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Non-Associative Algebra Redesigning Block Cipher with Color Image Encryption

Nazli Sanam1,*, Asif Ali1, Tariq Shah1, Ghazanfar Farooq2

1 Department of Mathematics, Quaid-i-Azam University, Islamabad, 44000, Pakistan
2 Department of Computer Science, Quaid-i-Azam University, Islamabad, 44000, Pakistan

* Corresponding Author: Nazli Sanam. Email: nazli.sanam@

(This article belongs to this Special Issue: Security and Computing in Internet of Things)

Computers, Materials & Continua 2021, 67(1), 1-21.


The substitution box (S-box) is a fundamentally important component of symmetric key cryptosystem. An S-box is a primary source of non-linearity in modern block ciphers, and it resists the linear attack. Various approaches have been adopted to construct S-boxes. S-boxes are commonly constructed over commutative and associative algebraic structures including Galois fields, unitary commutative rings and cyclic and non-cyclic finite groups. In this paper, first a non-associative ring of order 512 is obtained by using computational techniques, and then by this ring a triplet of 8 × 8 S-boxes is designed. The motivation behind the designing of these S-boxes is to upsurge the robustness and broaden the key space due to non-associative and non-commutative behavior of the algebraic structure under consideration. A novel color image encryption application is anticipated in which initially these 3 S-boxes are being used to produce confusion in three layers of a standard RGB image. However, for the sake of diffusion 3D Arnold chaotic map is used in the proposed encryption scheme. A comparison with some of existing chaos and S-box dependent color image encryption schemes specs the performance results of the anticipated RGB image encryption and observed as approaching the standard prime level.


Cite This Article

N. Sanam, A. Ali, T. Shah and G. Farooq, "Non-associative algebra redesigning block cipher with color image encryption," Computers, Materials & Continua, vol. 67, no.1, pp. 1–21, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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