Covert Identification over Binary-Input Discrete Memoryless Channels

TL;DR

This paper establishes the fundamental limits of covert identification over binary-input discrete memoryless channels, showing that exponentially large identification messages can be reliably and covertly transmitted without shared keys, using novel coding strategies.

Contribution

It proves a square-root law for covert identification capacity and characterizes the exact capacity, demonstrating it matches the covert capacity in standard covert communication without shared keys.

Findings

The covert identification capacity equals the standard covert capacity.

An exponential size of identification messages is achievable covertly.

No shared key is needed for achieving the covert identification capacity.

Abstract

This paper considers the covert identification problem in which a sender aims to reliably convey an identification (ID) message to a set of receivers via a binary-input discrete memoryless channel (BDMC), and simultaneously to guarantee that the communication is covert with respect to a warden who monitors the communication via another independent BDMC. We prove a square-root law for the covert identification problem. This states that an ID message of size \exp(\exp(\Theta(\sqrt{n}))) can be transmitted over n channel uses. We then characterize the exact pre-constant in the \Theta(.) notation. This constant is referred to as the covert identification capacity. We show that it equals the recently developed covert capacity in the standard covert communication problem, and somewhat surprisingly, the covert identification capacity can be achieved without any shared key between the sender and receivers. The achievability proof relies on a random coding argument with pulse-position modulation (PPM), coupled with a second stage which performs code refinements. The converse proof relies on an expurgation argument as well as results for channel resolvability with stringent input constraints.