Uses of second order variant Fibonacci universal code in cryptography

• Autorzy: Basu M. , Das M.
• Języki publikacji: EN

Abstrakty

EN

We know from Zeckendorf’s theorem that every positive integer n has unique representation of the form n =Pl k=1 akF(k), where ak ∈ {0,1} and F(k) is a Fibonacci number such that the string a1a2a3 ... does not contain any consecutive 1’s. In this paper we consider second order variant Fibonacci universal code from Gopala-Hemachandra sequence. Thereby, we describe the uses of this code in cryptography with an illustrative example.

Słowa kluczowe

EN

Fibonacci numbers; Fibonacci coding; GopalaHemachandra sequence; Zeckendorf’s representation; Gopala-Hemachandra code; GH code straight line; cryptography

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2016
• Tom: Vol. 45, no. 2
• Strony: 239--251
• Opis fizyczny: Bibliogr. 8 poz., rys.

Twórcy

autor

Basu M.

• Department of Mathematics, University of Kalyani, Kalyani, W.B., 741235, India

autor

Das M.

• Department of Mathematics, University of Kalyani, Kalyani, W.B., 741235, India

Bibliografia

• [1] Basu, M. and Prasad, B. (2010) Long range variations on the Fibonacci universal code. Journal of Number Theory 130, 1925-1931.
• [2] Das, M., Basu, M. and Bagchi, S. (2016) The Gopala-Hemachandra universal code. Communicated to Professor Gerhard Hiss, Lehrstuhl D fu¨r Mathematik, RWTH Aachen; Editor, Journal of Algebra. Daykin, D.E. (1960) Representation of natural numbers as sums of generalized Fibonacci numbers. J. Lond. Math. Soc. 35, 143-160.
• [3] Elias, P. (1975) Universal codeword sets and representations of the integers. IEEE Trans. Inform. Theory IT 21(2), 194-203.
• [4] Kak, S. (2008)Aristotle and Gautama on logic and physics. arxiv:physics/0505172.
• [5] Kak, S. (2005) Greek and Indian cosmology: Review of early history. In: G.C. Pande (ed.), The Golden Chain. CSC, New Delhi, (2005), arxiv: physics/0303001.
• [6] Kak, S. (2006) The golden mean and the physics of aesthetics. Foarm Magazine 5, 7381, arxiv:physics/0411195.
• [7] Pearce, I.G. (2002) Indian mathematics: Redressing the balance. http://www. history.mcs.st-andrews.ac.uk/history/projects/pearce/index.html. Stinson, Douglas R. (2006) Cryptography Theory and Practice, Third Edition. Chapman & Hall/CRC.
• [8] Thomas, J. H. (2007) Variation on the Fibonacci universal code. arXiv: cs/0701085v2. Zeckendorf, E. (1972) Representation des nombres naturels par une somme des nombres de Fibonacci ou de nombres de Lucas. Bull. Soc. Roy. Sci. Liege 41, 179-182.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).