Secret Key Capacity of Wiretapped Polytree-PIN

Abstract

In secret key agreement (SKA) in multiterminal channel model, terminals are connected by a noisy discrete memoryless channel (DMC) with multiple input and multiple outputs. Terminals can use the DMC to obtain correlated randomness, and communicate over a noiseless public channel to establish a shared secret key among a designated subset of terminals. We focus on a special class of multiterminal channel models, called wiretapped Polytree-PIN, in which the noisy channel consists of a set of independent point-to-point channels whose underlying undirected connectivity graph forms a tree. We consider a wiretap setting, where the output of each point-to-point channel is partially leaked to a passive wiretapper adversary, Eve, through a second independent noisy channel. A secure SKA protocol generates a group secret key such that Eve has no information about it. In this paper, we derive the wiretap secret key capacity, which is the largest achievable secret key rate, of the wiretapped PolytreePIN model. Our result also implies the key capacity of the non-wiretapped Polytree-PIN model, that is the case when there is no leakage from point-to-point channels to Eve.