An Encoding-Decoding Algorithm Based On Fermat And Mersenne Numbers∗

In this study, we present an encoding/decoding algorithm using Fermat and Mersenne numbers. Using Fermat and Mersenne numbers we define Fermat Q-matrices and Mersenne R-matrices. We process these matrices we defined in the same way as in Fibonacci Q-matrix. We can encode any given massage with a special encryption and we can decode the encrypted massage with the method we use. We describe these process step by step. First we define coding process and then we define decoding process. In addition we give a mix model named minesweeper using Fermat Q-and Mersenne R-matrices simultaneously. The purpose of this study is not only to increase the reliability of information security technology, but also to provide the ability to verify information at a high rate. © 2024, Tsing Hua University. All rights reserved.