Multipartite Monotones for Secure Sampling by Public Discussion From Noisy Correlations

TL;DR

This paper introduces multipartite monotones to quantify the cryptographic content of distributions, enabling secure sampling in multi-party settings without pre-shared correlations, and provides new operational interpretations.

Contribution

It generalizes assisted common information to multiple sources, defines a family of monotone regions, and introduces the residual total correlation as a new monotone.

Findings

Characterizes t-private distributions for secure sampling.

Introduces a new monotone called residual total correlation.

Shows differences in monotone regions for K > 2 in public discussion.

Abstract

We address the problem of quantifying the cryptographic content of probability distributions, in relation to an application to secure multi-party sampling against a passive t-adversary. We generalize a recently introduced notion of assisted common information of a pair of correlated sources to that of K sources and define a family of monotone rate regions indexed by K. This allows for a simple characterization of all t-private distributions that can be statistically securely sampled without any auxiliary setup of pre-shared noisy correlations. We also give a new monotone called the residual total correlation that admits a simple operational interpretation. Interestingly, for sampling with non-trivial setups (K > 2) in the public discussion model, our definition of a monotone region differs from the one by Prabhakaran and Prabhakaran (ITW 2012).