In cryptography, MD5 (Message-Digest algorithm 5) is a widely used, partially insecure^[1] cryptographic hash function with a 128-bit hash value. Ronald Linn Rivest (born 1947, Schenectady, New York) is a cryptographer. Message Digest Algorithm 2 (MD2 is a Cryptographic hash function developed by Ronald Rivest in 1989. MD4 is a message digest Algorithm (the fourth in a series designed by Professor Ronald Rivest of MIT in 1990 Digest size is a Magazine size smaller than a conventional size magazine but larger than a standard Paperback book approximately 5½ x 8¼ Inches but Cryptography (or cryptology; from Greek grc κρυπτός kryptos, "hidden secret" and grc γράφω gráphō, "I write" A cryptographic Hash function is a transformation that takes an input (or 'message' and returns a fixed-size string which is called the hash value (sometimes A bit is a binary digit, taking a value of either 0 or 1 Binary digits are a basic unit of Information storage and communication 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. The Internet is a global system of interconnected Computer networks A computer file is a block of Arbitrary Information, or resource for storing information which is available to a Computer program and is usually 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. Ronald Linn Rivest (born 1947, Schenectady, New York) is a cryptographer. Year 1991 ( MCMXCI) was a Common year starting on Tuesday (link will display full calendar of the Gregorian Calendar. MD4 is a message digest Algorithm (the fourth in a series designed by Professor Ronald Rivest of MIT in 1990 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 vulnerable itself). Year 1996 ( MCMXCVI) was a Leap year starting on Monday (link will display full 1996 Gregorian calendar) In 2004, more serious flaws were discovered making further use of the algorithm for security purposes questionable. "MMIV" redirects here For the Modest Mouse album see " Baron von Bullshit Rides Again " ^[2][3] In 2007 a group of researchers including Arjen Lenstra described how to create a pair of files that share the same MD5 checksum. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Arjen Klaas Lenstra (born 1956 Groningen) is a Dutch mathematician A checksum is a form of Redundancy check, a simple way to protect the integrity of data by detecting errors in data that are sent through space ( Telecommunications ^[4]

History and cryptanalysis

Message Digest is a series of message digest algorithms designed by Professor Ronald Rivest of MIT (Rivest, 1994). A cryptographic Hash function is a transformation that takes an input (or 'message' and returns a fixed-size string which is called the hash value (sometimes Ronald Linn Rivest (born 1947, Schenectady, New York) is a cryptographer. When analytic work indicated that MD5's predecessor—MD4—was likely to be insecure, MD5 was designed in 1991 to be a secure replacement. MD4 is a message digest Algorithm (the fourth in a series designed by Professor Ronald Rivest of MIT in 1990 (Weaknesses were indeed later found in MD4 by Hans Dobbertin. Hans Dobbertin, ( April 17 1952 - February 2 2006) was a German Cryptographer who is best known for his cryptanalysis of )

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 Computer science, a hash collision or hash clash is a situation that occurs when two distinct inputs into a Hash function produce identical outputs In Cryptography, a one-way compression function is a function that transforms two fixed length inputs to an output of the same size as one of the inputs In Cryptography, an initialization vector ( IV) is a block of bits that is required to allow a Stream cipher or a Block cipher to be executed

In 1996, Dobbertin announced a collision of the compression function of MD5 (Dobbertin, 1996). In Computer science, a hash collision or hash clash is a situation that occurs when two distinct inputs into a Hash function produce identical outputs 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. "WHIRLPOOL" redirects here This article is about the algorithm RIPEMD-160 ( RACE Integrity Primitives Evaluation Message Digest) is a 160-bit Message digest algorithm (and Cryptographic hash function) developed

The size of the hash—128 bits—is small enough to contemplate a birthday attack. A birthday attack is a type of cryptographic attack so named because it exploits the Mathematics behind the Birthday problem in Probability theory 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. In Cryptography, MD5CRK was a distributed effort (similar to Distributed Distributed computing deals with Hardware and Software Systems containing more than one processing element or Storage element concurrent

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. In Computer science, a hash collision or hash clash is a situation that occurs when two distinct inputs into a Hash function produce identical outputs Wang Xiaoyun ( (born 1966) is a researcher and professor in the Department of Mathematics and System Science Shandong University, Shandong, China ^[5][6][7] Their analytical attack was reported to take only one hour on an IBM p690 cluster. The IBM p690 was at the time of its release in late 2001 the flagship of IBM's high end unix servers ( PSeries) during the POWER4 era of processors

On 1 March 2005, Arjen Lenstra, Xiaoyun Wang, and Benne de Weger demonstrated^[8] construction of two X.509 certificates with different public keys and the same MD5 hash, a demonstrably practical collision. Arjen Klaas Lenstra (born 1956 Groningen) is a Dutch mathematician Wang Xiaoyun ( (born 1966) is a researcher and professor in the Department of Mathematics and System Science Shandong University, Shandong, China In Cryptography, X509 is an ITU-T standard for a Public key infrastructure (PKI for Single sign-on and Privilege Management Infrastructure The construction included private keys for both public keys. A few days later, Vlastimil Klima described^[9] 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^[10] that can find a collision within one minute on a single notebook computer, using a method he calls tunneling.

