Published: June 13, 2011
Author(s)
Dustin Moody
Conference
Name: 36th International Symposium on Symbolic and Algebraic Computation (ISSAC '11)
Dates: 06/08/2011 - 06/11/2011
Location: San Jose, California, United States
Citation: Proceedings of the 36th International Symposium on Symbolic and Algebraic Computation (ISSAC '11), pp. 265-272
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.
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...
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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.
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Keywords
algorithms; elliptic curves; division polynomials
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