Designing Higher-Dimensional Digital Chaotic Systems Via Reverse Derivation of Iterative Function from Strongly Connected Graph and its Application

Abstract

This paper describes a novel way to design higher-dimensional digital chaotic systems (HDDCSs). By reversing iterative function that is not governed by random sequences, from strongly connected graphs, the resulting HDDCS is demonstrated to fulfill Devaney's definition of chaos. These HDDCSs are then efficiently implemented in digital circuits. Furthermore, a novel method for generating measurement matrices using the designed HDDCS is proposed, and compressive sensing-based image encryption techniques make use of these matrices. Comparative analysis against deterministic random matrices and relevant experimental approaches showcases the remarkable efficacy of our method. The proposed technique substantially enhances reconstruction outcomes and the ability to conceal image correlations. This work not only contributes to the development of HDDCSs, but also diversifies the methods for constructing measurement matrix in image encryption.

Keywords: HDDCS, strongly connected graph, circuit implementation, image encryption