MD

In cryptography, MD5 (Message-Digest algorithm 5) is a widely-used cryptographic hash function with a 128-bit hash value. MD5 was designed by Ronald Rivest in 1991. Significant security flaws in MD5 were reported in 2004, and many systems that use it will probably switch to more secure alternatives.

Contents

History

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 1996, Dobbertin announced a collision of the compression function of MD5 (Dobbertin, 1996). This was not quite an attack on the full MD5 hash function, but it was close enough for cryptographers to recommend switching to a replacement, such as SHA-1 or RIPEMD-160. In August 2004, Chinese researchers found collisions for MD5. It is still unknown how this discovery will affect the widespread use of MD5.

MD5 hashes

The 128-bit 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

Algorithm

Figure 1. One MD5 operation — 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. Mi denotes a 32-bit block of the message input, and Ki denotes a 32-bit constant, different for each operation. s is a shift value, which also varies for each operation.
Enlarge
Figure 1. One MD5 operation — 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. Mi denotes a 32-bit block of the message input, and Ki denotes a 32-bit constant, different for each operation. s is a shift value, which also varies for each operation.

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.

A description of MD5

Pseudocode for the MD5 algorithm follows: 

Define r(i) as the following function:
    when
        (0  ≤ i ≤ 15): r(i) =  7 then 12 then 17 then 22, 4 times
        (16 ≤ i ≤ 31): r(i) =  5 then  9 then 14 then 20, 4 times
        (32 ≤ i ≤ 47): r(i) =  4 then 11 then 16 then 23, 4 times
        (48 ≤ i ≤ 63): r(i) =  6 then 10 then 15 then 21, 4 times

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 ≡ 448 (mod 512)
append 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:
        temp = ((a + f(b,c,d) + k(i) + w(g(i))) leftrotate r(i)) + b
            where:
            (0  ≤ i ≤ 15): f(b,c,d) = (b and c) or ((not b) and d),  g(i) = i
            (16 ≤ i ≤ 31): f(b,c,d) = (d and b) or ((not d) and c),  g(i) = (5*i + 1) mod 16
            (32 ≤ i ≤ 47): f(b,c,d) = (b xor c xor d),               g(i) = (3*i + 5) mod 16
            (48 ≤ i ≤ 63): f(b,c,d) = (c xor (b or (not d))),        g(i) = (7*i) mod 16
        d = c
        c = b
        b = a
        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(b,c,d) = (d xor (b and (c xor d)))
(16 ≤ i ≤ 31): f(b,c,d) = (c xor (d and (b xor c)))

Security

MD5 has been widely used, and was originally thought to be cryptographically secure. However, research has uncovered weaknesses which make further use of MD5 questionable. On 17 August, 2004, collisions for 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 attack was reported to take only one hour on an IBM P690 cluster.

Note that Wang et al's attack is a collision attack and not a preimage attack.

While Wang et al's attack was analytical, 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 insecure by finding a collision using a brute force attack, although it was ended shortly after Wang et al's announcement.

Because of the discovery of an easy method for generating collisions, many researchers recommend that replacement algorithms, such as SHA-1 or RIPEMD-160, be used instead of MD5.

Integrity checking

MD5 digests are widely used in the software world to provide assurance that a downloaded file has not been altered. By comparing a publicized MD5 sum with the checksum of a downloaded file, a user can have considerable confidence that the file is the same as that released by the developers. This protects against Trojan horses and computer viruses being added to the software surreptitiously. Checking a downloaded file against its MD5 sum does not only detect files purposefully altered in a malicious manner; it will also recognize a corrupt or incomplete download.

To check the integrity of a downloaded file, download the MD5SUM file in the same folder as the file you want to verify and use an MD5 utility to compare the MD5 sum of the file to the one from a trusted source. On Unix systems, the md5sum command is an example of such a utility.

See also

References

  • Hans Dobbertin, Cryptanalysis of MD5 compress. Announcement on Internet, May 1996 [3] (http://citeseer.ist.psu.edu/dobbertin96cryptanalysis.html).
  • Hans Dobbertin, The Status of MD5 After a Recent Attack, in CryptoBytes 2(2), 1996 [4] (http://www.rsasecurity.com/rsalabs/node.asp?id=2149).

External links

de:Message Digest Algorithm 5 fr:MD5 ja:MD5 pl:MD5 fi:MD5


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