Xin Wei, Separating hash families with large universe
Separating hash families are useful combinatorial structures that generalize several well-studied objects in cryptography and coding theory. Let $p_t(N, q)$ denote the maximum size of the universe for a $t$-perfect hash family of length $N$ over an alphabet of size $q$. We show that $q^{2 - o(1)} < p_t(t, q) = o(q^2)$ for all $t …