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A Family of Fast Syndrome Based Cryptographic Hash Functions

Abstract : Recently, some collisions have been exposed for a variety of cryptographic hash functions~\cite{WFLY04} including some of the most widely used today. Many other hash functions using similar constrcutions can however still be considered secure. Nevertheless, this has drawn attention on the need for new hash function designs. In this article is presented a familly of secure hash functions, whose security is directly related to the syndrome decoding problem from the theory of error-correcting codes. Taking into account the analysis by Coron and Joux~\cite{CJ04} based on Wagner's generalized birthday algorithm~\cite{Wag02} we study the asymptotical security of our functions. We demonstrate that this attack is always exponential in terms of the length of the hash value. We also study the work-factor of this attack, along with other attacks from coding theory, for non asymptotic range, i.e.\ for practical values. Accordingly, we propose a few sets of parameters giving a good security and either a faster hashing or a shorter desciption for the function.
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Submitted on : Wednesday, September 2, 2015 - 5:38:04 PM
Last modification on : Friday, February 4, 2022 - 3:08:17 AM
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Daniel Augot, Matthieu Finiasz, Nicolas Sendrier. A Family of Fast Syndrome Based Cryptographic Hash Functions. MYCRYPT 2005 : First International Conference on Cryptology in Malaysia, Sep 2005, Kuala Lumpur, Malaysia. pp.64-83, ⟨10.1007/11554868_6⟩. ⟨inria-00509188v2⟩



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