Quantum Computer-Resistant Electronic Signature Generation Using Gaussian Prime Numbers

Abstract

The use of electronic signature is one of the most widely used tools in the public and private sectors. Ownership and verification of the produced documents are mostly done by electronic signing. Signing algorithms utilized today are produced with the RSA algorithm or its derivatives. Classically generated digital signatures are produced utilizing very large prime numbers, open switching technologies, and modular mathematics. Many different algorithms are used in the generation of numbers ionosonde. In this study, we aim to produce electronic signatures and certificates by employing Gaussian prime numbers (GPN). The novel method considered within the scope of this study is the realization of quantum digital signature generation employing GPN to produce a common digital signature used by classical computers and quantum computers. The produced signing algorithm can be used for classical computers and quantum computers. It is foreseen that the proposed method will be both resistant to quantum computers and increase security in classical computers. The proposed method aims to maximize the security level of digital signature processes. Thus, the common use of classical and quantum computers is expected to provide an advantage in the science of cryptology in storing, securely sharing, and transferring information.

Keywords

• Quantum computers
• Gaussian prime numbers
• Digital signature
• Electronic certificate
• Quantum digital signature

Gauss Asal Sayıları Kullanarak Kuantum Bilgisayarlara Dayanıklı Elektronik İmza Üretimi

Öz

Elektronik imza, kamu ve özel sektörde en yaygın kullanılan araçlardan biridir. Üretilen belgelerin sahipliği ve doğrulaması çoğunlukla elektronik imza ile gerçekleştirilmektedir. Günümüzde kullanılan imzalama algoritmaları genellikle RSA algoritması veya türevleriyle üretilmektedir. Klasik olarak oluşturulan dijital imzalar, çok büyük asal sayılar, açık anahtarlı şifreleme teknolojileri ve modüler matematik kullanılarak üretilmektedir. Sayı üretiminde birçok farklı algoritma kullanılmaktadır. Bu çalışmada, elektronik imzalar ve sertifikalar üretmek için Gauss asal sayılarından (GPN) yararlanılması amaçlanmaktadır. Çalışma kapsamında ele alınan yenilikçi yöntem, kuantum dijital imza üretiminin GPN kullanılarak gerçekleştirilmesi ve böylece klasik bilgisayarlar ile kuantum bilgisayarlar tarafından ortak kullanılan bir dijital imza üretilmesidir. Önerilen imzalama algoritmasının hem klasik bilgisayarlarda hem de kuantum bilgisayarlarda kullanılabileceği öngörülmektedir. Önerilen yöntemin, kuantum bilgisayarlara karşı dirençli olması ve klasik bilgisayarlarda güvenliği artırması beklenmektedir. Bu yöntem, dijital imza süreçlerinin güvenlik seviyesini en üst düzeye çıkarmayı hedeflemektedir. Böylece, klasik ve kuantum bilgisayarların ortak kullanımı, kriptoloji biliminde bilgilerin saklanması, güvenli bir şekilde paylaşılması ve aktarılması açısından bir avantaj sağlayacaktır.

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