New Addition Operation and Its Application for Scalar Multiplication on Hessian Curves over Prime Fields.
Leibo Li, Mingqiang Wang, Zhanjiang Xia · IACR Cryptology ePrint Archive · 2009
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 wNAF and fractional wmbNAF, if n = 192 bits and 1I ≈ 30M , scheme 1 can save up to 31M , scheme 2 can save up to 28M with w ≥ 6, where I, M represent the inversion and the multiplication, respectively.