The Arbitrarily Varying Wiretap Channel - Secret Randomness, Stability and Super-Activation

Abstract

We define the common randomness assisted capacity of an arbitrarily varying channel (AVWC) when the Eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough common randomness is used, the capacity formula can be given a single-shot form again. We then consider the opposite extremal case, where no common randomness is available. It is known that the capacity of the system can be discontinuous under these circumstances. We prove here that it is still stable in the sense that it is continuous around its positivity points. We further prove that discontinuities can only arise if the legal link is symmetrizable and characterize the points where it is positive. These results shed new light on the design principles of communication systems with embedded security features. At last we investigate the effect of super-activation of the message transmission capacity of AVWCs under the average error criterion. We give a complete characterization of those AVWCs that may be super-activated. The effect is thereby also related to the (conjectured) super-activation of the common randomness assisted capacity of AVWCs with an eavesdropper that gets to know the common randomness. Super-activation is based on the idea of "wasting" a few bits of non-secret messages in order to enable provably secret transmission of a large bulk of data, a concept that may prove to be of further importance in the design of communication systems. In this work we provide further insight into this phenomenon by providing a class of codes that is capacity-achieving and does not convey any information to the Eavesdropper.

Significant changes again: now 53 pages, 2 figures. Modified and corrected Lemma 3. Added insightful example related to Lemma 3. Extended proof of Theorem 2

References in corpus (3)

• Quantum Communication With Zero-Capacity Channels
• A channel under simultaneous jamming and eavesdropping attack---correlated random coding capacities under strong secrecy criteria
• Positivity, Discontinuity, Finite Resources and Nonzero Error for Arbitrarily Varying Quantum Channels

Cited by in corpus (6)

• Classical-Quantum Arbitrarily Varying Wiretap Channel: Secret Message Transmission under Jamming Attacks
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• Arbitrarily Varying Wiretap Channel with State Sequence Known or Unknown at the Receiver
• The Arbitrarily Varying Relay Channel
• A Study on Arbitrarily Varying Channels with Causal Side Information at the Encoder
• Reliable Communication under the Influence of a State-Constrained Jammer: A Novel Perspective on Receive Diversity