Lucas Dizisinin Terimleri Kullanılarak Verinin Şifrelenmesi ve Şifrenin Çözülmesi

Abstract

Başlangıç şartı 2 ve 1 olan ve sonraki terimleri kendinden önceki iki terimin toplanmasıyla elde edilen diziye Lucas dizisi denir. Uygulamalı bilimlerde Lucas dizisi ile ilgili birçok çalışma yapılmıştır. Kriptoloji; verinin şifrelenmesi, güvenli bir şekilde bir noktadan başka bir noktaya transfer edilmesi ve şifrelenen verinin birebir önceki haline getirilmesi ile ilgilenen bilim dalıdır. Kriptoloji; kriptografi ve kriptoanalizi içerir. Geçmişten bugüne kadar verinin güvenliğini sağlamak amacıyla farklı kriptolama yöntemleri geliştirilmiştir. Bunlardan bazıları Sezar (Caesar), Affin, Vigenere ve RSA algoritmalarıdır. Kriptolojide iki çeşit şifreleme sistemi vardır. Birincisi simetrik (gizli anahtarlı) şifreleme diğeri ise asimetrik (açık anahtarlı) şifrelemedir. Bu çalışmada; Fibonacci dizisinin terimlerinden yararlanarak yeni bir şifreleme metodu geliştirildi. Bu şifreleme ile alfabemizdeki harflerin her biri Fibonacci dizisinin terimleri ile eşleştirildi. Böylece, şifrelenmek istenen metin, sayıların sembolik gösterimi haline getirildi. Şifreli metin oluşturulurken küçük harfler dikkate alındı. Daha sonra da sayılarla şifrelenmiş metnin deşifre edilmesi için gerekli olan dönüşüm hakkında bilgiler verildi.

Keywords

• Lucas sayıları
• kriptoloji
• bilgi güvenliği
• kriptografi

Encryption and Decryption of the Data by Using the Terms of the Lucas Series

Abstract

The sequence, whose initial condition is 2 and 1, obtained by summing the two terms preceding it, is called the Lucas sequence. The terms of this series continue as 2, 1, 3, 4, 7, 11, 18, 29, ... respectively. The features of the Lucas sequence have been studied in many projects in the literature and many studies have been done on Lucas series in applied sciences. Cryptology is the science that deals with encrypting data, transferring it securely from one point to another, and converting the encrypted data to the previous one. It includes cryptography and cryptoanalysis. Different encryption-decryption methods have been developed to ensure the security of the data from the past to the present. Some of these are Caesar, Affine, Vigenere and RSA. There are two types of encryption systems in cryptology. The first one is symmetric (secret key) encryption and the another one is asymmetric (public key) encryption. In this study; using the features of the Lucas sequence, studies on cryptology, which deals with the correct encryption, transfer and decryption of data, have been carried out and an example of cryptology algorithm has been given. With Lucas cipher, the letters in the alphabet and the space character are each mapped to the terms of the Lucas sequence. Later, starting from the first term of the Lucas sequence, the encryption was strengthened by adding Lucas terms. As a result, the text to be encrypted has been turned into a symbolic representation of the numbers. Then, the necessary information for deciphering the text which is encrypted with numbers is given.

Keywords

• Lucas numbers
• cryptology
• information security
• cryptography

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