Improving the Security of MACs Via Randomized Message Preprocessing

Hash then encrypt” is a popular approach to message authentication: 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 εq, where q is the number of MACs the adversary can request. As ε is at least 2, the best one can hope for is O(q/2) security. Unfortunately, such small ε is not achieved by simple constructions 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 randomized message preprocessing via a short random salt p, we can use the “hash then encrypt” paradigm with suboptimal “practical” ε-universal hash functions, and still improve its exact security to optimal O(q/2). Specifically, by using at most an O(logL)-bit salt p, one can always regain the optimal exact security O(q/2), even in situations where ε grows polynomially with L. We also give very simple preprocessing maps for the “suboptimal” hash functions used in practice, 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.