A channel under simultaneous jamming and eavesdropping attack---correlated random coding capacities under strong secrecy criteria

TL;DR

This paper characterizes the correlated random coding secrecy capacity of arbitrarily varying wiretap channels under strong secrecy criteria, revealing continuity properties and employing auxiliary channels for the proof.

Contribution

It provides a complete multi-letter formula for the secrecy capacity with correlated codes under strong secrecy, contrasting with uncorrelated code behavior.

Findings

Secrecy capacity is continuous with respect to the channel.

Two strong secrecy criteria yield the same capacity formula.

Auxiliary channels are used in the proof to handle varying conditions.

Abstract

We give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels (AVWCs). We apply two alternative strong secrecy criteria, which both lead to the same multi-letter formula. The difference of these criteria lies in the treatment of correlated randomness, they coincide in the case of uncorrelated codes. On the basis of the derived formula, we show that the correlated random coding secrecy capacity is continuous as a function of the AVWC, in contrast to the discontinuous uncorrelated coding secrecy capacity. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and arbitrarily varying from the sender to the eavesdropper.