An n-Dimensional Chaotic Map with Application in Reversible Data Hiding for Medical Images

Area of Science:

• Chaos Theory
• Cryptography
• Image Processing

Background:

• One-dimensional chaotic maps suffer from simple structures, narrow chaotic intervals, and predictability.
• Multidimensional chaotic systems are needed for richer performance and complex structures.
• Existing chaotic systems have limitations that necessitate novel approaches.

Purpose of the Study:

• To propose a novel n-dimensional cosine-transform-based chaotic system (nD-CTBCS) addressing the shortcomings of existing chaotic systems.
• To demonstrate the ability of nD-CTBCS to generate chaotic maps of any dimension using existing 1D chaotic maps as seeds.
• To validate the enhanced performance and hyperchaotic behavior of the newly generated chaotic maps.

Main Methods:

• Development of an n-dimensional cosine-transform-based chaotic system (nD-CTBCS) incorporating a chaotic coupling model.
• Utilizing existing 1D chaotic maps as seed maps to construct higher-dimensional chaotic maps.
• Implementation of a reversible data hiding scheme for secure medical image communication using the proposed nD-CTBCS.

Main Results:

• The proposed nD-CTBCS successfully generates multidimensional chaotic maps with improved functionality.
• Experimental results show broader chaotic intervals and the emergence of hyperchaotic behavior in the new maps.
• The reversible data hiding scheme demonstrated superior security compared to existing methods for medical image transmission.

Conclusions:

• The nD-CTBCS offers a flexible and effective framework for generating complex, high-dimensional chaotic maps.
• The system's ability to produce hyperchaotic behavior enhances its suitability for secure communication applications.
• The proposed data hiding scheme highlights the practical utility and enhanced security offered by the nD-CTBCS.