Welcome to the resource topic for 2005/222
Title:
Efficient Comb Elliptic Curve Multiplication Methods Resistant to Power Analysis
Authors: Min Feng, Bin B. Zhu, Maozhi Xu, Shipeng Li
Abstract:Elliptic Curve Cryptography (ECC) has found wide applications in
smart cards and embedded systems. Point multiplication plays a
critical role in ECC. Many efficient point multiplication methods
have been proposed. One of them is the comb method which
is much more efficient than other methods if precomputation points
are calculated in advance or elsewhere. Unfortunately, Many
efficient point multiplication methods including the comb method are
vulnerable to power-analysis attacks. Various algorithms to make
elliptic curve point multiplication secure to power-analysis attacks
have been proposed recently, such as the double-and-add-always
method, Möller’s window method, Okeya
et al.'s odd-only window method, and Hedabou et al.'s
comb method. In this paper, we first present a novel comb
recoding algorithm which converts an integer to a sequence of
signed, odd-only comb bit-columns. Using this recoding algorithm, we
then present several comb methods, both Simple Power Analysis
(SPA)-nonresistant and SPA-resistant, for point multiplication.
These comb methods are more efficient than the original
SPA-nonresistant comb method and Hedabou et al.'s SPA-resistant comb
method. Our comb methods inherit the advantage of a comb method,
running much faster than Möller’s window method and Okeya et
al.'s odd-only window method, as well as other window methods such
as the efficient signed m-ary window method, if only the
evaluation phase is taken into account. Combined with randomization
projective coordinates or other randomization techniques and certain
precautions in selecting elliptic curves and parameters, our
SPA-resistant comb methods are resistant to all power-analysis
attacks.
ePrint: https://eprint.iacr.org/2005/222
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