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MD5CRK : ウィキペディア英語版
MD5CRK
In cryptography, MD5CRK was a distributed effort (similar to distributed.net) launched by Jean-Luc Cooke and his company, (CertainKey Cryptosystems ), to demonstrate that the MD5 message digest algorithm is insecure by finding a collision — two messages that produce the same MD5 hash. The project went live on March 1, 2004. The project ended on August 24, 2004 after researchers independently demonstrated a technique for generating collisions in MD5 using analytical methods by Xiaoyun Wang, Feng, Xuejia Lai, and Yu(). (CertainKey ) awarded a 10,000 Canadian Dollar (prize to Wang, Feng, Lai and Yu ) for their discovery.
A technique called Floyd's cycle-finding algorithm was used to try to find a collision for MD5. The algorithm can be described by analogy with a random walk. Using the principle that any function with a finite number of possible outputs placed in a feedback loop will cycle, one can use a relatively small amount of memory to store outputs with particular structures and use them as "markers" to better detect when a marker has been "passed" before. These markers are called ''distinguished points'', the point where two inputs produce the same output is called a ''collision point''. MD5CRK considered any point whose first 32 bits were zeroes to be a distinguished point.
==Complexity==
The expected time to find a collision is not equal to 2^ where N is the number of bits in the digest output. It is in fact 2^N! \over , where K is the number of function outputs collected.
For this project, the probability of success after K MD5 computations can be approximated by: 1 \over }.
The expected number of computations required to produce a collision in the 128-bit MD5 message digest function is thus: }
To give some perspective to this, using (Virginia Tech's System X ) with a max performance of 12.25 Teraflops, it would take approximately \approx 1,770,000} seconds or about 3 weeks. Or for commodity processors at 2 gigaflops it would take 6,000 machines approximately the same amount of time.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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