A Framework for Private Communication with Secret Block Structure

TL;DR

This paper introduces a private communication method using secret block structures in compressed sensing, enabling secure transmission over public channels and analyzing its privacy guarantees and vulnerabilities.

Contribution

It proposes a novel framework leveraging block-sparse priors for secure communication and provides algorithms and analysis for privacy and potential eavesdropper attacks.

Findings

The legitimate receiver can recover messages using secret block structures.

The framework offers privacy guarantees for single and multiple transmissions.

An eavesdropper can potentially learn the block structure using the method of moments.

Abstract

Harnessing a block-sparse prior to recover signals through underdetermined linear measurements has been extensively shown to allow exact recovery in conditions where classical compressed sensing would provably fail. We exploit this result to propose a novel private communication framework where the secrecy is achieved by transmitting instances of an unidentifiable compressed sensing problem over a public channel. The legitimate receiver can attempt to overcome this ill-posedness by leveraging secret knowledge of a block structure that was used to encode the transmitter's message. We study the privacy guarantees of this communication protocol to a single transmission, and to multiple transmissions without refreshing the shared secret. Additionally, we propose an algorithm for an eavesdropper to learn the block structure via the method of moments and highlight the privacy benefits of this framework through numerical experiments.