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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.

Received 21 September 2020; Accepted 23 October 2020; Issue published 12 January 2021


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.


Block cipher; s-box; nonlinearity; color image encryption; 3D chaotic map

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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