md5

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. 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 SHA-1. In 2004, more serious flaws were discovered making further use of the algorithm for security purposes questionable.

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 "pseudo-collision" of the MD5 compression function. That is, two different initialisation vectors

I

and

J

with 4-bit difference between them, such that:

MD5compress(I,X) = MD5compress(J,X)

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. 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 http://eprint.iacr.org/2004/199.pdf 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 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. 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.

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 (2¹²⁸), 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 I present you with information such as a public key, its MD5 hash might not uniquely identify it; I may 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 128-byte 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 pre-existing 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 error-checking functionality: it will recognize a corrupt or incomplete download.

Algorithm

  left shift_s denotes a left bit rotation by s places; s varies for each operation. Addition denotes addition modulo 2³².

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 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. 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:

F(X,Y,Z) = (X\wedge{Y}) \vee (\neg{X} \wedge{Z})

G(X,Y,Z) = (X\wedge{Z}) \vee (Y \wedge \neg{Z})

H(X,Y,Z) = X \oplus Y \oplus Z

I(X,Y,Z) = Y \oplus (X \vee \neg{Z})

\oplus, \wedge, \vee, \neg

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(i) as the following function:  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:  h0 := 0x67452301  h1 := 0xEFCDAB89  h2 := 0x98BADCFE  h3 := 0x10325476    Pre-processing:  append "1" bit to message  append "0" bits until message length in bits ≡ 448 (mod 512)  append bit length of message as 64-bit little-endian integer to message    Process the message in successive 512-bit chunks:  break message into 512-bit chunks  for each chunk      break chunk into sixteen 32-bit little-endian words w(i), 0 ≤ i ≤ 15        Initialize hash value for this chunk:      a := h0      b := h1      c := h2      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    digest = hash = h0 append h1 append h2 append h3 (expressed as little-endian)

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 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:

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 zero-length string is:

MD5("") = d41d8cd98f00b204e9800998ecf8427e

References

Thomas A. Berson, Differential Cryptanalysis Mod 2³² 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 http://citeseer.ist.psu.edu/dobbertin96cryptanalysis.html.
Hans Dobbertin, The Status of MD5 After a Recent Attack, in CryptoBytes 2(2), 1996 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 http://www.infosec.sdu.edu.cn/paper/md5-attack.pdf.