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Md5

eg{D})

\oplus, \wedge, \vee, \neg denote the XOR, AND, OR and NOT operations respectively.


Pseudocode

The MD5 hash is calculated according to this algorithm. All values are in little-endian.

//Note: All variables are unsigned 32 bit and wrap modulo 2^32 when calculating
var int[64] s, K

//s specifies the per-round shift amounts
s[ 0..15] := { 7, 12, 17, 22,  7, 12, 17, 22,  7, 12, 17, 22,  7, 12, 17, 22 }
s[16..31] := { 5,  9, 14, 20,  5,  9, 14, 20,  5,  9, 14, 20,  5,  9, 14, 20 }
s[32..47] := { 4, 11, 16, 23,  4, 11, 16, 23,  4, 11, 16, 23,  4, 11, 16, 23 }
s[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))
end for
//(Or just use the following table):
K[ 0.. 3] := { 0xd76aa478, 0xe8c7b756, 0x242070db, 0xc1bdceee }
K[ 4.. 7] := { 0xf57c0faf, 0x4787c62a, 0xa8304613, 0xfd469501 }
K[ 8..11] := { 0x698098d8, 0x8b44f7af, 0xffff5bb1, 0x895cd7be }
K[12..15] := { 0x6b901122, 0xfd987193, 0xa679438e, 0x49b40821 }
K[16..19] := { 0xf61e2562, 0xc040b340, 0x265e5a51, 0xe9b6c7aa }
K[20..23] := { 0xd62f105d, 0x02441453, 0xd8a1e681, 0xe7d3fbc8 }
K[24..27] := { 0x21e1cde6, 0xc33707d6, 0xf4d50d87, 0x455a14ed }
K[28..31] := { 0xa9e3e905, 0xfcefa3f8, 0x676f02d9, 0x8d2a4c8a }
K[32..35] := { 0xfffa3942, 0x8771f681, 0x6d9d6122, 0xfde5380c }
K[36..39] := { 0xa4beea44, 0x4bdecfa9, 0xf6bb4b60, 0xbebfbc70 }
K[40..43] := { 0x289b7ec6, 0xeaa127fa, 0xd4ef3085, 0x04881d05 }
K[44..47] := { 0xd9d4d039, 0xe6db99e5, 0x1fa27cf8, 0xc4ac5665 }
K[48..51] := { 0xf4292244, 0x432aff97, 0xab9423a7, 0xfc93a039 }
K[52..55] := { 0x655b59c3, 0x8f0ccc92, 0xffeff47d, 0x85845dd1 }
K[56..59] := { 0x6fa87e4f, 0xfe2ce6e0, 0xa3014314, 0x4e0811a1 }
K[60..63] := { 0xf7537e82, 0xbd3af235, 0x2ad7d2bb, 0xeb86d391 }

//Initialize variables:
var int a0 := 0x67452301   //A
var int b0 := 0xefcdab89   //B
var int c0 := 0x98badcfe   //C
var int d0 := 0x10325476   //D

//Pre-processing: adding a single 1 bit
append "1" bit to message    /* Notice: the input bytes are considered as bits strings,
  where the first bit is the most significant bit of the byte.[47]
  

//Pre-processing: padding with zeros
append "0" bit until message length in bits ≡ 448 (mod 512)
append original length in bits mod (2 pow 64) to message


//Process the message in successive 512-bit chunks:
for each 512-bit chunk of message
    break chunk into sixteen 32-bit words M[j], 0 ≤ j ≤ 15
//Initialize hash value for this chunk:
    var int A := a0
    var int B := b0
    var int C := c0
    var int D := d0
//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
        dTemp := D
        D := C
        C := B
        B := B + leftrotate((A + F + K[i] + M[g]), s[i])
        A := dTemp
    end for
//Add this chunk's hash to result so far:
    a0 := a0 + A
    b0 := b0 + B
    c0 := c0 + C
    d0 := d0 + D
end for

var char digest[16] := a0 append b0 append c0 append d0 //(Output is in little-endian)

//leftrotate function definition
leftrotate (x, c)
    return (x << c) binary 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. 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.") = 
e4d909c290d0fb1ca068ffaddf22cbd0

