A tight bound on the size of certain separating hash families

TL;DR

This paper establishes a new tight lower bound on the size of certain separating hash families, extending previous work and providing constructions that meet this bound, thereby advancing understanding of hash family bounds.

Contribution

The paper introduces a novel lower bound for separating hash families of specific types and demonstrates its tightness through explicit constructions.

Findings

New lower bound on hash family size

Bound is tight with explicit constructions

Improves bounds for strong separating hash families

Abstract

In this paper, we present a new lower bound on the size of separating hash families of type {w_1^{q-1},w_2} where w_1 < w_2. Our result extends the paper by Guo et al. on binary frameproof codes. This bound compares well against known general bounds, and is especially useful when trying to bound the size of strong separating hash families. We also show that our new bound is tight by constructing hash families that meet the new bound with equality.