We consider keyless authentication for point-to-point communication in the presence of a myopic adversary. In particular, the adversary has access to a non-causal noisy version of the transmission and uses this knowledge to choose the state of an arbitrarily-varying channel between legitimate users. The receiver succeeds by either decoding accurately or correctly detecting adversarial interference. We introduce a single-letter channel condition called $U$-distribution overwritability, and show that as long as the channel does not satisfy this condition, the authentication capacity with stochastic coding is positive and equals the no-adversary channel capacity. Our encoding scheme relies on authentication tags that allow verifying the correctness of a message that has already been received. We provide multi-letter extensions of $U$-distribution overwritability and show that the infinite letter limit yields exact characterization for positivity of authentication capacity. Noting that this characterization may, in general, be uncomputable, we next provide a single-letter channel condition called $U$-overwritability and show that it is a sufficient condition for zero authentication capacity. When restricted to deterministic codes, we show that when the channel is not $I$-overwritable, the authentication capacity is strictly positive. Further, when the channel to the legitimate receiver is degraded with respect to the channel to the adversary, $I$-overwritability is also a sufficient condition for the deterministic authentication capacity to equal zero. Lastly, we give examples demonstrating that the various notions of overwritability presented in this paper differ from each other. Our results also show that stochastic encoders are necessary for positive authentication capacity in some cases. Illustrating this, we examine in detail a binary adversarial channel that illustrates this necessity.

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