MODIFIED METHOD FOR ELIPTIC CURVE SCALAR POINT MULTIPLICATION OVER GF(P)

Authors

  • I. A. Dychka NTUU «KPI», Kyiv, Ukraine, Ukraine
  • M. V. Onai NTUU «KPI», Kyiv, Ukraine, Ukraine
  • T. P. Drozda NTUU «KPI», Kyiv, Ukraine, Ukraine

DOI:

https://doi.org/10.15588/1607-3274-2016-2-12

Keywords:

computers, elliptic curve cryptography, scalar multiplication, precomputation table, elliptic curve, finite field.

Abstract

During development of many cryptographic applications, we need to perform fast algorithms of scalar multiplication. In this paper we
propose a modified window method of elliptic curve point multiplication over the GF(p). The object of the research are the processes of
performing operations in elliptic cryptosystems. The subject of the research are the methods and the algorithms of elliptic curve point
multiplication over the GF(p). The goal of the research is to develop and optimize the methods and the algorithms of performing elliptic curve
point multiplication operation over the GF(p) for improving the time characteristics. Existing and proposed algorithms were implemented
with C# programming language and integrated development environment – Visual Studio 2013. In this article we did an investigation of the existing algorithms of elliptic curve point multiplication and developed three versions of the window method LR-algorithm and generalized modification. Experimental studies of the implemented algorithms were performed according to the proposed methodology, which allows us to explore the impact of the multiplier and elliptical curve point on the results of the research. The experimental research of window methods and their modifications showed an increase speed of the modified algorithms compared to the existing algorithms in average of 13%.

References

Miller V. Use of elliptic curves in cryptography / V. Miller // Lecture Notes in Computer Science. Advances in cryptology – CRYPTO 85. – Springer, 1986. – P. 417–426. 10.1007/3-540-39799-X_31 2. Koblitz N. Introduction to Elliptic Curves and Modular Forms / Neal Koblitz. – New York : Springer, 1984. – 248 p. 10.1007/978-1-4684-0255-1 3. Knuth, D. The Art of Computer Programming. Volume 2 Seminumerical Algorithms, Third Edition / D. E. Knuth. – Massachusetts: Addison-Wesley, 1997. – 762 p. 4. Hankerson D. Guide to Elliptic Curve Cryptography / D. Hankerson, A. Menezes, S. Vanstone. – New York : Springer, 2004. – 311 p. 5. Crandall R. Prime Numbers. A Computational Perspective. Second Edition / Richard Crandall, Carl Pomerance. – New York : Springer, 2005. – 604 p. 10.1007/978-1-4684-9316-0 6. Rivain M. Fast and Regular Algorithms for Scalar Multiplication over Elliptic Curves / Matthieu Rivain. – IACR Cryptology ePrint Archive, 2011. – 338 p. 7. Болотов, А. А. Алгоритмические основы эллиптической криптографии / А. А. Болотов. – М. : Изд-во, 2004. – 499 с. 8. Elliptic Curve Point Multiplication [Electronic resource] // December 31, 2015: Proceedings. – Mode of access: https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication. – Last access: 2016. – Title from the screen. 9. Pathak H. Speeding Up Computation of Scalar Multiplication in Elliptic Curve Cryptosystem / H. Pathak, M. Sanghi // International Journal on Computer Science and Engineering. – 2010. – No. 04. – P. 1024–1028

Downloads

How to Cite

Dychka, I. A., Onai, M. V., & Drozda, T. P. (2016). MODIFIED METHOD FOR ELIPTIC CURVE SCALAR POINT MULTIPLICATION OVER GF(P). Radio Electronics, Computer Science, Control, (2). https://doi.org/10.15588/1607-3274-2016-2-12

Issue

No. 2 (2016): Radio Electronics, Computer Science, Control

Section

Progressive information technologies

License

Copyright (c) 2016 I. A., Dychka, M. V. Onai, T. P. Drozda

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Creative Commons Licensing Notifications in the Copyright Notices

The journal allows the authors to hold the copyright without restrictions and to retain publishing rights without restrictions.

The journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles.

The journal allows to reuse and remixing of its content, in accordance with a Creative Commons license СС BY -SA.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License CC BY-SA that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.