Cryptographic and Information-theoretic Security Capacities for General Arbitrarily Varying Wiretap Channels
This work advances theoretical understanding of secrecy capacities in wiretap channels with arbitrary variations, clarifying conditions under which different security notions coincide.
The paper compares strong secrecy and semantic secrecy capacities for Arbitrarily Varying Wiretap Channels (AVWCs) and General AVWCs (GAVWCs). It proves that for AVWCs the capacities are equal, but provides a counterexample showing they differ for general systems. For GAVWCs, semantic and cryptographic security measures achieve the same capacity, and the gap between strong and semantic secrecy capacities vanishes under a sub-double-exponential condition on the jammer.
We compare the strong secrecy capacities of Arbitrarily Varying Wiretap Channels (AVWCs) and General Arbitrary 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.