Cryptology ePrint Archive: Report 2006/348

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

Krzysztof Pietrzak

Abstract: 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).

Category / Keywords: foundations / hash functions, combiners

Date: received 16 Oct 2006

Contact author: pietrzak at di ens fr

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Version: 20061020:101039 (All versions of this report)

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