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

Year 2025, Volume: 18 Issue: 2, 521 - 536, 31.08.2025

Engin Eser , Bahar Kuloǧlu , Engin Özkan

https://doi.org/10.18185/erzifbed.1592108

Abstract

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.

Keywords

coding/decoding algorithm , Fermat Q-matrix , Mersenne R-matrix , minesweeper

k-Fermat ve k -Mersenne Sayılarına Dayalı Kodlama-Kod Çözme Algoritması

Abstract

Bu çalışmada k-Fermat ve k-Mersenne sayılarını kullanarak bir kodlama/kod çözme algoritması sunuyoruz. Fermat Q-matrisleri ve Mersenne R-matrislerini kullanıyoruz. Bu matrislerin terimleri sırasıyla k-Fermat ve k-Mersenne sayılarından oluşuyor ve bu matrisler Fibonacci Q-matrisine benziyor. Kare matrisler oluşturarak elde edeceğimiz bu yöntemde farklı anahtarlar ve mesajlar elde ediyoruz. Bu işlemin amacı yalnızca bilgi güvenliği teknolojisinin güvenilirliğini artırmak değil, aynı zamanda bilgilerin yüksek oranda doğrulanabilmesini sağlamaktır.

Keywords

kodlama/kod çözme algoritması , Fermat -Q matris , Mersenne R-matris , minesweeper

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