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International Conference on Cryptology and Network Security

CANS 2005: Cryptology and Network Security pp 223–235Cite as

A Note on Signed Binary Window Algorithm for Elliptic Curve Cryptosystems

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 3810))

Abstract

The window algorithms for various signed binary representations have been used to speed up point multiplication on elliptic curves. While there’s been extensive research on the non-adjacent form, little attention has been devoted to non-sparse optimal signed binary representations. In the paper, we prove some properties of non-sparse optimal signed binary representations and present a precise analysis of the non-sparse signed window algorithm. The main contributions are described as follows. Firstly, we attain the lower bound k+1/3 of the expected length of non-sparse optimal signed binary representations of k-bit positive integers. Secondly, we propose a new non-sparse signed window partitioning algorithm. Finally, we analyze Koyama-Tsuruoka’s non-sparse signed window algorithm and the proposed algorithm and compare them with other methods. The upper bound \(\frac{5}{6}\cdot 2^{w-1} -1+\frac{(-1)^{w}}{3}\) of the number of precomputed windows of the non-sparse signed window algorithms is attained.

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Authors and Affiliations

  1. Institute of Network Security, Shandong University, Shanda Nanlu Road, Jinan, 250100, Shandong, R.P. China

    Fanyu Kong & Daxing Li

Authors
  1. Fanyu Kong
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  2. Daxing Li
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University College London,  

    Yvo G. Desmedt

  2. Centre for Advanced Computing - Algorithms and Cryptography Department of Computing, Macquarie University, Australia

    Huaxiong Wang

  3. Centre for Computer and Information Security Research School of Computer Science and Software Engineering, University of Wollongong, Australia

    Yi Mu

  4. Fujian Normal University, 350007, Fuzhou, Fujian, China

    Yongqing Li

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Kong, F., Li, D. (2005). A Note on Signed Binary Window Algorithm for Elliptic Curve Cryptosystems. In: Desmedt, Y.G., Wang, H., Mu, Y., Li, Y. (eds) Cryptology and Network Security. CANS 2005. Lecture Notes in Computer Science, vol 3810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11599371_19

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  • DOI: https://doi.org/10.1007/11599371_19

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30849-2

  • Online ISBN: 978-3-540-32298-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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