Research on cascading high-dimensional isomorphic chaotic maps

Area of Science:

• Chaos theory
• Dynamical systems
• Cryptography

Background:

• Discrete chaotic sequences often suffer from small Lyapunov exponents and limited keyspaces, posing security risks.
• Enhancing chaotic map properties is crucial for robust cryptographic applications.

Purpose of the Study:

• To present a general chaotic construction method by cascading multiple high-dimensional isomorphic maps.
• To overcome the security weaknesses of existing chaotic sequences.

Main Methods:

• A general construction method involving cascading high-dimensional isomorphic maps.
• Analysis of dynamical behaviors using the generalized 3-D Hénon map under various cascade modes.
• Investigation of diverse maps generated through parameter variation and permutation.

Main Results:

• Cascaded systems exhibit enlarged parameter spaces and increased Lyapunov exponents compared to original maps.
• Discovery of new dynamical behaviors, including coexisting and hyperchaotic attractors.
• Demonstration of excellent performance in image encryption using the generated chaotic sequences.

Conclusions:

• The proposed cascading method effectively enhances the security of chaotic sequences.
• The method provides a flexible approach to generating complex chaotic behaviors.
• The resulting chaotic sequences are suitable for secure image encryption.