Identification Under the Semantic Effective Secrecy Constraint
Abdalla Ibrahim, Johannes Rosenberger, Boulat A. Bash, Christian Deppe, Roberto Ferrara, Uzi Pereg
TL;DR
This paper analyzes identification over a discrete memoryless wiretap channel under semantic effective secrecy, integrating secrecy and stealth (covert) requirements. It develops a capacity framework based on approximation-of-output statistics (AOS) and joint AOS-transmission concepts, proving a capacity theorem for AOS codes and deriving both lower and upper bounds on the effectively secret identification capacity (ESID). The bounds are tight for more capable channels, with a constructive ESID scheme leveraging $\\\ ext{epsilon}$-almost universal hashing together with stealthy AOS components; in other channel classes, a gap between bounds can occur and auxiliary pre-channels may enhance rates. The work combines tools from channel resolvability, secrecy in identification, and covert communications to characterize ESID capabilities and highlight open questions for tightening converses, illustrated through multiple channel examples.
Abstract
The problem of identification over a discrete memoryless wiretap channel is examined under the criterion of semantic effective secrecy. This secrecy criterion guarantees both the requirement of semantic secrecy and of stealthy communication. Additionally, we introduce the related problem of combining approximation-of-output statistics and transmission. We derive a capacity theorem for approximation-of-output statistics transmission codes. For a general model, we present lower and upper bounds on the capacity, showing that these bounds are tight for more capable wiretap channels. We also provide illustrative examples for more capable wiretap channels, along with examples of wiretap channel classes where a gap exists between the lower and upper bounds.