Geometric constructions of optimal linear perfect hash families

Authors:
S. G. Barwick;Wen-Ai Jackson
Affiliations:
School of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia;School of Pure Mathematics, University of Adelaide, Adelaide 5005, Australia
Venue:
Finite Fields and Their Applications
Year:
2008

Citing 6
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Broadcast encryption

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Optimal linear perfect hash families

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A sequence approach to linear perfect hash families

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EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques

Linear hash families and forbidden configurations

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Abstract

A linear (q^d,q,t)-perfect hash family of size s in a vector space V of order q^d over a field F of order q consists of a sequence @f"1,...,@f"s of linear functions from V to F with the following property: for all t subsets X@?V there exists i@?{1,...,s} such that @f"i is injective when restricted to F. A linear (q^d,q,t)-perfect hash family of minimal size d(t-1) is said to be optimal. In this paper we use projective geometry techniques to completely determine the values of q for which optimal linear (q^3,q,3)-perfect hash families exist and give constructions in these cases. We also give constructions of optimal linear (q^2,q,5)-perfect hash families.