Covert communication: From classical channels to quantum channels
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The objective of this dissertation is to study covert communications over classical and quantum channels. In contrast to the well-studied notion of secrecy, in which one attempts to protect the content of information, covertness constraint requires that the communication remains undetectable from an unwanted party warden. A fundamental result states that the optimal number of transmitted bits scale as square root of the number of channel uses when covertness is achieved. Many standard information-theoretic tools therefore fail in this zero-rate regime and one has to resort to finite-length analysis of a protocol. In the first half of this dissertation, we establish results pertaining the fundamental limits of covert communication over classical channels. In the second half of this dissertation, we investigate the fundamental limits of covert secret key generation, in which two parties attempt to generate a secret key by using a classical or quantum channel and a public authenticated channel.