Covert Identification over Binary-Input Discrete Memoryless Channels
This work addresses secure and covert communication for scenarios where identification must be hidden from a warden, offering a foundational result with potential applications in cryptography and surveillance-resistant systems.
The paper tackles the problem of covert identification over binary-input discrete memoryless channels, proving a square-root law that allows transmitting an identification message of size exp(exp(Θ(√n))) over n channel uses, and characterizes the exact covert identification capacity, which equals the covert capacity in standard covert communication and can be achieved without shared keys.
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(Θ(\sqrt{n}))) can be transmitted over n channel uses. We then characterize the exact pre-constant in the Θ(.) 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.