ε-Almost Collision-Flat Universal Hash Functions Motivated by Information-Theoretic Security

ε-Almost Collision-Flat Universal (ACFU) hash functions are defined and analyzed. They are motivated by their use in achieving information-theoretic key indistinguishability in privacy amplification. Lower bounds for the size of the seed set are given. A general method is presented by which to construct an ε-ACFU hash function from any ε-almost universal hash function. Several examples are studied. In particular, it turns out that all security functions known so far which achieve key indistinguishability universally are ε-ACFU hash functions.