Fast point quadrupling on elliptic curves

Duc-Phong Le; Binh P Nguyen

Paper 2011/039 Original: eprint.iacr.org/2011/039 ↗

Fast point quadrupling on elliptic curves

Duc-Phong Le

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).

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
History: 2020-12-30: last updated; 2011-01-21: published
Short URL: https://ia.cr/2011/039
License: https://creativecommons.org/licenses/by/4.0/

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},
      url = {https://eprint.iacr.org/2011/039}
}