[Resource Topic] 2006/348: Non-Trivial Black-Box Combiners for Collision-Resistant Hash-Functions don't Exist

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Non-Trivial Black-Box Combiners for Collision-Resistant Hash-Functions don’t Exist

Authors: Krzysztof Pietrzak


A (k,\ell)-robust combiner for collision-resistant hash-functions is a construction which from \ell hash-functions constructs a hash-function which is collision-resistant if at least k of the components are collision-resistant. One trivially gets a (k,\ell)-robust combiner by concatenating the output of any \ell-k+1 of the components, unfortunately this is not very practical as the length of the output of the combiner is quite large. We show that this is unavoidable as no black-box (k,\ell)-robust combiner whose output is significantly shorter than what can be achieved by concatenation exists. This answers a question of Boneh and Boyen (Crypto’06).

ePrint: https://eprint.iacr.org/2006/348

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