The hash of the zero-length string is:

MD5("") = 
d41d8cd98f00b204e9800998ecf8427e

The MD5 algorithm is specified for messages consisting of any number of bits; it is not limited to multiples of eight bit (octets, bytes) as shown in the examples above. Some MD5 implementations such as md5sum might be limited to octets, or they might not support streaming for messages of an initially undetermined length

See also

Notes

  1. ^ RFC 1321, section 3.4, "Step 4. Process Message in 16-Word Blocks", page 5.
  2. ^ Xie Tao, Fanbao Liu, and Dengguo Feng (2013). "Fast Collision Attack on MD5.". 
  3. ^ Ciampa, Mark (2009). CompTIA Security+ 2008 in depth. Australia ; United States: Course Technology/Cengage Learning. p. 290. 
  4. ^ Hans Dobbertin (Summer 1996). "The Status of MD5 After a Recent Attack". CryptoBytes 2 (2). Retrieved 22 October 2013. 
  5. ^ Xiaoyun Wang and Hongbo Yu (2005). "How to Break MD5 and Other Hash Functions". Advances in Cryptology – Lecture Notes in Computer Science 3494. pp. 19–35. Retrieved 21 December 2009. 
  6. ^ Xiaoyun Wang, Dengguo ,k.,m.,m, HAVAL-128 and RIPEMD, Cryptology ePrint Archive Report 2004/199, 16 August 2004, revised 17 August 2004. Retrieved 27 July 2008.
  7. ^ a b J. Black, M. Cochran, T. Highland: A Study of the MD5 Attacks: Insights and Improvements, 3 March 2006. Retrieved 27 July 2008.
  8. ^ Marc Stevens, Arjen Lenstra, Benne de Weger: Vulnerability of software integrity and code signing applications to chosen-prefix collisions for MD5, 30 November 2007. Retrieved 27 July 2008.
  9. ^ a b c d e Announced at the 25th Chaos Communication Congress.
  10. ^
  11. ^ "CERT Vulnerability Note VU#836068". Kb.cert.org. Retrieved 9 August 2010. 
  12. ^ "NIST.gov — Computer Security Division — Computer Security Resource Center". Csrc.nist.gov. Retrieved 9 August 2010. 
  13. ^ Philip Hawkes and Michael Paddon and Gregory G. Rose: Musings on the Wang et al. MD5 Collision, 13 October 2004. Retrieved 27 July 2008.
  14. ^ Bishop Fox (26 September 2013). "Fast MD5 and MD4 Collision Generators". Retrieved 10 February 2014. Faster implementation of techniques in How to Break MD5 and Other Hash Functions, by Xiaoyun Wang, et al. Old (2006) average run time on IBM P690 supercomputer: 1 hour. New average run time on P4 1.6ghz PC: 45 minutes. 
  15. ^ 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 27 July 2008.
  16. ^ Vlastimil Klima: Finding MD5 Collisions – a Toy For a Notebook, Cryptology ePrint Archive Report 2005/075, 5 March 2005, revised 8 March 2005. Retrieved 27 July 2008.
  17. ^ 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 27 July 2008.
  18. ^ "MD5 test suite". 17 January 2013. Retrieved 10 February 2014. 
  19. ^ "Code Cracked! Cyber Command Logo Mystery Solved".  
  20. ^ Tao Xie, Dengguo Feng (2010). "Construct MD5 Collisions Using Just A Single Block Of Message" (PDF). Retrieved 28 July 2011. 
  21. ^ "Marc Stevens – Research – Single-block collision attack on MD5". Marc-stevens.nl. 2012. Retrieved 10 April 2014. 
  22. ^ "RFC 6151 – Updated Security Considerations for the MD5 Message-Digest and the HMAC-MD5 Algorithms". Internet Engineering Task Force. March 2011. Retrieved 11 November 2013. 
  23. ^ "RFC 1321 – The MD5 Message-Digest Algorithm". Internet Engineering Task Force. April 1992. Retrieved 5 October 2013. 
