Dynamic analysis of a novel hyperchaotic system based on STM32 and application in image encryption

Area of Science:

• Chaos theory and complex systems dynamics.
• Cryptography and information security.
• Applied mathematics and computational modeling.

Background:

• The need for advanced chaotic systems in secure communication.
• Limitations of existing chaotic models in terms of complexity and security.
• The significance of hyperchaotic systems for enhanced cryptographic applications.

Purpose of the Study:

• To introduce a novel 4D hyperchaotic system with a single equilibrium point.
• To analyze the system's dynamic properties and validate its behavior.
• To develop and evaluate a new image encryption algorithm based on the proposed hyperchaotic system.

Main Methods:

• Modification of a 3D Lorenz chaotic system to create a 4D hyperchaotic system.
• Mathematical analysis of the system's equilibrium point and stability.
• Numerical simulations using MATLAB to study Lyapunov exponents, bifurcation, and attractors.
• Experimental validation using STM32 embedded hardware.
• Application to image encryption with rigorous security testing (NIST SP800-22, key space, entropy, etc.).

Main Results:

• The 4D hyperchaotic system demonstrates complex dynamics with transitions through hyperchaotic, chaotic, periodic, and quasi-periodic states.
• Experimental validation confirms the system's ability to generate diverse chaotic attractors.
• The generated hyperchaotic key sequence successfully passes 15 NIST SP800-22 tests.
• The proposed image encryption algorithm exhibits high security, robustness, and effectiveness.

Conclusions:

• The novel 4D hyperchaotic system offers a rich platform for generating complex dynamics.
• The developed image encryption method provides a secure and reliable solution.
• The system's versatility allows for potential applications in diverse security domains like IoT and medical data protection.