD5 (MessageDigest algorithm 5) is a widelyused cryptographic hash function with a 128bit 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.
MD5 was designed by Ronald Rivest in 1991 to replace an earlier hash function, MD4. In 1996, a flaw was found with the design; while it was not a clearly fatal weakness, cryptographers began to recommend using other algorithms, such as SHA1 (recent claims suggest that SHA1 was broken, however). In 2004, more serious flaws were discovered making further use of the algorithm for security purposes questionable.
Contents 
History and cryptanalysis
MD5 is one of a series of message digest algorithms designed by Professor Ronald Rivest of MIT (Rivest, 1994). When analytic work indicated that MD5's predecessor — MD4 — 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).
In 1993, den Boer and Bosselaers gave an early, although limited, result of finding a "pseudocollision" of the MD5 compression function; that is, two different initialisation vectors <math>I<math> and <math>J<math> with 4bit difference between them, such that:
 <math>MD5compress(I,X) = MD5compress(J,X)<math>
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, SHA1 or RIPEMD160.
The size of the hash — 128 bits — is small enough to contemplate a brute force birthday attack. MD5CRK was a 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.
However, MD5CRK ended shortly after 17 August, 2004, when collisions for the full MD5 were announced by Xiaoyun Wang, Dengguo Feng, Xuejia Lai and Hongbo Yu [1] (http://eprint.iacr.org/2004/199.pdf) [2] (http://eprint.iacr.org/2004/264.pdf). Their analytical attack was reported to take only one hour on an IBM P690 cluster.
On 1 March 2005, Arjen Lenstra, Xiaoyun Wang, and Benne de Weger demonstrated [3] (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 [4] (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 collisionfree.
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 collisionfinding 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 128byte block of data aligned on a 64byte boundary, that can be changed freely by the collisionfinding algorithm.
Practical effect of cryptanalysis
It is now known how to, with a few hours' work, generate an MD5 collision. That is, to generate two byte strings with the same hash. Since there are a finite number of MD5 outputs (2^{128}), but an infinite number of possible inputs, it has long been known that such collisions must exist, but it had been previously believed to be impractically difficult to find one.
The result is that the MD5 hash of some information no longer uniquely identifies it. If someone presents you with information such as a public key, its MD5 hash might not uniquely identify it: the other person might have a second public key with the same MD5 hash.
However, the present attacks require the ability to choose both messages of the collision. They do not make it easy to perform a preimage attack, finding a message with a specified MD5 hash, or a second preimage attack, finding a message with the same MD5 hash as a given message.
Thus, old MD5 hashes, made before these attacks were known, are safe for now. In particular, old digital signatures can still be considered reliable. A user might not wish to generate or trust any new signatures using MD5 if there is any possibility that a small change to the text (the collisions being constructed involve flipping a few bits in a 128byte section of hash input) would constitute a meaningful change.
This assurance is based on the current state of cryptanalysis. The situation may change suddenly, but finding a collision with some preexisting data is a much more difficult problem, and there should be time for an orderly transition.
Integrity checking
MD5 digests are widely used in the software world to provide some assurance that a downloaded file has not been altered. A user can compare a publicized MD5 sum with the checksum of a downloaded file. On the assumption that publicized checksum can be trusted to be authentic, a user can have considerable confidence that the file is the same as that released by the developers, protecting against Trojan horses and computer viruses being added to the software surreptitiously. However, it is 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 errorchecking functionality: it will recognize a corrupt or incomplete download.
Algorithm
MD5.png
MD5 processes a variable length message into a fixedlength output of 128 bits. The input message is broken up into chunks of 512bit blocks; the message is 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 64bit integer representing the length of the original message. The message is always padded with at least a single 1bit, such that if the message length is a multiple of 512 minus the 64 bits for the length representation (that is, length mod(512) = 448), a new block of 512 bits is added with a 1bit followed by 447 0bits followed by the 64 length.
The main MD5 algorithm operates on a 128bit state, divided into four 32bit words, denoted A, B, C and D. These are initialised to certain fixed constants. The main algorithm then operates on each 512bit 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 nonlinear 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:
 <math>F(X,Y,Z) = (X\wedge{Y}) \vee (\neg{X} \wedge{Z})<math>
 <math>G(X,Y,Z) = (X\wedge{Z}) \vee (Y \wedge \neg{Z})<math>
 <math>H(X,Y,Z) = X \oplus Y \oplus Z<math>
 <math>I(X,Y,Z) = Y \oplus (X \vee \neg{Z})<math>
<math>\oplus, \wedge, \vee, \neg<math> denote the XOR, AND, OR and NOT operations respectively.
Pseudocode
Pseudocode for the MD5 algorithm follows.
