Cryptographic and Information-theoretic Security Capacities for General Arbitrarily Varying Wiretap Channels

TL;DR

This paper compares various secrecy capacities of Arbitrarily Varying Wiretap Channels, showing conditions under which different secrecy measures yield the same capacity and analyzing the capacity gap.

Contribution

It establishes the equivalence of secrecy capacities under different measures for AVWCs and GAVWCs, and provides bounds on their capacity differences.

Findings

Strong secrecy capacity equals semantic secrecy capacity for AVWCs.

Semantic security and cryptographic measures achieve the same capacity for GAVWCs.

The capacity gap vanishes if the jammer's choice is sub-double-exponential in block length.

Abstract

We compare the strong secrecy capacities of Arbitrarily Varying Wiretap Channels (AVWCs) and General Arbitrarily Varying Wiretap Channels (GAVWCs) with their capacities under semantic secrecy constraint and other equivalent cryptographic secrecy constraints. It turns out that the average error and strong secrecy capacity of an AVWC is always equal to its maximal error and semantic secrecy capacity. However, this equivalence does not hold for all general communication systems, and we prove this by a counterexample. We also show that, for the GAVWC, semantic security and the other cryptographic security measures considered achieve the same capacity values. Finally, we bound the gap between the strong secrecy capacity and the semantic secrecy capacity for the GAVWC. The gap vanishes if the choice of the jammer is sub-double-exponential with respect to the block length n, which gives a sufficient condition for the strong and semantic secrecy capacities to be equal for GAVWCs.