On the Okamoto-Uchiyama cryptosystem: (A brief essay on basic mathematics applied in cryptography)

Abstract

The Okamoto-Uchiyama cryptosystem applies many consepts of basic abstract algebra, discrete mathematics and number theory. Many of these concepts are elementary and used in other branches of cryptography. However, those elementary concepts are not enough provided in the mathematics curriculla in under developed and developing countries despite the fact that in early stages teaching of those basic mathematics concepts, there is no need to provide sophiticated nor rigorous treatments beyond computations of integers. By exploring the basic mathematics applied in Okamoto-Uchiyama's algorithm and its re-lated concepts, this exploration should make mathematics teachers, educators and instructors to be aware of the important teaching the basic abstract algebra, discrete mathematics and number theory as early as high school senior level or at the first year in colleges and universities.