CRYPTO '93 Proceedings of the 13th annual international cryptology conference on Advances in cryptology
Optimal linear perfect hash families
Journal of Combinatorial Theory Series A
Perfect hash families: probabilistic methods and explicit constructions
Journal of Combinatorial Theory Series A
Explicit constructions of perfect hash families from algebraic curves over finite fields
Journal of Combinatorial Theory Series A
Efficient multiplicative sharing schemes
EUROCRYPT'96 Proceedings of the 15th annual international conference on Theory and application of cryptographic techniques
Explicit constructions for perfect hash families
Designs, Codes and Cryptography
Linear hash families and forbidden configurations
Designs, Codes and Cryptography
Geometric constructions of optimal linear perfect hash families
Finite Fields and Their Applications
| Hi-index | 0.00 |
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 set $$S=\{\phi_1,\ldots,\phi_s\}$$ of linear functionals from V to F with the following property: for all t subsets $$X\subseteq V$$ there exists $$\phi_i\in S$$ such that $$\phi_i$$ is injective when restricted to F. A linear (q d , q, t)-perfect hash family of minimal size d(t 驴 1) is said to be optimal. In this paper, we extend the theory for linear perfect hash families based on sequences developed by Blackburn and Wild. We develop techniques which we use to construct new optimal linear (q 2, q, 5)-perfect hash families and (q 4, q, 3)-perfect hash families. The sequence approach also explains a relationship between linear (q 3, q, 3)-perfect hash families and linear (q 2, q, 4)-perfect hash families.