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

Abstract

The substitution box (S-box) plays a vital role in creating confusion during the encryption process of digital data. The quality of encryption schemes depends upon the S-box. There have been several attempts to enhance the quality of the S-box by using fractal chaotic mechanisms. However, there is still weakness in the robustness against cryptanalysis of fractal-based S-boxes. Due to their chaotic behavior, fractals are frequently employed to achieve randomness by confusion and diffusion process. A complex number-based S-box and a chaotic map diffusion are proposed to achieve high nonlinearity and low correlation. This study proposed a Mandelbrot set S-box construction based on the complex number and Chen chaotic map for resisting cryptanalytic attacks by creating diffusion in our proposed algorithm. The cryptosystem was built on the idea of substitution permutation networks (SPN). The complex nature of the proposed S-box makes it more random than other chaotic maps. The robustness of the proposed system was analyzed by different analysis properties of the S-box, such as nonlinearity, strict avalanche criterion, Bit independent criterion, and differential and linear probability. Moreover, to check the strength of the proposed S-box against differential and brute force attacks, we performed image encryption with the proposed S-box. The security analysis was performed, including statistical attack analysis and NIST analysis. The analysis results show that the proposed system achieves high-security standards than existing schemes.

Innovative Transformation of S-Box Through Chaotic Map Using a Pragmatic Approach

“…In recent times, a significant amount of research has been dedicated to enhancing the security of data and information, with a specific emphasis on developing novel S-Boxes [16,[20][21][22]. When an S-box has been constructed, it undergoes testing to evaluate its performance and determine how well it defends itself against a variety of assaults (linear and differential).…”

“…Since static S-Box block ciphers employ the same S-Box for every input, they are weak and open to intrusion [17][18] [19]. Dynamic S-Boxes, on the other hand, are more robust and provide greater protection via confusion since they are reliant on key [20][21] [22]. Researchers in the field of cryptography have developed many different kinds of S-Boxes from chaotic maps, DNA computing, optimization, elliptic curves, linear fractional transformation, dynamic random growth, cellular automata, and many more [23] [24].…”