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On quasigroups with few associative triples

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Abstract

There are numerous application of quasigroups in cryptology. It turns out that quasigroups with the relatively small number of associative triples can be utilized in designs of hash functions. In this paper we provide both a new lower bound and a new upper bound on the minimum number of associative triples over quasigroups of a given order.

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Authors and Affiliations

  1. Department of Applied Informatics & Information Technology, Slovak University of Technology, 812 19, Bratislava, Slovakia

    Otokar Grošek

  2. Interdisciplinary Arts & Sciences, University of Washington, Tacoma, WA, 98402, USA

    Peter Horák

Authors
  1. Otokar Grošek
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  2. Peter Horák
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Correspondence to Otokar Grošek.

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This is one of several papers published together in Designs, Codes and Cryptography on the special topic: Geometry, Combinatorial Design & Cryptology.

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Grošek, O., Horák, P. On quasigroups with few associative triples. Des. Codes Cryptogr. 64, 221–227 (2012). https://doi.org/10.1007/s10623-010-9482-9

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  • DOI: https://doi.org/10.1007/s10623-010-9482-9

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