GRAPH-BASED CRYPTOGRAPHIC KEY GENERATION FOR SECURE TEXT ENCRYPTION

Öz

The purpose of this article is to use a novel text encryption technique that ensures secure communication through a two-phase process and to use the encryption technique to demonstrate the connection between graph theory and cryptography. In this article, the spanning tree graph, which is a subgraph of an undirected graph used in graph theory and includes all vertices of the graph G, will be used. The first phase employs a monoalphabetic substitution cipher, utilizing predefined character-swapping arrangements between authorized individuals along with an alphabetical encryption table. The second phase enhances security by leveraging graph theory for key generation. Specifically, the Kruskal algorithm is used to compute the minimum spanning tree, enabling the creation of intricate encrypted text with a shared key derived from graph structures. By utilizing properties such as adjacency matrices, spanning trees, and graph isomorphisms, the proposed method strengthens cryptographic security while maintaining computational efficiency. The security analysis demonstrates its resilience against common cryptographic attacks, making it a promising alternative for secure text encryption and communication.

Anahtar Kelimeler

• Graphs
• Encryption
• Decryption
• Cryptography

GÜVENLİ METİN ŞİFRELEMESİ İÇİN GRAF TEORİSİ TABANLI KRİPTOGRAFİK ANAHTAR ÜRETİMİ

Öz

Bu makalenin amacı, güvenli iletişimi sağlamak için iki aşamalı bir süreçle yeni bir metin şifreleme tekniği kullanmak ve bu şifreleme tekniği aracılığıyla graf teorisi ile kriptografi arasındaki bağlantıyı göstermektir. Bu çalışmada, graf teorisinde kullanılan ve G grafının tüm düğümlerini içeren bir alt graf olan minumum spanning tree grafı kullanılmıştır. İlk aşama, yetkilendirilmiş kişiler arasında önceden belirlenmiş karakter değişim düzenlemeleri ile bir monoalfabetik ikame şifresi kullanarak bir alfabe şifreleme tablosu uygulamaktadır. İkinci aşama ise güvenliği, anahtar şifresi üretimi için graf teorisinin kullanılması ile arttırılmaktadır. Özellikle, Kruskal algoritması minimum spanning tree kullanılmaktadır. Adjacency matrisleri, yayılma ağaçları ve graf izomorfizmleri gibi özellikler kullanılarak, önerilen yöntem kriptografik güvenliği güçlendirirken hesaplama verimliliğini de korumaktadır. Güvenlik analizi, yaygın kriptografik saldırılara karşı direncini ortaya koyarak, güvenli metin şifrelemesi ve iletişimi için umut verici bir alternatif sunduğunu göstermektedir.

Anahtar Kelimeler

• Graf Teorisi
• Şifreleme
• Şifre Çözme
• Kriptografi

Kaynakça

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