Improved 2D Discrete Hyperchaos Mapping with Complex Behaviour and Algebraic Structure for Strong S-Boxes Generation

Abstract

This paper proposes to present a novel method of generating cryptographic dynamic substitution-boxes, which makes use of the combined effect of discrete hyperchaos mapping and algebraic group theory. Firstly, an improved 2D hyperchaotic map is proposed, which consists of better dynamical behaviour in terms of large Lyapunov exponents, excellent bifurcation, phase attractor, high entropy, and unpredictability. Secondly, a hyperchaotic key-dependent substitution-box generation process is designed, which is based on the bijectivity-preserving effect of multiplication with permutation matrix to obtain satisfactory configuration of substitution-box matrix over the enormously large problem space of 256!. Lastly, the security strength of obtained S-box is further elevated through the action of proposed algebraic group structure. The standard set of performance parameters such as nonlinearity, strict avalanche criterion, bits independent criterion, differential uniformity, and linear approximation probability is quantified to assess the security and robustness of proposed S-box. The simulation and comparison results demonstrate the effectiveness of proposed method for the construction of cryptographically sound S-boxes.

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

“…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]. A novel technique, presented in [25], builds robust S-Boxes via matrix rotation and affine transformation. Dynamic optimization and static S-Box design are the two phases of the method presented in [26].…”

Novel image cryptosystem based on new 2D hyperchaotic map and dynamical chaotic S-box

“…However, two-dimensional discrete chaotic systems are more used due to their simple form and strong anti-degeneration ability. At present, many discrete two-dimensional chaotic systems have been proposed [20][21][22][23][24][25][26]. Hua et al proposed a two-dimensional (2D) modular chaotic system that can improve the chaotic complexity of any two-dimensional chaotic map [20].…”

“…Hua et al designed a two-dimensional chaotic system with continuous and wide chaotic range and designed a color image encryption algorithm based on this system [23]. Ahmad et al proposed an improved 2D hyperchaotic system and used it for S-box generation [24]. Qi et al proposed a 2D-TSCC chaotic system and used it for image protection [25].…”

Comparison of Nonlinearity Value of Substitution Box Generation Approaches

“…More than 100 sbox generation algorithms have been proposed using many approaches from the past to the present. Among these approaches, the most; mathematical transformations [3][4][5][6][7][8], chaotic systems [9][10][11][12][13][14] and optimization techniques [15][16][17][18][19][20][21][22] are used. In addition, hybrid approaches have been developed [23][24][25] by combining DNA coding, cellular automata, and the benefits of existing approaches.…”