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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. However, it has been shown that MD5 is not collision resistant[1]; as such, MD5 is not suitable for applications that rely on this property. An MD5 hash is typically expressed as a 32 digit hexadecimal number.

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VulnerabilityEdit

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. However, if passwords are combined with a salt before the MD5 digest is generated, rainbow tables become much less useful.

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.[2] This technique is rendered ineffective by the use of a salt.

On December 30, 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.[3]. The researchers used a cluster of Sony Playstation 3s at the EPFL in Lausanne, Switzerland.[4] 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.[5]

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 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[6][7][8]. To mitigate against 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 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 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 completely 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.") 
  = e4d909c290d0fb1ca068ffaddf22cbd0

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 July 27, 2008
  2. Steven J. Murdoch: Google as a password cracker, Light Blue Touchpaper Blog Archive, Nov 16, 2007. Retrieved July 27, 2008.
  3. Sotirov, Alexander; Marc Stevens, Jacob Appelbaum, Arjen Lenstra, David Molnar, Dag Arne Osvik, Benne de Weger (2008-12-30). "MD5 considered harmful today". http://www.win.tue.nl/hashclash/rogue-ca/. Retrieved on 2008-12-30. Announced at the 25th Chaos Communication Congress.
  4. "Researchers Use PlayStation Cluster to Forge a Web Skeleton Key". Wired. 2008-12-31. http://blog.wired.com/27bstroke6/2008/12/berlin.html. Retrieved on 2008-12-31.
  5. Callan, Tim (2008-12-31). "This morning's MD5 attack - resolved". Verisign. https://blogs.verisign.com/ssl-blog/2008/12/on_md5_vulnerabilities_and_mit.php. Retrieved on 2008-12-31.
  6. FreeBSD Handbook, Security - DES, Blowfish, MD5, and Crypt[1]
  7. RedHat Linux 8.0 Password Security [2]
  8. Solaris 10 policy.conf(4) man page [3]

ReferencesEdit

  • 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. pp. 293–304. ISBN 3-540-57600-2.
  • Hans Dobbertin, Cryptanalysis of MD5 compress. Announcement on Internet, May 1996 [4].
  • Dobbertin, Hans (1996). "The Status of MD5 After a Recent Attack". CryptoBytes 2 (2). ftp://ftp.rsasecurity.com/pub/cryptobytes/crypto2n2.pdf.
  • Xiaoyun Wang; Hongbo Yu (2005). "How to Break MD5 and Other Hash Functions". EUROCRYPT. ISBN 3-540-25910-4.

External linksEdit

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