Secret-Key Generation Using Compound Sources and One-Way Public Communication

TL;DR

This paper studies secret-key generation from compound sources with unknown statistics, deriving capacity bounds under various constraints and source models to ensure security and reliability.

Contribution

It introduces new capacity formulas for secret-key generation from compound sources with unknown parameters, extending classical models.

Findings

Derived a single-letter lower bound for finite compound sources.

Computed a multi-letter capacity formula for unconstrained public communication.

Established a single-letter capacity formula for degraded compound sources.

Abstract

In the classical Secret-Key generation model, Common Randomness is generated by two terminals based on the observation of correlated components of a common source, while keeping it secret from a non-legitimate observer. It is assumed that the statistics of the source are known to all participants. In this work, the Secret-Key generation based on a compound source is studied where the realization of the source statistic is unknown. The protocol should guarantee the security and reliability of the generated Secret-Key, simultaneously for all possible realizations of the compound source. A single-letter lower-bound of the Secret-Key capacity for a finite compound source is derived as a function of the public communication rate constraint. A multi-letter capacity formula is further computed for a finite compound source for the case in which the public communication is unconstrained. Finally a single-letter capacity formula is derived for a degraded compound source with an arbitrary set of source states and a finite set of marginal states.