A strong construction of S-box using Mandelbrot set an image encryption scheme

Area of Science:

• Cryptography
• Applied Mathematics
• Computer Science

Background:

• Substitution boxes (S-boxes) are crucial for confusion in digital encryption.
• Fractal chaotic mechanisms enhance S-boxes but face cryptanalysis weaknesses.
• Achieving high nonlinearity and low correlation in S-boxes remains a challenge.

Purpose of the Study:

• To propose a new S-box construction using the Mandelbrot set and complex numbers.
• To enhance the robustness of encryption schemes against cryptanalytic attacks.
• To improve confusion and diffusion through chaotic map integration.

Main Methods:

• A complex number-based S-box construction utilizing the Mandelbrot set.
• Integration of the Chen chaotic map for diffusion in a substitution permutation network (SPN).
• Analysis of S-box properties including nonlinearity, Strict Avalanche Criterion, and Bit Independent Criterion.

Main Results:

• The proposed Mandelbrot set S-box exhibits high nonlinearity and low correlation.
• The system demonstrated strong resistance against differential and linear cryptanalysis.
• Image encryption tests confirmed the S-box's effectiveness and security.

Conclusions:

• The proposed complex number-based S-box with Chen chaotic map offers superior security standards.
• This novel approach enhances randomness and robustness against various attacks.
• The method provides a promising direction for secure digital encryption systems.