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Template:Infobox cryptographic hash function In cryptography, MD5 (Message-Digest algorithm 5) is a widely used cryptographic hash function with a 128-bit hash value. Specified in RFC 1321, MD5 has been employed in a wide variety of security applications, and is also commonly used to check the integrity of files. However, it has been shown that MD5 is not collision resistant;[1] as such, MD5 is not suitable for applications like SSL certificates or digital signatures that rely on this property. An MD5 hash is typically expressed as a 32-digit hexadecimal number.

MD5 was designed by Ron 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 recommending the use of other algorithms, such as SHA-1 (which has since been found also to be vulnerable). In 2004, more serious flaws were discovered, making further use of the algorithm for security purposes questionable; specifically, a group of researchers described how to create a pair of files that share the same MD5 checksum.[2][3] Further advances were made in breaking MD5 in 2005, 2006, and 2007.[4] In an attack on MD5 published in December 2008, a group of researchers used this technique to fake SSL certificate validity.[5][6] US-CERT of the U. S. Department of Homeland Security said MD5 "should be considered cryptographically broken and unsuitable for further use,"[7] and most U.S. government applications will be required to move to the SHA-2 family of hash functions after 2010.[8]

## History and cryptanalysisEdit

MD5 is one in 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 later 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 initialization vectors which produce an identical digest.

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 SHA-1 or RIPEMD-160.

The size of the hash—128 bits—is small enough to contemplate a 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 birthday attack.

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.[2][3][9] 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[10] 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. A few days later, Vlastimil Klima described[11] an improved algorithm, able to construct MD5 collisions in a few hours on a single notebook computer. On 18 March 2006, Klima published an algorithm[12] that can find a collision within one minute on a single notebook computer, using a method he calls tunneling.

In 2009, the United States Cyber Command used an MD5 hash of their mission statement as a part of their official emblem.

## SecurityEdit

The security of the MD5 hash function is severely compromised. A collision attack exists that can find collisions within seconds on a computer with a 2.6Ghz Pentium4 processor (complexity of 224.1).[13] Further, there is also a chosen-prefix collision attack that can produce a collision for two chosen arbitrarily different inputs within hours, using off-the-shelf computing hardware (complexity 239).[14]

These collision attacks have been demonstrated in the public in various situations, including colliding document files[15][16] and digital certificates.[5]

As of 2009, a theoretical attack also breaks MD5's preimage resistance.

### Collision vulnerabilitiesEdit

In 1996, collisions were found in the compression function of MD5, and Hans Dobbertin wrote in the RSA Laboratories technical newsletter, "The presented attack does not yet threaten practical applications of MD5, but it comes rather close ... in the future MD5 should no longer be implemented...where a collision-resistant hash function is required."[17]

In 2005, researchers were able to create pairs of PostScript documents[18] and X.509 certificates[19] with the same hash. Later that year, MD5's designer Ron Rivest wrote, "md5 and sha1 are both clearly broken (in terms of collision-resistance),"[20] and RSA Laboratories wrote that "[n]ext-generation products will need to move to new algorithms."[21]

On 30 December 2008, a group of researchers announced at the 25th Chaos Communication Congress how they had used MD5 collisions to create an intermediate certificate authority certificate which appeared to be legitimate when checked via its MD5 hash.[5] The researchers used a cluster of Sony Playstation 3s at the EPFL in Lausanne, Switzerland[22] to change a normal SSL certificate issued by RapidSSL into a working CA certificate for that issuer, which could then be used to create other certificates that would appear to be legitimate and issued by RapidSSL. VeriSign, the issuers of RapidSSL certificates, said they stopped issuing new certificates using MD5 as their checksum algorithm for RapidSSL once the vulnerability was announced.[23] Although Verisign declined to revoke existing certificates signed using MD5, their response was considered adequate by the authors of the exploit (Alexander Sotirov, Marc Stevens, Jacob Appelbaum, Arjen Lenstra, David Molnar, Dag Arne Osvik, and Benne de Weger).[5] Bruce Schneier wrote of the attack that "[w]e already knew that MD5 is a broken hash function" and that "no one should be using MD5 anymore."[24] The SSL researchers wrote, "Our desired impact is that Certification Authorities will stop using MD5 in issuing new certificates. We also hope that use of MD5 in other applications will be reconsidered as well."[5]

MD5 makes only one pass over the data, so if two prefixes with the same hash can be constructed, a common suffix can be added to both to make the collision more likely to be accepted as valid data by the application using it. Furthermore, current collision-finding techniques allow to specify an arbitrary prefix: an attacker can create two colliding files that both begin with the same content. All the attacker needs 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.

### Preimage vulnerabilityEdit

In April 2009, a preimage attack against MD5 was published that breaks MD5's preimage resistance. This attack is only theoretical, with a computational complexity of 2123.4 for full preimage and 2116.9 for a pseudo-preimage.[25]

### Other vulnerabilitiesEdit

A number of projects have published MD5 rainbow tables online, that can be used to reverse many MD5 hashes into strings that collide with the original input, usually for the purposes of password cracking.

The use of MD5 in some websites' URLs means that search engines such as Google can also sometimes function as a limited tool for reverse lookup of MD5 hashes.[26]

Both these techniques are rendered ineffective by the use of a sufficiently long salt.

## ApplicationsEdit

MD5 digests have been widely used in the software world to provide some assurance that a transferred file has arrived intact. For example, file servers often provide a pre-computed MD5 (known as Md5sum) checksum for the files, so that a user can compare the checksum of the downloaded file to it. Unix-based operating systems include MD5 sum utilities in their distribution packages, whereas Windows users use third-party applications.

