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
Pub Type: Conferences
algorithms, elliptic curves, division polynomials