Quantum Authentication of Classical Messages with Perfect Security

In this work we have investigated how quantum resources can improve the security of protocol for authentication of classical messages, introduced by Brassard in 1983. In that protocol, the shared key is the seed of a pseudo-random generator (PRG) and a hash function is used to create the authentication tag of a public message. We have started by showing that a BB84-like encoding of secret bits offers more security than the classical XOR function introduced by Brassard. Furthermore, we established the conditions a general PRG must satisfy for our quantum-enhanced protocol to yield information-theoretical security. Altogether, our proposal represents a twofold improvement: first it offer proven information-theoretical security under somo assumptions on the PRG; secondly, these assumptions are weaker thant the requirements for the PRG in Brassard's protocol. Additionally, our proposal is also more practical in the sense that it requires a shorter key than the classical scheme by using the pseudorandom bits to choose the tag's hash function.