Keyless Authentication and Authenticated Capacity

We consider the problem of keyless message authentication over noisy channels in the presence of an active adversary. Different from the existing models, in our model, the legitimate users do not have any pre-shared key for authentication. Instead, we use the noisy channel connecting the legitimate users for authentication. The main idea is to utilize the noisy channel connecting the legitimate users to generate an output at the receiver that is difficult for the adversary to replicate through his noisy channel, and then use this output to distinguish legitimate messages from fake messages. By interpreting the message authentication as a hypothesis testing problem, we investigate the authentication exponent and authenticated channel capacity of a noisy channel. In the authentication exponent problem, for a given message rate, we investigate the speed at which the optimal successful attack probability can be driven to zero. We fully characterize the authentication exponent for the zero-rate message case and a broad class of non-zero message rate cases. In the authenticated capacity problem, we study the largest data transmission rate under which the attacker’s optimal successful attack probability can still be made arbitrarily small. We establish an all or nothing result. In particular, we show that the authenticated channel capacity is the same as the classic channel capacity, if a simulatability condition is not satisfied, while the authenticated capacity will be zero if this condition is satisfied. We also provide efficient algorithms to check this condition. We further show that our results are robust to modelling uncertainties in the eavesdropper’s channels.