Vernam Şifreleme ve Pell-Lucas Dizileriyle Güçlendirilmiş Sayısal İmza Tasarımı

Year 2025, Volume: 1 Issue: 1, 68 - 80, 20.07.2025

Tuğba Göresim Toska , Ahmet Karaoğlu , Emel Soylu

Abstract

Bugünün dijital dünyasında veri güvenliği sadece şifreleme ile değil, aynı zamanda verilerin bütünlüğünü vurgulayarak ve koruyarak mümkündür.Sayısal imza algoritmaları bu gerekliliği karşılamak için geliştirilmiş mekanizmalardır. Bu çalışma, Pell-Lucas dizisi kullanılarak güçlendirilen klasik Vernam şifrelemesine dayalı bir sayısal imza algoritmasıdır. Pell-Lucas dizisi, deterministik yapısı ve hızlı büyümesi sayesinde, rastgelelik gerektirmeden yüksek entropili anahtar üretimine olanak sağlamaktadır (Koshy, 2001; Vajda, 1989).Bu yöntemde açık anahtar dizisi, Pell-Lucas dizisinin modüler şekliyle XOR’lanarak özel anahtar elde edilmekte ve bu özel anahtar ile mesaj karakterleri tekrardan XOR işlemi yapılarak sayısal imza üretilmektedir. Doğrulama süreci, iletilen imza ve açık anahtar ile mesajın tutarlılığının test edilmesine dayanmaktadır. Lucas dizisi tabanlı benzer çalışmalardan farklı olarak (Duman & Duman, 2021), bu çalışma daha yüksek sayı alanı, lineer olmayan yapı ve doğrudan imza üretimi gibi özelliklerle literatüre yenilikçi bir katkı sunmaktadır.

Keywords

Pell-Lucas dizileri , Vernam , Kriptoloji , İmza algoritmaları

Vernam Encryption and Number Series of Pell-Lucas for A Reinforced Digital Signature Design

Abstract

In today's digital world, data security is possible not only through encryption, but also by emphasizing and protecting the integrity of the data.. Digital signature algorithms are mechanisms developed to meet this requirement. This work is a digital signature algorithm based on the classical Vernam encryption strengthened using the Pell-Lucas sequence. Due to its deterministic structure and fast growth, the Pell-Lucas sequence enables high-entropy key generation without randomization (Koshy, 2001; Vajda, 1989). In this method, the public key sequence is XOR with the modular form of the Pell-Lucas sequence to obtain a private key and the message characters are XOR again with this private key to generate a digital signature.. The verification process is based on testing the consistency of the message with the transmitted signature and public key. Unlike similar works based on Lucas sequences (Duman & Duman, 2021), this work makes an innovative contribution to the literature with features such as higher number field, non-linear structure and direct signature generation.

Keywords

Pell-Lucas sequences , Vernam , Cryptology , Signature algorithms

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