Division polynomials for Jacobi quartic curves

Authors:
Dustin Moody
Affiliations:
National Institute of Standards and Technology, Gaithersburg, MD, USA
Venue:
Proceedings of the 36th international symposium on Symbolic and algebraic computation
Year:
2011

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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.