Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Division Polynomials for Jacobi Quartic Curves

Published

Author(s)

Dustin Moody

Abstract

In this paper we fi nd division polynomials for Jacobi quartics. These curves are an alternate model for elliptic curves to the more common Weierstrass equation. Division polynomials for Weierstrass curves are well known, and the division polynomials we fi nd are analogues for Jacobi quartics. Using the division polynomials, we show recursive formulas for the n-th multiple of a point on the quartic curve. As an application, we prove a type of mean-value theorem for Jacobi quartics. These results can be extended to other models of elliptic curves, namely, Jacobi intersections and Huff curves.
Proceedings Title
Proceedings of ISSAC 2011
Conference Dates
June 8-11, 2011
Conference Location
San Jose, CA
Conference Title
International Symposium on Symbolic and Algebraic Computation

Keywords

algorithms, elliptic curves, division polynomials

Citation

Moody, D. (2011), Division Polynomials for Jacobi Quartic Curves, Proceedings of ISSAC 2011, San Jose, CA, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=908330 (Accessed April 18, 2024)
Created June 13, 2011, Updated June 2, 2021