Cryptology ePrint Archive: Report 2009/573

New Addition Operation and Its Application for Scalar Multiplication on Hessian Curves over Prime Fields

Leibo Li and Mingqiang Wang and Zhanjiang Xia

Abstract: In this paper, we present a new addition operation on Hessian curves with low cost. It can be applied to resist the side channel attacks for scalar multiplication, and also can be used to compute precomputation points for window-based scalar multiplication on Hessian curves over prime fields. We propose two new precomputation schemes that are shown to achieve the lowest cost among all known methods. By using the fractional $w$NAF and fractional $wmb$NAF, if $n=192$ bits and $1I\approx30M$, scheme 1 can save up to $31M$, scheme 2 can save up to $28M$ with $w\geq 6$, where $I$, $M$ represent the inversion and the multiplication, respectively.

Category / Keywords: implementation /

Date: received 26 Nov 2009, last revised 9 Dec 2009

Contact author: llbsdu at 163 com

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Version: 20091209:083923 (All versions of this report)

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