Paper 2011/039
Fast point quadrupling on elliptic curves
Duc-Phong Le and Binh P Nguyen
Abstract
Ciet et al.(2006) proposed an elegant method for trading inversions for multiplications when computing [2] P+Q from two given points P and Q on elliptic curves of Weierstrass form. Motivated by their work, this paper proposes a fast algorithm for computing [4] P with only one inversion in affine coordinates. Our algorithm that requires 1I+ 8S+ 8M, is faster than two repeated doublings whenever the cost of one field inversion is more expensive than the cost of four field multiplications plus four field squarings (ie I> 4M+ 4S). It saves one field multiplication and one field squaring in comparison with the Sakai-Sakurai method (2001). Even better, for special curves that allow" a= 0"(or" b= 0") speedup, we obtain [4] P in affine coordinates using just 1I+ 5S+ 9M (or 1I+ 5S+ 6M, respectively).
Note: correct publication information.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Minor revision. Third Symposium on Information and Communication Technology
- DOI
- 10.1145/2350716.2350750
- Keywords
- Elliptic curve cryptographyfast arithmeticaffine coordinates
- Contact author(s)
- le duc phong @ gmail com
- History
- 2020-12-30: last of 6 revisions
- 2011-01-21: received
- See all versions
- Short URL
- https://ia.cr/2011/039
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2011/039,
author = {Duc-Phong Le and Binh P Nguyen},
title = {Fast point quadrupling on elliptic curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2011/039},
year = {2011},
doi = {10.1145/2350716.2350750},
url = {https://eprint.iacr.org/2011/039}
}
