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All Journal Mikailalsys Journal of Advanced Engineering International
Domven, Lohcwat
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Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Electrical & Electronics Engineering Engineering Mechanical Engineering

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The Concept of Differentiation and Integration of Paraletrix: A Generalization of Rhotrix Domven, Lohcwat; Saleh, Abbas B; Danladi, Daniel; Peter, Patrick Pam
Mikailalsys Journal of Advanced Engineering International Vol 2 No 3 (2025): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v2i3.6807

Abstract

The concepts of matrix-tertions and matrix-noittrets were first introduced by Atanssov, K. T. and Shannon, A. G. [1] as mathematical enrichment exercises involving objects that lie between two-dimensional vectors and 2×2 matrices. This idea was later extended by Ajibade, A. O. [2] through the introduction of rhotrices, mathematical structures positioned between 2×2 and 3×3 matrices. Various multiplication operations for rhotrices, including heart-oriented and row–column multiplications, have been studied extensively, yielding several important results. Building on these developments, the paraletrix was introduced as a generalization of the rhotrix, defined as a structure in which the number of rows and columns need not be equal. In this paper, we extend the theory of paraletrices by introducing the concepts of differentiation and integration with respect to an independent variable occurring in a function, thereby contributing to the broader mathematical framework of generalized matrix-like objects.
Enhancing TARIG Transform-Based Encryption Using Nonlinear Permutation Polynomial over Prime Fields Domven, Lohcwat; Danladi, Daniel; Peter, Patrick Pam; Bailey, Abbas Saleh
Mikailalsys Journal of Advanced Engineering International Vol 2 No 3 (2025): Mikailalsys Journal of Advanced Engineering International
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjaei.v2i3.7367

Abstract

The Affine Cipher, when implemented via the Tarig Transform, provides a straightforward and efficient approach to data encryption but is constrained by a limited key space and susceptibility to known-plaintext attacks. To overcome these shortcomings, this study proposes an enhanced encryption scheme that incorporates polynomial-based transformations into the Affine-based Tarig Transform framework. By introducing nonlinear polynomial mappings, the proposed method significantly expands the key space, enhances diffusion properties, and strengthens resistance to cryptanalytic techniques. Experimental evaluations confirm that the polynomial-based approach offers improved security metrics, including greater statistical randomness, while preserving computational efficiency comparable to the original implementation. These findings indicate that the enhanced scheme presents a viable and more secure alternative to conventional Affine Cipher methods for robust data communication.
Co-Authors Bailey, Abbas Saleh Danladi, Daniel Peter, Patrick Pam Saleh, Abbas B