Vulnerability

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.

Because the current collision-finding techniques allow the preceding hash state to be specified arbitrarily, a collision can be found for any desired prefix; that is, for any given string of characters X, two colliding files can be determined which both begin with X.

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.

Recently, a number of projects have created MD5 "rainbow tables" which are easily accessible online, and can be used to reverse many MD5 hashes into strings that collide with the original input, usually for the purposes of password cracking. A rainbow table is a Lookup table offering a time-memory tradeoff used in recovering the Plaintext Password from a password hash generated by In computing a password is a Word or string of characters that is entered often along with a user name, in modern times usually into a computer system However, if passwords are combined with a salt before the MD5 digest is generated, rainbow tables become much less useful. In Cryptography, a salt comprises random Bits that are used as one of the inputs to a Key derivation function.

The use of MD5 in some websites' URLs means that Google can also sometimes function as a limited tool for reverse lookup of MD5 hashes. Uniform Resource Locator is an URI which also specifies where the identified resource is available and the protocol for retrieving it Google Inc is an American public corporation, earning revenue from advertising related to its Internet search, e-mail, online ^[11] This technique is rendered ineffective by the use of a salt. In Cryptography, a salt comprises random Bits that are used as one of the inputs to a Key derivation function.

Applications

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 checksum for the files, so that a user can compare the checksum of the downloaded file to it. A checksum is a form of Redundancy check, a simple way to protect the integrity of data by detecting errors in data that are sent through space ( Telecommunications Unix-based operating systems include MD5 sum utilities in their distribution packages, whereas Windows users use third-party applications. Unix (officially trademarked as UNIX, sometimes also written as Unix with Small caps) is a computer

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. In computing a password is a Word or string of characters that is entered often along with a user name, in modern times usually into a computer system To mitigate against the vulnerabilities mentioned above, one can add a salt to the passwords before hashing them. In Cryptography, a salt comprises random Bits that are used as one of the inputs to a Key derivation function. Some implementations may apply the hashing function more than once—see key strengthening. In Cryptography, key strengthening or key stretching refer to techniques used to make a possibly-weak key, typically a Password or Passphrase

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. M_i denotes a 32-bit block of the message input, and K_i denotes a 32-bit constant, different for each operation.

_s denotes a left bit rotation by s places; s varies for each operation. 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 (sixteen 32-bit little endian integers); the message is padded so that its length is divisible by 512. In Cryptography, padding refers to a number of distinct practices 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. In Mathematics, modular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of Arithmetic for Integers Figure 1 illustrates one operation within a round. There are four possible functions F; a different one is used in each round:

denote the XOR, AND, OR and NOT operations respectively. In Logic and/or Mathematics, logical conjunction or and is a two-place Logical operation that results in a value of true if both of In Logic and Mathematics, negation or not is an operation on Logical values for example the logical value of a Proposition

Pseudocode

Pseudocode for the MD5 algorithm follows. Pseudocode is a compact and informal high-level description of a Computer programming Algorithm that uses the structural conventions of some Programming language

//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 h2 := 0x98BADCFE
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[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 := 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 int digest := 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 hashes

The 128-bit (16-byte) MD5 hashes (also termed message digests) are typically represented as a sequence of 32 hexadecimal digits. In Mathematics and Computer science, hexadecimal (also base -, hexa, or hex) is a Numeral system with a 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, due to the avalanche effect. American Standard Code for Information Interchange ( ASCII) " The quick brown fox jumps over the lazy dog " is a Panagram (a Phrase that uses all the letters of the Alphabet) that has been used to test This article is about Cryptography; for other meanings see Snowball effect and Avalanche (disambiguation. For example, changing d to e:

 MD5("The quick brown fox jumps over the lazy eog") 
  = ffd93f16876049265fbaef4da268dd0e

The hash of the zero-length string is:

 MD5("") 
  = d41d8cd98f00b204e9800998ecf8427e

References

• Berson, Thomas A. (1992). "Differential Cryptanalysis Mod 2³² with Applications to MD5". EUROCRYPT: 71–80. ISBN 3-540-56413-6.  
• Bert den Boer; Antoon Bosselaers (1993). Collisions for the Compression Function of MD5, 293–304. ISBN 3-540-57600-2.  
• Hans Dobbertin, Cryptanalysis of MD5 compress. Announcement on Internet, May 1996 [1].
• Dobbertin, Hans (1996). "The Status of MD5 After a Recent Attack". CryptoBytes 2 (2).  
• Xiaoyun Wang; Hongbo Yu (2005). "How to Break MD5 and Other Hash Functions". EUROCRYPT. ISBN 3-540-25910-4.  

See also

• md5deep

External links

• RFC 1321 The MD5 Message-Digest Algorithm
• W3C recommendation on MD5
• Two colliding PostScript files with the same size
• Two colliding executable files
• C, Delphi, Java, JavaScript, Perl, PHP, and Python implementations of MD5
• Online MD5 hash generator
• Filesystem-based MD5 tool
• MD5 Collision Generation

Test Vectors

The NESSIE project test vectors for MD5