On the Adaptive Security of MACs and PRFs

Andrew Morgan, Rafael Pass, Elaine Shi

Abstract: We consider the security of two of the most commonly used cryptographic primitives—message authentication codes (MACs) and pseudorandom functions (PRFs)—in a multi-user setting with adaptive corruption. Whereas is it well known that any secure MAC or PRF is also multi-user secure under adaptive corruption, the trivial reduction induces a security loss that is linear in the number of users. Our main result shows that black-box reductions from “standard” assumptions cannot be used to provide a tight, or even a linear-preserving, security reduction for adaptive multi-user secure deterministic stateless MACs and thus also PRFs. In other words, a security loss that grows with the number of users is necessary for any such black-box reduction.