Secure Communications over Arbitrarily Varying Wiretap Channels

In this thesis, we consider a class of information protection problems requiring confidentiality (secrecy) from eavesdropping and integrity (reliability) from jamming in an information-theoretic context. For this purpose, we introduce the arbitrarily varying wire-tap channel (AVWTC) model consisting of a family of wiretap channels indexed by some state that is selected by the jammer in an arbitrary and time-varying manner. We study this model for traditional wiretap codes and randomized wiretap codes, and develop insights about the corresponding secrecy capacity and randomized-code secrecy capacity, respectively. We characterize a lower bound on the randomized-code secrecy capacity of the AVWTC that suggests the secrecy is mainly dictated by a worst-case scenario. Additionally, we establish two upper bounds on the randomized-code secrecy capacity that suggest a single bad ``averaged' state can preclude secure communication, while certain superiorities of the legitimate receiver over the eavesdropper in all ``averaged' states result in a positive secrecy capacity. Finally, we prove that the secrecy capacity of the AVWTC is either zero or equal to its randomized-code secrecy capacity. We show that a ``two-layer' wiretap code is appropriate for combatting the two non-colluding jamming and eavesdropping adversaries.