Improving the Security of MACs via Randomized Message Preprocessing

Abstract. “Hash then encrypt ” is an approach to message authentica-tion, where first the message is hashed down using an ε-universal hash function, and then the resulting k-bit value is encrypted, say with a block-cipher. The security of this scheme is proportional to εq2, where q is the number of MACs the adversary can request. As ε is at least 2−k, the best one can hope for is O(q2/2k) security. Unfortunately, such small ε is not achieved by simple hash functions used in practice, such as the polynomial evaluation or the Merkle-Damg̊ard construction, where ε grows with the message length L. The main insight of this work comes from the fact that, by using random-ized message preprocessing via a short random salt p (which must then be sent as part of the authentication tag), we can use the “hash then encrypt ” paradigm with suboptimal “practical ” ε-universal hash func-tions, and still improve its exact security to optimal O(q2/2k). Specif-ically, by using at most an O(logL)-bit salt p, one can always regain the optimal exact security O(q2/2k), even in situations where ε grows polynomially with L. We also give very simple preprocessing maps for popular “suboptimal ” hash functions, namely polynomial evaluation and the Merkle-Damg̊ard construction. Our results come from a general extension of the classical Carter-Wegman paradigm, which we believe is of independent interest. On a high level, it shows that public randomization allows one to use the potentially much smaller “average-case ” collision probability in place of the “worst-case” collision probability ε.