Security of cryptographic hash functions: Difference between revisions

Revision as of 16:00, 28 June 2010

Revision as of 10:58, 12 September 2010

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* [[Fast Syndrome Based Hash|FSB - Fast Syndrome-Based hash function]] - it can be proven that breaking FSB is at least as difficult as solving a certain NP-complete problem known as Regular Syndrome Decoding.

* [[SWIFFT]] - SWIFFT is based on the [[Fast Fourier transform]] and is provably collision resistant, under a relatively mild assumption about the worst-case difficulty of finding short vectors in cyclic/ideal [[lattice]]s.

* [[Chaum, van Heijst, Pfitzmann hash function]] - A compression function where finding collisions is as hard as findingsolving athe [[discrete logarithm|discrete logarithm problem]] in a finite group <math>F_{2p+1}</math>.

* [[Knapsack-based hash functions]] - A family of hash functions based on the [[Knapsack problem]].

* [[The Zémor-Tillich hash function]] - A family of hash functions that rely on the arithmetic of the group of matrices [[Special linear group|SL2]]. Finding collisions is at least as difficult as finding factorization of certain elements in this group. This is supposed to be hard, at least [[PSPACE-complete]]. For this hash, an attack was eventually discovered with a time complexity close to <math>2^{n/2}</math>. This beat by far the birthday bound and ideal pre-image complexities which are <math>2^{3n/2}</math> and <math>2^{3n}</math> for the Zémor-Tillich hash function. As the attacks include a birthday search in a reduced set of size <math>2n</math> they indeed do not destroy the idea of provable security of invalidate the scheme but rather suggest that the initial parameters were too small. <ref>{{Citation