On Lucas Sequences Computation
Aleksey Koval
DOI: 10.4236/ijcns.2010.312128   PDF    HTML     6,220 Downloads   10,640 Views   Citations


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].

Share and Cite:

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.


[1] M. Joye and J. J. Quisquater, “Efficient Computation of Full Lucas Sequences,” Electronics Letters, Vol. 32, No. 6, 1996, pp. 537-538.
[2] P. Smith, “Cryptography without Exponentiation,” Dr. Dobb’s Journal, Vol. 19, No. 4, April 1994, pp. 26-30.
[3] P. Smith, “Luc Public Key Encryption: A Secure Alternative to RSA,” Dr. Dobb’s Journal, Vol. 18, No. 1, 1993, pp. 44-49.
[4] S. M. Yen and C. S. Laih, “Fast Algorithms for Luc Digital Signature Computation,” IEE Proceedings: Computers and Digital Techniques, Vol. 142, No. 2, 1995, pp. 165-169.
[5] C.-T. Wang, C.-C. Chang and C.-H. Lin, “A Method for Computing Lucas Sequences,” Computers & Mathematics with Applications, Vol. 38, No. 11-12, 1999, pp. 187- 196.
[6] M. Othman, E. M. Abulhirat, Z. M. Ali, M. R. M. Said and R. Johari, “A New Computation Algorithm for a Cryptosystem Based on Lucas Functions,” Journal of Computer Science, Vol. 4, No. 12, 2008, pp. 1056-1060.
[7] A. El-Kassar, M. Rizk, N. Mirza and Y. Awad, “El-Gamal Public-Key Cryptosystem in the Domain of Gaussian Integers,” International Journal of Applied Mathematics, Vol. 7, No. 4, 2001, pp. 405-412.
[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.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.