User authentication (UA) supports the receiver in deciding whether a message comes from the claimed transmitter or from an impersonating attacker. In cryptographic approaches messages are signed with either an asymmetric or symmetric key, and a source of randomness is required to generate the key. In physical layer authentication (PLA) instead the receiver checks if received messages presumably coming from the same source undergo the same channel. We compare these solutions by considering the physical-layer channel features as randomness source for generating the key, thus allowing an immediate comparison with PLA (that already uses these features). For the symmetric-key approach we use secret key agreement, while for asymmetric-key the channel is used as entropy source at the transmitter. We focus on the asymptotic case of an infinite number of independent and identically distributed channel realizations, showing the correctness of all schemes and analyzing the secure authentication rate, that dictates the rate at which the probability that UA security is broken goes to zero as the number of used channel resources (to generate the key or for PLA) goes to infinity. Both passive and active attacks are considered and by numerical results we compare the various systems.