Paper Info
Title
Sole Inversion Precomputation For Elliptic Curve Scalar Multiplications
Abstract
This paper presents a new approach to precompute points [3]P, [5]1P, ..., [2k-1]P, for some k >= 2 on an elliptic curve over F-p. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.
Year
DOI
Venue
2010
10.1587/transfun.E93.A.1140
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES
Keywords
Field
DocType
affine coordinates, elliptic curve cryptosystem, precomputation, scalar multiplication
Discrete mathematics,Theoretical computer science,Montgomery curve,Elliptic curve point multiplication,Jacobian curve,Hessian form of an elliptic curve,Edwards curve,Schoof's algorithm,Counting points on elliptic curves,Mathematics,Tripling-oriented Doche–Icart–Kohel curve
Journal
Volume
Issue
ISSN
E93A
6
0916-8508
Citations 
PageRank 
References 
0
0.34
9
Authors
2
Name
Order
Citations
PageRank
Erik Dahmen118610.71
Katsuyuki Okeya244738.47