Skip to main content

NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.

Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.

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 October 2, 2025)

Issues

If you have any questions about this publication or are having problems accessing it, please contact [email protected].

Created June 13, 2011, Updated June 2, 2021
Was this page helpful?