//Note: All variables are unsigned 32 bits and wrap modulo 2^32 when calculating //Define r as the following var int[64] r, k r[ 0..15] := {7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22, 7, 12, 17, 22} r[16..31] := {5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20, 5, 9, 14, 20} r[32..47] := {4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23, 4, 11, 16, 23} r[48..63] := {6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21, 6, 10, 15, 21} //Use binary fractional part of the sines of integers as constants: for i from 0 to 63 k[i] := floor(abs(sin(i + 1)) × 2^32) //Initialize variables: var int h0 := 0x67452301 var int h1 := 0xEFCDAB89 var int h2 := 0x98BADCFE var int h3 := 0x10325476 //Preprocessing: append "1" bit to message append "0" bits until message length in bits ≡ 448 (mod 512) append bit length of message as 64bit littleendian integer to message //Process the message in successive 512bit chunks: for each 512bit chunk of message break chunk into sixteen 32bit littleendian words w(i), 0 ≤ i ≤ 15 //Initialize hash value for this chunk: var int a := h0 var int b := h1 var int c := h2 var int d := h3 //Main loop: for i from 0 to 63 if 0 ≤ i ≤ 15 then f := (b and c) or ((not b) and d) g := i else if 16 ≤ i ≤ 31 f := (d and b) or ((not d) and c) g := (5×i + 1) mod 16 else if 32 ≤ i ≤ 47 f := b xor c xor d g := (3×i + 5) mod 16 else if 48 ≤ i ≤ 63 f := c xor (b or (not d)) g := (7×i) mod 16 temp := d d := c c := b b := ((a + f + k(i) + w(g)) leftrotate r(i)) + b a := temp //Add this chunk's hash to result so far: h0 := h0 + a h1 := h1 + b h2 := h2 + c h3 := h3 + d var int digest := h0 append h1 append h2 append h3 //(expressed as littleendian)
Note: Instead of the formulation from the original RFC 1321 shown, the following may be used for improved efficiency:
(0 ≤ i ≤ 15): f := d xor (b and (c xor d)) (16 ≤ i ≤ 31): f := c xor (d and (b xor c))
MD5 hashes
The 128bit (16byte) MD5 hashes (also termed message digests) are typically represented as 32digit hexadecimal numbers. The following demonstrates a 43byte ASCII input and the corresponding MD5 hash:
 MD5("The quick brown fox jumps over the lazy dog") = 9e107d9d372bb6826bd81d3542a419d6
Even a small change in the message will (with overwhelming probability) result in a completely different hash, e.g. changing d to c:
 MD5("The quick brown fox jumps over the lazy cog") = 1055d3e698d289f2af8663725127bd4b
The hash of the zerolength string is:
 MD5("") = d41d8cd98f00b204e9800998ecf8427e
See also
References
 Thomas A. Berson, Differential Cryptanalysis Mod 2^{32} with Applications to MD5, EUROCRYPT 1992, pp71–80.
 Bert den Boer and Antoon Bosselaers, Collisions for the Compression Function of MD5, EUROCRYPT 1993, pp293–304.
 Hans Dobbertin, Cryptanalysis of MD5 compress. Announcement on Internet, May 1996 [5] (http://citeseer.ist.psu.edu/dobbertin96cryptanalysis.html).
 Hans Dobbertin, The Status of MD5 After a Recent Attack, in CryptoBytes 2(2), 1996 [6] (http://www.rsasecurity.com/rsalabs/node.asp?id=2149).
 Xiaoyun Wang and Hongbo Yu, How to Break MD5 and Other Hash Functions, to appear, EUROCRYPT 2005 [7] (http://www.infosec.sdu.edu.cn/paper/md5attack.pdf).
External links
MD5 information:
 RFC 1321 — The MD5 MessageDigest Algorithm
 Using MD5 to verify the integrity of file contents (http://www.cert.org/securityimprovement/implementations/i002.01.html)
 Annotated bibliography of MD5 cryptanalysis (http://groups.google.com/groups?selm=fgrieuAE7D15.18300202042004%40news.fuberlin.de)
 Hash Collision Q&A (http://www.cryptography.com/cnews/hash.html)
 Online MD5 passwordhash cracking (http://passcracking.com/)
 Online MD5 password database (about 6 million entries) (http://prefect.ch/)
 Online MD5 password database (about 2 million entries) (http://md5.rednoize.com/)
 MD5 Hash Example/Generator (http://www.phpbbsupport.co.uk/md5.php)
Implementations:
 MD5 Unofficial homepage (http://userpages.umbc.edu/~mabzug1/cs/md5/md5.html) — contains links to several implementations in various programming languages
 Paj's Home: Cryptography (http://pajhome.org.uk/crypt/md5/) (Javascript MD4 and MD5, plus SHA1)
 A Javascript MD5 calculator showing intermediate values in the calculation (http://www.cs.eku.edu/faculty/styer/460/Encrypt/JSMD5.html)
 Jacksum (http://www.jonelo.de/java/jacksum/index.html) (a program with various message verification functions)
 wxChecksums (http://wxchecksums.sourceforge.net/) (Free software for Microsoft Windows)
Collisions:
 Faster collisions finding by V. Klima (http://cryptography.hyperlink.cz/MD5_collisions.html)
 Two colliding Postscript files with the same size (http://www.cits.rub.de/MD5Collisions/)
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