Another Look at Tightness

We examine a natural, but non-tight, reductionist security proof for deterministic message authentication code (MAC) schemes in the multi-user setting. If security parameters for the MAC scheme are selected without accounting for the non-tightness in the reduction, then the MAC scheme is shown to provide a level of security that is less than desirable in the multi-user setting. We find similar deficiencies in the security assurances provided by non-tight proofs when we analyze some protocols in the literature including ones for network authentication and aggregate MACs. Our observations call into question the practical value of non-tight reductionist security proofs. We also exhibit attacks on authenticated encryption schemes, disk encryption schemes, and stream ciphers in the multi-user setting.