Öz
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.
Anahtar Kelimeler
Kaynakça
- [1] D. Kahn, The Codebreakers, rev. sub. ed., New York, USA: Scribner Publishing, 1996.
- [2] S. Yılmaz, O. Salcan, Siber Uzayda Güvenlik ve Türkiye, 1st ed., İstanbul, Turkey: Milenyum Publishing, 2008.
- [3] National Research Institute of Electronics and Cryptology, TÜBİTAK, [Online]. Available: https://uekae.bilgem.tubitak.gov.tr/tr/kurumsal/tarihce Accessed: 1 May, 2020,
- [4] H. Kodaz, F. M. Botsalı, “Simetrik ve asimetrik şifreleme algoritmalarının karşılaştırılması,” Journal of Selcuk-Technic, vol. 9, pp. 10 – 23, 2010.
- [5] E. Yeşilbaş, “Cebirsel kriptoloji yöntemleri ve bazı uygulamaları,” MSc Thesis, Department of Mathematics, Recep Tayyip Erdoğan University, Rize, Turkey, 2016.
- [6] J. S. Kraft, L. C. Washington, An Introduction to Number Theory with Cryptography, 2nd ed., Broken Sound Parkway, Northwestern United States: Chapman and Hall/CRC Press, Taylor & Francis Group, 2018.
- [7] D. R. Stinson, Cryptography Theory and Practise, 3rd ed., London, UK: Chapman & Hall/CRC Press Taylor & Francis Group, 2006.
- [8] D. R. Stinson, Cryptography Theory and Practice, New York, USA: Chapman & Hall / CRC, 2002.
- [9] Data Encryption Standard, Federal Information Processing Standards Publication 46-1, National Institute of Standards and Technology 1988.
- [10] R. A. Mollin, An Introduction to Cryptography, Boca Raton, New York, London, Chapman and Hall/CRC, 2006
- [12] R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, 1st ed., 5 Toh Tuck Link, Singapore: World Scientific Publishing, 1997.
- [13] S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section, Theory and Applications, Chichester, UK: Ellis Horwood Ltd. Pub., 1989.
- [14] T. Koshy, Fibonacci and Lucas Numbers with Applications, New York, USA, Toronto, Canada: John Wiley & Sons, Proc., 2001.
- [15] P. Ribenboim, W. L. McDaniel, My Numbers, My Friends, New York, USA: Springer – Verlag Publishing, 2000.
- [16] T. Nagell, Introduction to Number Theory, 2nd ed., New York, USA: W. C. Brown Publisher, 1989.
- [17] M. Basu, B. Prasad, “The Generalized Relations Among the Code Elements for Fibonacci Coding Theory,” Chaos Solitons Fractals, vol. 41, no. 5, pp. 2517-2525, 2019.
- [18] S. Prajapat, A. Jain, R. S. Thakur, “A Novel Approach for Information Security with Automatic Variable Key Using Fibonacci Q-Matrix,” IJCCT, vol. 3, no. 3, pp. 54–57, 2012.
- [19] B. Prasad, “Coding Theory on Lucas p Numbers,” Discrete Mathematics, Algorithms and Applications, vol. 8, no. 4, 2016.
- [20] A. Stakhov, V. Massingue, A. Sluchenkov, “Introduction into Fibonacci Coding and Cryptography”, Osnova, Kharkov, 1999.
- [21] P. Stakhov, “Fibonacci Matrices, a Generalization of the Cassini Formula and a New Coding Theory,” Chaos Solitons Fractals, vol. 30, no. 1, pp. 56–66, 2006.
Öz
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.
Anahtar Kelimeler
Kaynakça
- [1] D. Kahn, The Codebreakers, rev. sub. ed., New York, USA: Scribner Publishing, 1996.
- [2] S. Yılmaz, O. Salcan, Siber Uzayda Güvenlik ve Türkiye, 1st ed., İstanbul, Turkey: Milenyum Publishing, 2008.
- [3] National Research Institute of Electronics and Cryptology, TÜBİTAK, [Online]. Available: https://uekae.bilgem.tubitak.gov.tr/tr/kurumsal/tarihce Accessed: 1 May, 2020,
- [4] H. Kodaz, F. M. Botsalı, “Simetrik ve asimetrik şifreleme algoritmalarının karşılaştırılması,” Journal of Selcuk-Technic, vol. 9, pp. 10 – 23, 2010.
- [5] E. Yeşilbaş, “Cebirsel kriptoloji yöntemleri ve bazı uygulamaları,” MSc Thesis, Department of Mathematics, Recep Tayyip Erdoğan University, Rize, Turkey, 2016.
- [6] J. S. Kraft, L. C. Washington, An Introduction to Number Theory with Cryptography, 2nd ed., Broken Sound Parkway, Northwestern United States: Chapman and Hall/CRC Press, Taylor & Francis Group, 2018.
- [7] D. R. Stinson, Cryptography Theory and Practise, 3rd ed., London, UK: Chapman & Hall/CRC Press Taylor & Francis Group, 2006.
- [8] D. R. Stinson, Cryptography Theory and Practice, New York, USA: Chapman & Hall / CRC, 2002.
- [9] Data Encryption Standard, Federal Information Processing Standards Publication 46-1, National Institute of Standards and Technology 1988.
- [10] R. A. Mollin, An Introduction to Cryptography, Boca Raton, New York, London, Chapman and Hall/CRC, 2006
- [12] R. A. Dunlap, The Golden Ratio and Fibonacci Numbers, 1st ed., 5 Toh Tuck Link, Singapore: World Scientific Publishing, 1997.
- [13] S. Vajda, Fibonacci & Lucas Numbers, and the Golden Section, Theory and Applications, Chichester, UK: Ellis Horwood Ltd. Pub., 1989.
- [14] T. Koshy, Fibonacci and Lucas Numbers with Applications, New York, USA, Toronto, Canada: John Wiley & Sons, Proc., 2001.
- [15] P. Ribenboim, W. L. McDaniel, My Numbers, My Friends, New York, USA: Springer – Verlag Publishing, 2000.
- [16] T. Nagell, Introduction to Number Theory, 2nd ed., New York, USA: W. C. Brown Publisher, 1989.
- [17] M. Basu, B. Prasad, “The Generalized Relations Among the Code Elements for Fibonacci Coding Theory,” Chaos Solitons Fractals, vol. 41, no. 5, pp. 2517-2525, 2019.
- [18] S. Prajapat, A. Jain, R. S. Thakur, “A Novel Approach for Information Security with Automatic Variable Key Using Fibonacci Q-Matrix,” IJCCT, vol. 3, no. 3, pp. 54–57, 2012.
- [19] B. Prasad, “Coding Theory on Lucas p Numbers,” Discrete Mathematics, Algorithms and Applications, vol. 8, no. 4, 2016.
- [20] A. Stakhov, V. Massingue, A. Sluchenkov, “Introduction into Fibonacci Coding and Cryptography”, Osnova, Kharkov, 1999.
- [21] P. Stakhov, “Fibonacci Matrices, a Generalization of the Cassini Formula and a New Coding Theory,” Chaos Solitons Fractals, vol. 30, no. 1, pp. 56–66, 2006.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 29 Mayıs 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 9 Sayı: 3 - Ek Sayı |
