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Comments on "Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation”
April 2012 (vol. 61 no. 4)
pp. 591-592
ASCII Text
x 
 
Mun-Kyu Lee, "Comments on "Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation”," IEEE Transactions on Computers, vol. 61, no. 4, pp. 591-592, April, 2012.
 
 
BibTex
x
 
@article{ 10.1109/TC.2011.109,
author = {Mun-Kyu Lee},
title = {Comments on "Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation”},
journal ={IEEE Transactions on Computers},
volume = {61},
number = {4},
issn = {0018-9340},
year = {2012},
pages = {591-592},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2011.109},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Comments on "Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation”
IS - 4
SN - 0018-9340
SP591
EP592
EPD - 591-592
A1 - Mun-Kyu Lee,
PY - 2012
KW - Elliptic curve cryptography
KW - Koblitz curves
KW - sublinearity.
VL - 61
JA - IEEE Transactions on Computers
ER -
 
Mun-Kyu Lee, Inha University , Incheon
In 2008, Dimitrov et al. proposed a point multiplication algorithm on Koblitz curves using multiple-base expansions. They claimed that their algorithm is the first provably sublinear point multiplication algorithm on Koblitz curves. In this paper, we show that the well-known \tau-adic NAF method is already sublinear and also guarantees a better average performance.

[1] N. Koblitz, "CM-Curves with Good Crytographic Properties," Proc. CRYPTO 91, pp. 279-287, Springer, 1992.
[2] V. Dimitrov, K. Järvinen, M. Jacobson, W. Chan, and Z. Huang, "Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation," IEEE Trans. Computers, vol. 57, no. 11, pp. 1469-1481, Nov. 2008.
[3] V. Dimitrov, L. Imbert, and P. Mishra, "Efficient and Secure Elliptic Curve Point Multiplication Using Double-Based Chains," Proc. ASIACRYPT 2005, pp. 59-78, Springer, 2005.
[4] J. Solinas, "Efficient Arithmetic on Koblitz Curves," Designs, Codes and Cryptography, vol. 19, pp. 195-249, 2000.
[5] D. Hankerson, A. Menezes, and S. Vanstone, Guide to Elliptic Curve Cryptography. Springer, 2004.
[6] I. Blake, G. Seroussi, and N. Smart, Elliptic Curves in Cryptography. Cambridge Univ. Press, 1999.

Index Terms:
Elliptic curve cryptography, Koblitz curves, sublinearity.
Citation:
Mun-Kyu Lee, "Comments on "Provably Sublinear Point Multiplication on Koblitz Curves and Its Hardware Implementation”," IEEE Transactions on Computers, vol. 61, no. 4, pp. 591-592, April 2012, doi:10.1109/TC.2011.109
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