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

2026-05-07

AI Summary

This study investigates the capacity equivalence under different security constraints—specifically strong secrecy and semantic secrecy—for the general arbitrarily varying wiretap channel (GAVWC). By integrating information-theoretic and cryptographic techniques, the authors construct secure codes, devise counterexamples, and analyze asymptotic performance to establish, for the first time, the relationship between semantic security and other cryptographic security metrics in terms of channel capacity for GAVWCs. The main contributions include proving that strong secrecy and semantic secrecy capacities are identical for the standard arbitrarily varying wiretap channel (AVWC), whereas they generally differ for the GAVWC. However, the gap vanishes when the number of adversarial strategies grows sub-double-exponentially with blocklength, and the paper provides sufficient conditions under which the two capacities coincide.

Abstract

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.

Problem

• Arbitrarily Varying Wiretap Channels
• Semantic Secrecy
• Strong Secrecy
• Cryptographic Security
• Information-theoretic Security

Innovation

• Arbitrarily Varying Wiretap Channel
• Semantic Security
• Strong Secrecy
• Information-theoretic Security
• Secrecy Capacity