Multiple Private Key Generation for Continuous Memoryless Sources with A Helper

TL;DR

This paper introduces a new method for analyzing the secrecy constraints in multi-user key generation problems with side information, deriving capacity regions for continuous sources with untrusted helpers.

Contribution

It generalizes existing results to multi-terminal scenarios and provides the first capacity region for multiple private keys with untrusted helpers in continuous memoryless sources.

Findings

Derived the capacity region for multiple private key generation with untrusted helpers.

Extended Rénnyi divergence techniques to multi-terminal settings.

Generalized converse proofs to include side information at untrusted users.

Abstract

We propose a method to study the secrecy constraints in key generation problems where side information might be present at untrusted users. Our method is inspired by a recent work of Hayashi and Tan who used the R\'enyi divergence as the secrecy measure to study the output statistics of applying hash functions to a random sequence. By generalizing the achievability result of Hayashi and Tan to the multi-terminal case, we obtain the output statistics of applying hash functions to multiple random sequences, which turn out to be an important tool in the achievability proof of strong secrecy capacity regions of key generation problems with side information at untrusted users. To illustrate the power of our method, we derive the capacity region of the multiple private key generation problem with an untrusted helper for continuous memoryless sources under Markov conditions. The converse proof of our result follows by generalizing a result of Nitinawarat and Narayan to the case with side information at untrusted users.