Finite Semi-group Modulo and Its Application to Symmetric Cryptography

Authors: Frank Emmanuel Akpan, Udoaka Otobong Gabriel

Abstract: In this paper, the application of finite semi-group structure S is studied. In particular, the study uses finite semi-group modulo n $$FS(n)=(Z_{p}, +)\left<θ \right>$$ to generate Mutually Orthogonal Latin Squares (MOLS) and applied same to symmetric cryptography. It is shown in the study that for any $$n>1$$, the maximum number of mutually orthogonal Latin squares in a finite semi-group modulo n $$FS(n)=(Z_{p}, +)\left<θ \right>=\left\{0,1,2,3, ..... p-1, φ,φ^{2},φ^{3}......nth \space element\right\} is\space n-1$$. Finally, the study shows manual Algorithm for the generation of mutually orthogonal Latin squares from a finite semi-group modulo and its application to symmetric cryptography which has been seen to be an effective coding technique for hiding sensitive information and suitable for reducing crime rate if not totally eradicated.

Pages: 90-98

DOI: 10.46300/91019.2022.9.13

International Journal of Pure Mathematics, E-ISSN: 2313-0571, Volume 9, 2022, Art. #13