A Family of Fast Syndrome Based Cryptographic Hash Functions

Daniel Augot, Matthieu Finiasz and Nicolas Sendrier

INRIA-projet Codes and EPFL-Lausanne (Swizerland)


Proceedings of International Conference on Cryptology in Malaysia (Mycrypt 2005).
LNCS 3715, pp. 64-83, 2005, Springer-Verlag..


Recently, some collisions have been exposed for a variety of cryptographic hash functions, including some of the most widely used today. Many other hash functions using similar constructions 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 family 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 based on Wagner's generalized birthday algorithm, 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 description for the function.