A Three-Dimensional Infinite Collapse Map with Image Encryption.

Area of Science:

• Cryptography
• Dynamical Systems
• Information Security

Background:

• Low-dimensional chaotic systems are susceptible to security defects in encryption.
• Enhancing dynamic complexity is crucial for robust chaotic encryption.

Purpose of the Study:

• To propose a novel 3D infinite collapse map (3D-ICM) for improved chaotic encryption.
• To analyze the performance and complexity of the 3D-ICM.
• To develop and evaluate an image encryption scheme using the 3D-ICM.

Main Methods:

• Analysis of the 3D-ICM using phase diagrams, Lyapunov exponents, and Sample Entropy.
• Development of an image encryption algorithm based on the 3D-ICM.
• Security analysis of the encryption scheme against common cryptanalytic attacks.

Main Results:

• The 3D-ICM exhibits complex chaotic behavior and high complexity.
• The proposed image encryption scheme demonstrates resistance to brute-force, correlation, and differential attacks.
• The system achieves a higher security level compared to existing methods.

Conclusions:

• The 3D-ICM is a promising tool for developing secure chaotic encryption systems.
• The proposed image encryption scheme offers enhanced security and robustness.
• Complex chaotic dynamics are essential for effective cryptographic applications.