One-Shot Perfect Secret Key Agreement for Finite Linear Sources

Chung Chan, Navin Kashyap, Praneeth Kumar Vippathalla, Qiaoqiao Zhou

Abstract: We consider a non-asymptotic (one-shot) version of the multiterminal secret key agreement problem on a finite linear source model. In this model, the observation of each terminal is a linear function of an underlying random vector composed of finitely many i.i.d. uniform random variables. By restricting the public discussion to be a linear function of the terminals' observations, we obtain a characterization of the communication complexity (minimum number of symbols of public discussion) of generating a secret key of maximum length. More precisely, we show that the minimum discussion can be achieved by a non-interactive protocol in which each terminal first does a linear processing of its own private observations, following which the terminals all execute a discussion-optimal communication-for-omniscience protocol. The secret key can be chosen to be a linear function of the vector of all observations.