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Publication Citation: Division Polynomials for Jacobi Quartic Curves

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Author(s): Dustin Moody;
Title: Division Polynomials for Jacobi Quartic Curves
Published: June 13, 2011
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.
Conference: International Symposium on Symbolic and Algebraic Computation
Proceedings: Proceedings of ISSAC 2011
Pages: pp. 265 - 272
Location: San Jose, CA
Dates: June 8-11, 2011
Keywords: algorithms, elliptic curves, division polynomials
Research Areas: Math
PDF version: PDF Document Click here to retrieve PDF version of paper (401KB)