Arbitrarily Varying Wiretap Channels With Non-Causal Side Information at the Jammer

Abstract

Secure communication in a potentially hostile environment is becoming more and more critical. The <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</b> rbitrarily <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">V</b> arying <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">W</b> iretap <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> hannel (AVWC) provides information-theoretical bounds on how much information can be exchanged even in the presence of an active attacker. If the active attacker has non-causal side information, situations in which a legitimate communication system has been hacked can be modeled. We investigate the AVWC with non-causal side information at the jammer for the case that there exists a best channel to the eavesdropper. Non-causal side information means that the transmitted codeword is known to an active adversary before it is transmitted. By considering the maximum error criterion, we also allow messages to be known at the jammer before the corresponding codeword is transmitted. A single-letter formula for the <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</b> ommon <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</b> andomness (CR)-assisted secrecy capacity is derived. Additionally, we provide a formula for the CR-assisted secrecy capacity for the cases where the channel to the eavesdropper is strongly degraded, strongly noisier, or strongly less capable with respect to the main channel. Furthermore, we compare our results to the CR-assisted secrecy capacity for the cases of maximum error criterion but without non-causal side information at the jammer (blind adversary), maximum error criterion with non-causal side information of the messages at the jammer (semi-blind adversary), and the case of average error criterion without non-causal side information at the jammer (blind adversary).