对抗干扰信道上的隐蔽通信
Covert Communication over Adversarially Jammed Channels
摘要：
假设发射机Alice潜在地希望通过对抗性干扰的二进制信道与接收机Bob通信。一个活跃的对手詹姆斯窃听他们在二进制对称信道（BSC（q））上的通信，并可能基于他的观察恶意地翻转（高达）他们发送的比特的某个分数p。我们考虑一种通信必须同时隐蔽和可靠的设置，即，詹姆斯应该无法准确区分爱丽丝是否在通信，而鲍勃应该能够正确地恢复爱丽丝的消息，无论对抗性干扰策略如何。我们表明，与被动的对手，隐蔽通信对主动对手的设置需要爱丽丝和鲍勃有一个共享的密钥（长度至少欧米茄（log n）），即使鲍勃有一个更好的通道比詹姆斯。我们提出的信息理论上的最佳吞吐量的信道参数的函数，所需的隐蔽性水平，和可用的共享密钥的量的上下界。这些界限与广泛的感兴趣参数相匹配。我们还开发了一个计算效率高的编码方案（级联码的基础上）时，可用的共享密钥的量是$Ω(\sqrt{n} \log n)$，并进一步表明，该方案可以实现更少的共享密钥量时，假设对手是计算上有界的。
英文摘要：
Suppose that a transmitter Alice potentially wishes to communicate with a receiver Bob over an adversarially jammed binary channel. An active adversary James eavesdrops on their communication over a binary symmetric channel (BSC(q)), and may maliciously flip (up to) a certain fraction p of their transmitted bits based on his observations. We consider a setting where the communication must be simultaneously covert as well as reliable, i.e., James should be unable to accurately distinguish whether or not Alice is communicating, while Bob should be able to correctly recover Alice's message with high probability regardless of the adversarial jamming strategy. We show that, unlike the setting with passive adversaries, covert communication against active adversaries requires Alice and Bob to have a shared key (of length at least Omega(log n)) even when Bob has a better channel than James. We present lower and upper bounds on the information-theoretically optimal throughput as a function of the channel parameters, the desired level of covertness, and the amount of shared key available. These bounds match for a wide range of parameters of interest. We also develop a computationally efficient coding scheme (based on concatenated codes) when the amount of shared key available is $Ω(\sqrt{n} \log n)$, and further show that this scheme can be implemented with much less amount of shared key when the adversary is assumed to be computationally bounded.
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