We consider the problem of authenticated communication over a discrete arbitrarily varying channel where the legitimate parties are unaware of whether or not an adversary is present. When there is no adversary, the channel state always takes a default value $s_0$. When the adversary is present, they may choose the channel state sequence based on a non-causal noisy view of the transmitted codewords and the encoding and decoding scheme. We require that the decoder output the correct message with a high probability when there is no adversary, and either output the correct message or reject the transmission when the adversary is present. Further, we allow the transmitter to employ private randomness during encoding that is known neither to the receiver nor the adversary. Our first result proves a dichotomy property for the capacity for this problem -- the capacity either equals zero or it equals the non-adversarial capacity of the channel. Next, we give a sufficient condition for the capacity for this problem to be positive even when the non-adversarial channel to the receiver is stochastically degraded with respect to the channel to the adversary. Our proofs rely on a connection to a standalone authentication problem, where the goal is to accept or reject a candidate message that is already available to the decoder. Finally, we give examples and compare our sufficient condition with other related conditions known in the literature

翻译：我们考虑在离散任意变化信道上的认证通信问题，其中合法通信方无法知道对手是否存在。当没有对手时，信道状态始终取默认值$s_0$。当对手存在时，他们可以根据非因果的、包含噪声的传输码字观测以及编解码方案来选择信道状态序列。我们要求：在没有对手时，解码器以高概率输出正确消息；当对手存在时，解码器要么输出正确消息，要么拒绝传输。此外，我们允许发射机在编码过程中使用私有随机性，这些随机性既不被接收机也不被对手所知。我们的第一个结果证明了该问题容量的二分性质——容量要么为零，要么等于信道的非对抗容量。其次，我们给出了一个充分条件，使得即使到接收机的非对抗信道相对于到对手的信道在随机退化意义上更差时，该问题的容量仍为正数。我们的证明依赖于与一个独立认证问题的关联，在该问题中目标是接受或拒绝解码器已获得的候选消息。最后，我们给出示例，并将我们的充分条件与文献中已知的其他相关条件进行比较。