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Security and Communication Networks
Volume 2017, Article ID 5101934, 16 pages
Research Article

A Novel Construction of Substitution Box Involving Coset Diagram and a Bijective Map

1Department of Mathematics, University of Education Lahore, Jauharabad Campus, Jauharabad, Pakistan
2Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur, Pakistan
3Department of Mathematics, Government College University Faisalabad, Faisalabad, Pakistan
4Department of Basic Sciences, University of Engineering and Technology, Taxila, Punjab, Pakistan
5Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan
6Department of Information Technology, University of Education Lahore, Jauharabad Campus, Jauharabad, Pakistan

Correspondence should be addressed to Abdul Razaq; moc.liamg@uaqnekam

Received 15 August 2017; Accepted 10 October 2017; Published 20 November 2017

Academic Editor: Zheng Yan

Copyright © 2017 Abdul Razaq et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The substitution box is a basic tool to convert the plaintext into an enciphered format. In this paper, we use coset diagram for the action of on projective line over the finite field to construct proposed S-box. The vertices of the cost diagram are elements of which can be represented by powers of , where is the root of irreducible polynomial over . Let denote the elements of which are of the form of even powers of . In the first step, we construct a matrix with the elements of in a specific order, determined by the coset diagram. Next, we consider defined by to destroy the structure of . In the last step, we apply a bijective map on each element of the matrix to evolve proposed S-box. The ability of the proposed S-box is examined by different available algebraic and statistical analyses. The results are then compared with the familiar S-boxes. We get encouraging statistics of the proposed box after comparison.