Paper 2010/630 Original: eprint.iacr.org/2010/630 ↗
Divison Polynomials for Alternate Models of Elliptic Curves
Abstract
In this paper we find division polynomials for Huff curves, Jacobi quartics, and Jacobi intersections. These curves are alternate models for elliptic curves to the more common Weierstrass curve. Division polynomials for Weierstrass curves are well known, and the division polynomials we find are analogues for these alternate models. Using the division polynomials, we show recursive formulas for the $n$-th multiple of a point on each curve. As an application, we prove a type of mean-value theorem for Huff curves, Jacobi quartics and Jacobi intersections.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2010-12-13: last updated
- 2010-12-13: published
- Short URL
- https://ia.cr/2010/630
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2010/630,
author = {Dustin Moody},
title = {Divison Polynomials for Alternate Models of Elliptic Curves},
howpublished = {Cryptology {ePrint} Archive, Paper 2010/630},
year = {2010},
url = {https://eprint.iacr.org/2010/630}
}