Key Recycling in Authentication
In their paper on authentication, Wegman and Carter propose that to authenticate multiple messages, it is sufficient to reuse the same hash function as long as each tag is encrypted with a one-time pad. They argue that because the one-time pad is perfectly hiding, the hash function used remains completely unknown to the adversary. Since their proof is not composable, the authors revisit it using a universally composable framework. It turns out that the above argument is insufficient: information about the hash function is in fact leaked in every round to the adversary, and after a bounded finite amount of rounds it is completely known.