Some Notes on Odd or Even Indexed Fibonacci And Lucas Sequences

Year 2019, Volume: 23 Issue: 5, 929 - 933, 01.10.2019

Alparslan Kargın Emre Kişi , Halim Özdemir

https://izlik.org/JA47ZS23YX

Abstract

The uniqueness of the sum of the elements of finite subsets of the odd or
even indexed Fibonacci and Lucas sequences are proved. Moreover, it is shown
that the odd or even indexed Fibonacci and Lucas sequences are superincreasing
sequences. Furthermore, by utilizing the uniqueness properties established a
new cryptology method is presented and exemplified.

Keywords

Fibonacci numbers , Lucas numbers , odd index , even index

References

• Merkle-Hellman kripto sistemi – https://tr.vikipedi.org, Erişim Tarihi: 20.11.2018
• Koshy, T., 2001, Fibonacci and Lucas numbers with applications, John Wiley & Sons, New York-Toronto
• Vajda, S., 1989, Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications, Courier CorporationBrannan, D.A., 2006, A First Course in Mathematical Analysis, Cambridge University Press
• Mollin, R.A., 2007, An Introduction to Cryptography, Chapman&Hall/CRC, Boca Raton
• Uçar, S., Taş, N., Özgür, N.Y., A new cryptography model via Fibonacci and Lucas numbers, arXiv: 1709.10355 [cs.CR].
• N Taş, S Uçar, N.Y. Özgür, Ö.Ö. Kaymak, 2018, A new coding/decoding algorithm using Fibonacci numbers, Discrete Mathematics, Algorithms and Applications 10 (02)
• M. Basu, B. Prasad, The generalized relations among the code elements for Fibonacci coding theory, Chaos Solitons Fractals 41 (2009), no. 5, 2517–2525
• S. Prajapat, A. Jain, R. S. Thakur, A Novel Approach For Information Security With Automatic Variable Key Using Fibonacci Q-Matrix, IJCCT 3 (2012), no. 3, 54–57.
• A. Stakhov, V. Massingue, A. Sluchenkov, Introduction into Fibonacci Coding and Cryptography, Osnova, Kharkov (1999).A. P. Stakhov, Fibonacci matrices, a generalization of the Cassini formula and a new coding theory, Chaos Solitons Fractals 30 (2006), no. 1, 56–66.