An Encoding –Decoding Algorithm Based on k-Fermat and k-Mersenne Numbers

In this study, we present an encoding/decoding algorithm using k-Fermat and k-Mersenne numbers. We use Fermat Q-matrices and Mersenne R-matrices, the terms of these matrices are composed of k-Fermat and k-Mersenne numbers, respectively, and look like Fibonacci Q-matrix. In this method, which we will obtain by creating square matrices, we obtain different keys and messages. The purpose of this process is not only to increase the reliability of information security technology, but also to provide the ability to verify information at a high rate.