  24. ^ "RFC 2104 – HMAC: Keyed-Hashing for Message Authentication". Internet Engineering Task Force. February 1997. Retrieved 5 October 2013. 
  25. ^ M.M.J. Stevens (June 2007). "On Collisions for MD5". [...] we are able to find collisions for MD5 in about 224.1 compressions for recommended IHV's which takes approx. 6 seconds on a 2.6GHz Pentium 4. 
  26. ^ Marc Stevens, Arjen Lenstra, Benne de Weger (16 June 2009). "Chosen-prefix Collisions for MD5 and Applications". 
  27. ^ "New GPU MD5 cracker cracks more than 200 million hashes per second..". 
  28. ^
  29. ^ Max Gebhardt, Georg Illies, Werner Schindler. "A Note on the Practical Value of Single Hash Collisions for Special File Formats". 
  30. ^ Dobbertin, Hans (Summer 1996). "The Status of MD5 After a Recent Attack" (PDF). RSA Laboratories CryptoBytes 2 (2): 1. Retrieved 10 August 2010. The presented attack does not yet threaten practical applications of MD5, but it comes rather close. .... [ 
  31. ^ "Schneier on Security: More MD5 Collisions". Schneier.com. Retrieved 9 August 2010. 
  32. ^ "Colliding X.509 Certificates". Win.tue.nl. Retrieved 9 August 2010. 
  33. ^ "[Python-Dev] hashlib — faster md5/sha, adds sha256/512 support". Mail.python.org. Retrieved 9 August 2010. 
  34. ^ "Researchers Use PlayStation Cluster to Forge a Web Skeleton Key". Wired. 31 December 2008. Retrieved 31 December 2008. 
  35. ^ Callan, Tim (31 December 2008). "This morning's MD5 attack — resolved". Verisign. Retrieved 31 December 2008. 
  36. ^ Bruce Schneier (31 December 2008). "Forging SSL Certificates". Schneier on Security. Retrieved 10 April 2014. 
  37. ^ "Flame malware collision attack explained". 
  38. ^ Eric Rescorla (17 August 2004). "A real MD5 collision". Educated Guesswork (blog). 
  39. ^ Anton A. Kuznetsov. "An algorithm for MD5 single-block collision attack using highperformance computing cluster". IACR. Retrieved 2014-11-03. 
  40. ^ Yu Sasaki, Kazumaro Aoki (16 April 2009). "Finding Preimages in Full MD5 Faster Than Exhaustive Search".  
  41. ^ Ming Mao and Shaohui Chen and Jin Xu (2009). "Construction of the Initial Structure for Preimage Attack of MD5". International Conference on Computational Intelligence and Security ( 
  42. ^ Steven J. Murdoch: Google as a password cracker, Light Blue Touchpaper Blog Archive, 16 November 2007. Retrieved 27 July 2008.
  43. ^ "Availability and description of the File Checksum Integrity Verifier utility". Microsoft Support. 17 June 2013. Retrieved 10 April 2014. 
  44. ^ "How to compute the MD5 or SHA-1 cryptographic hash values for a file". Microsoft Support. 23 January 2007. Retrieved 10 April 2014. 
  45. ^
  46. ^ "Synopsis – man pages section 4: File Formats". Docs.oracle.com. 1 January 2013. Retrieved 10 April 2014. 
  47. ^ RFC 1321, section 2, "Terminology and Notation", Page 2.

References

  • Berson, Thomas A. (1992). "EUROCRYPT". pp. 71–80.  
  • Bert den Boer; Antoon Bosselaers (1993). "Collisions for the Compression Function of MD5". EUROCRYPT. Berlin; London: Springer. pp. 293–304.  
  • Hans Dobbertin, Cryptanalysis of MD5 compress. Announcement on Internet, May 1996. "CiteSeerX". Citeseer.ist.psu.edu. Retrieved 9 August 2010. 
  • Dobbertin, Hans (1996). "The Status of MD5 After a Recent Attack". CryptoBytes 2 (2). 
  • Xiaoyun Wang; Hongbo Yu (2005). "EUROCRYPT".  

External links

  • W3C recommendation on MD5
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