We study a keyless authentication problem in a new noisy model, where there is a discrete memoryless channel (DMC) W ₁ from sender Alice to receiver Bob and a DMC W ₂ from adversary Oscar to Bob. In addition, there is an insecure noiseless channel between Alice and Bob. Under this model, we characterize the condition under which an authentication from Alice to Bob is possible. We also construct a secure authentication protocol that has an authentication rate approaching infinity. Finally, we prove that the authentication capacity of a noninteractive authentication over binary symmetric channels is exactly 1. This is an interesting result as Shannon capacity of channel W ₁ is strictly less than 1 while the noiseless channel is completely unreliable.