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

Leibo Li; Mingqiang Wang; Zhanjiang Xia

Paper 2009/573

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

Leibo Li, 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.

Metadata

Available format(s): PDF
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): llbsdu @ 163 com
History: 2009-12-09: revised; 2009-12-01: received; See all versions
Short URL: https://ia.cr/2009/573
License: CC BY

BibTeX

@misc{cryptoeprint:2009/573,
      author = {Leibo Li and Mingqiang Wang and Zhanjiang Xia},
      title = {New Addition Operation and Its Application for Scalar Multiplication on Hessian Curves over Prime Fields},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/573},
      year = {2009},
      url = {https://eprint.iacr.org/2009/573}
}