On Lucas Sequences Computation
Aleksey Koval
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DOI: 10.4236/ijcns.2010.312128   PDF    HTML     6,149 Downloads   10,535 Views   Citations

Abstract

This paper introduces an improvement to a currently published algorithm to compute both Lucas "sister" sequences Vk and Uk. The proposed algorithm uses Lucas sequence properties to improve the running time by about 20% over the algorithm published in [1].

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A. Koval, "On Lucas Sequences Computation," International Journal of Communications, Network and System Sciences, Vol. 3 No. 12, 2010, pp. 943-944. doi: 10.4236/ijcns.2010.312128.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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[8] H. Elkamchouchi, K. Elshenawy and H. Shaban, “Extended RSA Cryptosystem and Digital Signature Schemes in the Domain of Gaussian Integers,” Proceedings of the 8th IEEE International Conference on Communication Systems, Singapore, Vol. 1, 25-28 November 2002, pp. 91-95.
[9] A. Koval and B. S. Verkhovsky, “On Discrete Logarithm Problem for Gaussian Integers,” Proceedings of International Conference on Information Security and Privacy, Orlando, 13-16 July 2009, pp. 79-84.
[10] L. E. Dickson, "Recurring Series; Lucas' Un, Vn," History of the Theory of Numbers: Divisibility and Primality, Dover Publications, New York, Vol. 1, 2005, pp. 393-411.

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