## Cryptology ePrint Archive: Report 2010/630

Divison Polynomials for Alternate Models of Elliptic Curves

Dustin Moody

Abstract: In this paper we find division polynomials for Huff curves, Jacobi quartics, and Jacobi intersections. These curves are alternate models for elliptic curves to the more common Weierstrass curve. Division polynomials for Weierstrass curves are well known, and the division polynomials we find are analogues for these alternate models. Using the division polynomials, we show recursive formulas for the $n$-th multiple of a point on each curve. As an application, we prove a type of mean-value theorem for Huff curves, Jacobi quartics and Jacobi intersections.

Category / Keywords: foundations / elliptic curves, division polynomials