Division Polynomials for Jacobi Quartic Curves

Moody, Dustin

doi:https://doi.org/10.1145/1993886.1993927

Conference Proceedings

Division Polynomials for Jacobi Quartic Curves

Documentation

Published: June 13, 2011

Author(s)

Dustin Moody

Conference

Name: 36th International Symposium on Symbolic and Algebraic Computation (ISSAC '11)
Dates: June 8-11, 2011
Location: San Jose, California, United States
Citation: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (ISSAC '11), pp. 265-272

Announcement

Abstract

In this paper we find 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 find 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.

Keywords

algorithms; elliptic curves; division polynomials

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Documentation

Publication:
Conference Proceedings (DOI)

Supplemental Material:
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Document History:
06/13/11: Conference Proceedings (Final)