Divison Polynomials for Alternate Models of Elliptic Curves

Dustin Moody

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.

Available format(s)
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
elliptic curvesdivision polynomials
Contact author(s)
dbmoody25 @ gmail com
History
Short URL
https://ia.cr/2010/630

CC BY

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},
note = {\url{https://eprint.iacr.org/2010/630}},
url = {https://eprint.iacr.org/2010/630}
}

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