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Journals / Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi / 2025 / Cilt: 18 Sayı: 2

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

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

Engin Eser(ERZINCAN UNIVERSITY)0000-0001-5965-4162
Bahar Kuloǧlu(SİVAS BİLİM VE TEKNOLOJİ ÜNİVERSİTESİ)0000-0001-7624-8270
Engin Özkan(MARMARA UNIVERSITY)0000-0002-4188-7248
Pages
521–536
Publication Date
2025-08-31
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we present an encoding/decoding algorithm using k-Fermat and k-Mersenne numbers.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:kodlama/kod çözme algoritması · Fermat -Q matris · Mersenne R-matris

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.

Özet

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.

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Cite This Article

Eser, E., Kuloǧlu, B., Özkan, E., *, B. K. (2025). An Encoding –Decoding Algorithm Based on k-Fermat and k-Mersenne Numbers. Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi, Cilt: 18 Sayı: 2, 521–536. https://doi.org/10.18185/erzifbed.1592108

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