Perfect Secrecy Using Compressed Sensing

TL;DR

This paper explores how compressed sensing can be used for encryption, establishing conditions under which perfect secrecy, as defined by Shannon, can be achieved with certain measurement and sparsity conditions.

Contribution

It provides theoretical conditions for perfect secrecy in compressed sensing-based encryption, specifically relating to the Restricted Isometry Property and measurement count.

Findings

Perfect secrecy is achievable when RIP holds and measurements are at least twice the sparsity level.

The paper proves conditions under which Shannon's perfect secrecy is attainable.

Results apply to non-zero message blocks or infinite block lengths.

Abstract

In this paper we consider the compressed sensing-based encryption and proposed the conditions in which the perfect secrecy is obtained. We prove when the Restricted Isometery Property (RIP) is hold and the number of measurements is more than two times of sparsity level i.e. M \geq 2k, the perfect secrecy condition introduced by Shannon is achievable if message block is not equal to zero or we have infinite block length