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Construction of 4 × 4 Substitution Box Using Elliptic Curves and Algebraic Group Structures

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Abstract

The substitution box (S-box) is the only nonlinear component of any block cipher. It hides the relationship between the key and the cipher text. Several methods are available in the literature for creating S-boxes of different sizes. However, the need to design \(4\; \times \;4\) S-boxes for lightweight encryption is in demand. The suggested method first generates the initial S-boxes from the elliptic curve points, and then the S-boxes are evolved with the help of algebraic group structures. Algebraic group structures have the potential to improve their cryptographic strength. The cryptographic properties of the suggested S-boxes, such as nonlinearity, algebraic degree, branch number, and bijectivity, are analyzed. We also present a comparative analysis of the suggested S-boxes with different standard S-boxes. The offered S-boxes are utilized in an image steganography scheme. First, the secret image is encrypted through the combination of the substitution operation and the bitwise XOR of the key. The enciphered image is hidden in the cover image using the least significant bit of steganographic scheme. Experimental results show that the suggested algorithm has a high security level and better stego-image quality.

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  1. Department of Applied Mathematics and Statistics, Institute of Space Technology, Islamabad, Pakistan

    Sadiqa Arshad

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Arshad, S. Construction of 4 × 4 Substitution Box Using Elliptic Curves and Algebraic Group Structures. Wireless Pers Commun 131, 1913–1927 (2023). https://doi.org/10.1007/s11277-023-10526-w

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