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We are not sure whether MD5 has fixed point or not. But since the sample space is finite, it must have cycles:

$$ A →(MD5)→ B →(MD5)→ C →(MD5)→ D →(MD5)→ A $$

Has any research been done on MD5 to find cycles?

What caused I think about it is that if S is the sample space and R1 the range of MD5(once or taken in any number) them R1⊆S also R2⊆R1

MD5(one or multiple): S → R1

MD5(one or multiple): R1 → R2

...

Willie Wong
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gerrnar
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  • This is not called a ring, but a cycle. – Yoni Rozenshein Jun 18 '13 at 11:45
  • @YoniRozenshein thanks I modified. please help in me tagging too if there is any mistake – gerrnar Jun 18 '13 at 11:55
  • There was a distributed computing project to find MD5 cycles, but it was abandoned once a general-purpose collision algorithm was demonstrated in 2004. – Foo Barrigno Jun 18 '13 at 12:24
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    Related info: http://security.stackexchange.com/questions/26043/how-big-is-the-risk-of-hash-fixed-points-cycles http://elliottkember.com/kember_identity.html – leonbloy Jun 18 '13 at 12:42
  • thank. I was using wrong keyword so I could not find the answer on web. please post solutions as answer to close this thread. – gerrnar Jun 18 '13 at 15:54

1 Answers1

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Not yet*.

The only major project to try to find a cycle shut down in 2004 once a general collision vulnerability was found, due to the fact that a latter is a much more severe vulnerability.

I was unable to find anything other than that Wikipedia article and this very thread on the topic. (There is a group that looked into ways to improve the internal state's cycle length, to help engineer future editions or hash functions to be more robust; however, this is unrelated to cycles of the digest itself when feeding the digest back into the function wholesale.)

*Do you want to find one?

To get a cycle for MD5 would require nowhere near as much power as breaking it.

Wikipedian Taxman estimated in 2004 that it would take a 12.25-Teraflops supercomputing cluster about 1.77Ms (i.e. just under 3 weeks) to find a cycle. These days, an arbitrary provider, Nimbix, could allegedly provide this [if my math is correct] on the order of 1 business day and $800.

JamesTheAwesomeDude
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