Work

Separating hash families with large universe

Year: 2025

Type: article

Abstract: Separating hash families are useful combinatorial structures which generalize several well-studied objects in cryptography and coding theory. Let p t ( N , q ) denote the maximum size of universe for a t -perfect hash family of length N over an alphabet of size q . In this paper, we show that q 2 − o ( 1 ) < p t ( t , q ) = o ( q 2 ) for all t ≥ 3 , which answers an open problem about separating hash families raised by Blackburn et al. in 2008 for certain parameters. Previously, this result was known only for t = 3 , 4 . Our proof is obtained by establishing the existence of a large set of integers avoiding nontrivial solutions to a set of correlated linear equations.

Source: Journal of Combinatorial Theory Series A

DOI: 10.1016/j.jcta.2025.106075

Authors: Xin Wei, Xiande Zhang, Gennian Ge

Institutions: University of Science and Technology of China, Capital Normal University

Language: English

Topic: Coding theory and cryptography

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,210

Funders: Capital Normal University, National Natural Science Foundation of China, National Key Research and Development Program of China, Division of Mathematical Sciences