Abstract
In this paper new families of strongly universal hash functions, or equivalently, authentication codes, are proposed. Their parameters are derived from bounds on exponential sums over finite fields and Galois rings. This is the first time hash families based upon such exponential sums have been considered. Their performance improves the previously best known constructions and they can be made general in their choice of parameters. Furthermore, the constructions are suitable both for hardware and software implementations. The latter is an aspect that is significant and has been considered in several recent papers.
This research was partly done during a visit by the authors to the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, 1996. The first author was supported in part by The Norwegian Research Council under grant numbers 107542/410 and 107623/420. The second author was supported in part by NUTEK under grant number P5892-1.
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Helleseth, T., Johansson, T. (1996). Universal Hash Functions from Exponential Sums over Finite Fields and Galois Rings. In: Koblitz, N. (eds) Advances in Cryptology — CRYPTO ’96. CRYPTO 1996. Lecture Notes in Computer Science, vol 1109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-68697-5_3
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DOI: https://doi.org/10.1007/3-540-68697-5_3
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