New adaptive synchronization algorithm for a general class of hyperchaotic complex-valued systems with unknown parameters and its application to secure communication

TL;DR

This paper introduces a new adaptive synchronization algorithm for hyperchaotic complex-valued systems with unknown parameters, enhancing secure communication methods by making decryption more difficult for intruders while ensuring accurate message retrieval.

Contribution

The paper proposes a novel adaptive synchronization scheme for hyperchaotic complex systems with unknown parameters, including a secure communication application with improved cryptosystem robustness.

Findings

The scheme successfully synchronizes hyperchaotic systems with unknown parameters.

It enables secure communication with robust message encryption and decryption.

The method effectively handles noisy message transmission scenarios.

Abstract

This report aims to study adaptive synchronization between a general class of hyperchaotic complex-valued systems with unknown parameters, which is motivated by extensive application areas of this topic in nonlinear sciences (e.g., secure communications, encryption techniques, etc.). Based on the complexity of hyperchaotic dynamical systems, which may be beneficial in secure communications, a scheme to achieve adaptive synchronization of a general class of hyperchaotic complex-valued systems with unknown parameters is proposed. To verify scheme's consistency, the control functions based on adaptive laws of parameters are derived analytically, and the related numerical simulations are performed. The complex-valued Rabinovich system describing the parametric excitation of waves in a magneto-active plasma is considered as an interesting example to study this kind of synchronization. A scheme for secure communication and improving the cryptosystem is proposed; the sketch is constructed to split the message and inject some bit of information signal into parameters modulation and the other bit into the transmitter system's states, which, in turn, complicates decryption task by intruders. Meanwhile, the information signal can be accurately retrieved at the receiver side by adaptive techniques and decryption function. Different types of encrypted messages are considered for testing the robustness of the proposed scheme (e.g., plain text and gray images with diverse scales of white Gaussian noise).