Multivariable extension of m sequences for Fibonacci numbers in cryptography

• Autorzy: Prasad B.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce multivariable extension of m sequences of the Fibonacci number polynomials of order m and a new Sn matrix of order m. Consequently, we discuss various properties of the Sn matrix. The polynomial, derived therefrom, hj, contains m multiple variables which improves the cryptography protection and security, and complexity increases as m increases.

Słowa kluczowe

EN

Fibonacci p-numbers; Fibonacci numbers of order m; golden mean; code matrix

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2015
• Tom: Vol. 44, no. 4
• Strony: 519--526
• Opis fizyczny: Bibliogr. 10 poz., rys., tab.

Twórcy

autor

Prasad B.

• Department of Mathematics Kandi Raj College Kandi - 742137, India

Bibliografia

• 1. Byrd, P.E. (1975) New relations between Fibonacci and Bernoulli numbers. The Fibonacci Quarterly 13, 1, 59–69.
• 2. Cover, T. M. and Thomas, J. A. (1991) Elements of Information Theory. A Wiley-Interscience Publication, New York.
• 3. El Naschie M.S. (2009) The theory of cantorian space time and high energy particle physics. Chaos, Solitons and Fractals 41, 2635-2646.
• 4. Er M.C. (1984) Sums of Fibonacci numbers by matrix methods. The Fibonacci Quarterly 22, 204–207. Esmaeili M., Gulliver T.A., Kakhbod A. (2009) The Golden mean, Fibonacci matrices and partial weakly super-increasing sources. Chaos, Solitons and Fractals 42, 435-440.
• 5. Koshy, Th. (2001) Fibonacci and Lucas Numbers with Applications. J. Wiley & Sons, New York. MacWilliams F. J. and Sloane N. J. A. (1977) Theory of Error-Correcting Codes. North-Holland, Amsterdam.
• 6. Miles EP. (1960) Generalized Fibonacci numbers and associated matrices. Am. Math. Month. 67, 745-752.
• 7. Nalli A., Haukkanen P. (2009) On generalized Fibonacci and Lucas polynomials. Chaos, Solitons and Fractals 42, 3179-3186.
• 8. Prasad B. (2015) Coding theory on h(x) extension of m sequences for Fibonacci numbers. Discrete Mathematics, Algorithms and Applications 7 (2), 1550008–1550025.
• 9. Stakhov A.P. (1977) Introduction into Algorithm Measurement Theory. Soviet Radio, Moscow. (In Russian).
• 10. Stakhov A.P. (2006) Fibonacci matrices, a generalization of the cassini formula and a new coding theory. Chaos, Solitons and Fractals 30, 56-66.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.