However, now that it is easy to generate MD5 collisions, it is possible for the person who created the file to create a second file with the same checksum, so this technique cannot protect against some forms of malicious tampering. Also, in some cases the checksum cannot be trusted (for example, if 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, which becomes more likely when downloading larger files.

MD5 is widely used to store passwords.[27][28] To mitigate the vulnerabilities mentioned above, one can add a salt to the passwords before hashing them. Some implementations may apply the hashing function more than once—see key strengthening.

## AlgorithmEdit

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 (sixteen 32-bit little endian integers); 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, in bits.

The main MD5 algorithm operates on a 128-bit state, divided into four 32-bit words, denoted A, B, C and D. These are initialized 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.

### PseudocodeEdit

Pseudocode for the MD5 algorithm follows.

//Note: All variables are unsigned 32 bits and wrap modulo 2^32 when calculating
var int[64] r, k

//r specifies the per-round shift amounts
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 integer part of the sines of integers (Radians) as constants:
for i from 0 to 63
k[i] := floor(abs(sin(i + 1)) × (2 pow 32))

//Initialize variables:
var int h0 := 0x67452301
var int h1 := 0xEFCDAB89
var int h3 := 0x10325476

//Pre-processing:
append "1" bit to message
append "0" bits until message length in bits ≡ 448 (mod 512)
append bit /* bit, not byte */ length of unpadded message as 64-bit little-endian integer to message

//Process the message in successive 512-bit chunks:
for each 512-bit chunk of message
break chunk into sixteen 32-bit little-endian words w[j], 0 ≤ j ≤ 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 := b + leftrotate((a + f + k[i] + w[g]) , r[i])
a := temp

//Add this chunk's hash to result so far:
h0 := h0 + a
h1 := h1 + b
h2 := h2 + c
h3 := h3 + d

var char digest[16] := h0 append h1 append h2 append h3 //(expressed as little-endian)

//leftrotate function definition
leftrotate (x, c)
return (x << c) or (x >> (32-c));


Note: Instead of the formulation from the original RFC 1321 shown, the following may be used for improved efficiency (useful if assembly language is being used - otherwise, the compiler will generally optimize the above code. Since each computation is dependent on another in these formulations, this is often slower than the above method where the nand/and can be parallelised):

(0  ≤ i ≤ 15): f := d xor (b and (c xor d))
(16 ≤ i ≤ 31): f := c xor (d and (b xor c))


## MD5 hashesEdit

The 128-bit (16-byte) MD5 hashes (also termed message digests) are typically represented as a sequence of 32 hexadecimal digits. 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 mostly different hash, due to the avalanche effect. For example, adding a period to the end of the sentence:

 MD5("The quick brown fox jumps over the lazy dog.")


The hash of the zero-length string is:

 MD5("")
= d41d8cd98f00b204e9800998ecf8427e


## NotesEdit

1. Xiaoyun Wang and Hongbo Yu: How to Break MD5 and Other Hash Functions. Retrieved December 21, 2009.
2. 2.0 2.1 Xiaoyun Wang, Dengguo Feng, Xuejia Lai, Hongbo Yu: Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD, Cryptology ePrint Archive Report 2004/199, 16 August 2004, revised 17 August 2004. Retrieved July 27, 2008.
3. 3.0 3.1 J. Black, M. Cochran, T. Highland: A Study of the MD5 Attacks: Insights and Improvements, March 3, 2006. Retrieved July 27, 2008.
4. Marc Stevens, Arjen Lenstra, Benne de Weger: Vulnerability of software integrity and code signing applications to chosen-prefix collisions for MD5, Nov 30, 2007. Retrieved Jul 27, 2008.
5. 5.0 5.1 5.2 5.3 5.4
6. Template:Cite web
7. Template:Cite web
8. Template:Cite web
9. Philip Hawkes and Michael Paddon and Gregory G. Rose: Musings on the Wang et al. MD5 Collision, 13 Oct 2004. Retrieved July 27, 2008.
10. Arjen Lenstra, Xiaoyun Wang, Benne de Weger: Colliding X.509 Certificates, Cryptology ePrint Archive Report 2005/067, 1 March 2005, revised 6 May 2005. Retrieved July 27, 2008.
11. Vlastimil Klima: Finding MD5 Collisions – a Toy For a Notebook, Cryptology ePrint Archive Report 2005/075, 5 March 2005, revised 8 March 2005. Retrieved July 27, 2008.
12. Vlastimil Klima: Tunnels in Hash Functions: MD5 Collisions Within a Minute, Cryptology ePrint Archive Report 2006/105, 18 March 2006, revised 17 April 2006. Retrieved July 27, 2008.
13. Template:Cite journal
14. Template:Cite journal
15. Template:Cite web
16. Template:Cite journal
17. [citation needed]
18. Template:Cite web
19. Template:Cite web
20. Template:Cite web
21. [1]. The quote refers to moving away from SHA-1, the de facto successor to MD5.
22. Template:Cite web
23. Template:Cite web
24. Forging SSL Certificates
25. Template:Cite journal
26. Steven J. Murdoch: Google as a password cracker, Light Blue Touchpaper Blog Archive, Nov 16, 2007. Retrieved July 27, 2008.
27. FreeBSD Handbook, Security - DES, Blowfish, MD5, and Crypt
28. Solaris 10 policy.conf(4) man page

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