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|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|
|PDF version:||Click here to retrieve PDF version of paper (401KB)|