带因果对手的任意可变信道上的认证
Authentication over Arbitrarily Varying Channels with Causal Adversaries
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中文总结 AI 辅助
该研究针对带因果对手的离散无记忆任意可变信道，证明其认证容量正性条件，提出“等待-覆盖”攻击，构造正码率码并结合鞅论证，区分不同对手场景的认证容量特性。
中文摘要 AI 辅助
我们研究离散无记忆任意可变信道（AVC）上的认证问题，其中对手基于过往信道输出因果地选择信道状态。我们证明，仅当信道在随机编码下不具备分布可覆盖性、且在确定性编码下不具备I-可覆盖性时，认证容量为正。在随机编码场景中，只要认证容量为正，其就等于无对手时的香农容量。两个反向结果均源于一种新颖的“等待-覆盖”攻击：对手通过后验猜测概率跟踪消息的无对手后验分布，一旦该分布集中至某一阈值，便从后验分布中采样一个猜测值和一个诱饵，并覆盖信道以模拟诱饵的无对手传输。正性结果通过构造码间重叠受控制的正码率码，结合处理自适应对手策略的鞅集中论证得到。对于随机编码，全容量可达性进一步结合了容量可达信道码与认证标签。这些刻画将因果随机编码、因果确定性编码场景，与Kosut和Kliewer研究的无感知对手场景区分开来。
英文摘要
We study authentication over a discrete memoryless arbitrarily varying channel (AVC) in which the adversary selects the channel state causally based on past channel outputs. We prove that the authentication capacity is positive exactly when the channel is not distribution-overwritable under stochastic encoding, and not I-overwritable under deterministic encoding. In the stochastic case, whenever the authentication capacity is positive, it coincides with the no-adversary Shannon capacity. Both converses follow from a novel wait-and-overwrite attack: the adversary tracks the no-adversary posterior over the message via the posterior guessing probability, and once it concentrates past a threshold, it samples a guess and a decoy from the posterior and overwrites the channel to mimic a no-adversary transmission of the decoy. The positivity results are obtained by constructing positive-rate codes with controlled overlap between codewords, together with a martingale concentration argument that handles adaptive adversarial strategies. For stochastic encoding, the full-capacity achievability further combines a capacity-achieving channel code with an authentication tag. These characterizations separate the causal stochastic-code and causal deterministic-code settings from each other and from the oblivious-adversary setting studied by Kosut and Kliewer.
