Bijective S-Boxes Method Using Improved Chaotic Map-Based Heuristic Search and Algebraic Group Structures

Abstract

This paper presents a hybrid method for the construction of cryptographically strong bijective substitution-boxes by utilizing the merits of chaotic map and algebraic groups. The hybrid method first generates the key-dependent dynamic S-boxes using chaotic heuristic search strategy and then the S-boxes are evolved with the help of potent proposed algebraic group structures. This paper proposes a new improved combination chaotic map to operate initial search strategy. To augment the strength of generated S-boxes, the algebraic group structures are discovered which have the power to improve their cryptographic strength. The performance assessments using standard criterions are rendered to quantify the strengths of proposed bijective S-boxes. The experimental results and comparisons with recent S-box research findings justify the effectiveness and competence of the proposed bijective S-boxes and anticipated hybrid generation method.

A Novel Construction of Dynamic S-Box With High Nonlinearity Using Heuristic Evolution

“…Consequently, the protection that a block cipher provides to a given plaintext by employing one or more S-boxes is directly reliant on the strength of the respective S-boxes. Other constituents of a cipher work in a linear manner, while an S-box operates in a nonlinear fashion to increase the security of the plaintext [8,9]. Modern-day ciphers employ two kinds of S-boxes known as static S-boxes and dynamic S-boxes.…”

A highly nonlinear substitution-box (S-box) design using action of modular group on a projective line over a finite field

“…In [ 33 ], the authors proposed a hybrid scheme based on chaotic map and affine transformation to generate multiple S-boxes using rotational matrices. The research work in [ 34 ] utilized a chaotic map along with algebraic groups to proposed another hybrid method for generating non-linear S-boxes. A. Razzaq et al [ 35 ] presented a new scheme for S-box design, which is based on the coset graphs and symmetric groups.…”

A Novel Optimization Method for Constructing Cryptographically Strong Dynamic S-Boxes

“…One of the most important blocks in many encryption systems is the Sbox. An S-box must satisfy certain design criteria pertaining to its resistance to a variety of cryptanalysis attacks [1]. Among these criteria, the bitwise functional nonlinearity (NL) and the linear approximation probability (LAP) tests determine the S-box resistance to linear cryptanalysis [2].…”

“…On the other hand, algebraic methods, such as [1,2,4,[21][22][23][24][25][26][27], use efficient algebraic construction to generate 8 × 8 Sboxes with high nonlinearity reaching = 112. However, they can only generate a limited number of different S-boxes.…”