Lists that are smaller than their parts: A coding approach to tunable secrecy

TL;DR

This paper introduces a new information-theoretic framework for list-source codes and psilon-symbol secrecy, providing bounds and practical coding solutions for secure source coding.

Contribution

It proposes a novel psilon-symbol secrecy metric and analyzes list-source codes within this framework, including bounds and MDS code constructions.

Findings

Fundamental bounds for psilon-symbol secrecy established

MDS codes can achieve these bounds for uniform sources

Framework applicable in non-asymptotic cryptographic settings

Abstract

We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show that such codes can be analyzed in the context of a novel information-theoretic metric, \epsilon-symbol secrecy, that encompasses both the one-time pad and traditional rate-based asymptotic metrics, but, like most cryptographic constructs, can be applied in non-asymptotic settings. We derive fundamental bounds for \epsilon-symbol secrecy and demonstrate how these bounds can be achieved with MDS codes when the source is uniformly distributed. We discuss applications and implementation issues of our codes.