Arbitrarily varying wiretap channels with type constrained states

Z. Goldfeld, P. Cuff, and H. H. Permuter

In Proceedings of the 2016 IEEE GLOBECOM Workshop on Physical Layer Security, Washington DC, WA, USA, December 2016, and in IEEE Transactions on Information Theory, vol. 62, no. 12, pp. 7216-7244, December 2016.

—The arbitrarily varying wiretap channel (AVWTC) is an open problem largely because of two main challenges. Not only does it capture the difficulty of the compound wiretap channel (another open problem) as a special case, it also requires that secrecy is ensured with respect to exponentially many possible channel state sequences. This work overcomes the second aforementioned difficulty. To that end, we consider an AVWTC with a type constraint on the allowed state sequences, and derive a single-letter characterization of its correlated-random (CR) assisted semantic-security (SS) capacity. The allowed state sequences are the ones in a typical set around a single constraining type. SS is established by showing that the mutual information between the message and the eavesdropper’s observations is negligible even when maximized over all message distributions, choices of state sequences and realizations of the CR-code. Both the achievability and the converse proofs of the type constrained coding theorem rely on stronger claims than actually required. The direct part establishes a novel single-letter lower bound on the CR-assisted SS-capacity of an AVWTC with state sequences constrained by any convex and closed set of state probability mass functions. This bound achieves the best known single-letter secrecy rates for a corresponding compound wiretap channel over the same constraint set. In contrast to other singleletter results in the AVWTC literature, the derivation does not assume the existence of a best channel to the eavesdropper. Optimality is a consequence of an max-inf upper bound on the CR-assisted SS-capacity of an AVWTC with state sequences constrained to any collection of type-classes. When adjusted to the aforementioned compound WTC, the upper bound simplifies to a max-min structure, thus strengthening the previously best known single-letter upper bound by Liang et al. that has a minmax form.