Security of cryptographic hash functions: Difference between revisions

Revision as of 09:59, 15 December 2015

Revision as of 23:49, 12 June 2016

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==Cryptographic hash functions==

{{Main article|Cryptographic hash function}}

Most hash functions are built on an ad hoc basis, where the bits of the message are nicely mixed to produce the hash. Various [[bitwise operation]]s (e.g. rotations), [[Modular arithmetic|modular additions]] and [[One-way compression function|compression functions]] are used in iterative mode to ensure high complexity and pseudo-randomness of the output. In this way, the security is very hard to prove and the proof is usually not done. Only a few years ago, one of the most popular hash functions, [[SHA-1]], was shown to be less secure than its length suggested: collisions could be found in only 2⁵¹<ref>http://eprint.iacr.org/2008/469.pdf</ref> tests, rather than the brute-force number of 2⁸⁰.

In other words, most of the hash functions in use nowadays are not provably collision-resistant. These hashes are not based on purely mathematical functions. This approach results generally in more effective hashing functions, but with the risk that a weakness of such a function will be eventually used to find collisions. The famous case is [[MD5]].

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| contribution = Hard and easy Components of Collision Search in the Zémor-Tillich hash function:new Attacks and Reduced Variants with Equivalent Security

| contribution-url = http://www-rocq.inria.fr/secret/Jean-Pierre.Tillich/publications/CTRSA.pdf }}</ref>

* [[Hash functions from Sigma Protocols]] - there exists a general way of constructing a provably secure hash, specifically from any (suitable) [[Proof_of_knowledgeProof of knowledge#Sigma_protocolsSigma protocols|sigma protocol]]. A faster version of [[Very smooth hash|VSH]] (called VSH*) could be obtained in this way.

==References==