Division Polynomials for Jacobi Quartic Curves

被引：0

作者：

Moody, Dustin ^{[1
]}

机构：

[1] Natl Inst Stand & Technol, Gaithersburg, MD 20899 USA

来源：

ISSAC 2011: PROCEEDINGS OF THE 36TH INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION | 2011年

关键词：

Algorithms; Elliptic Curves; Division Polynomials; ELLIPTIC CURVE;

D O I：

暂无

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we find division polynomials for Jacobi guartics. 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.

引用

页码：265 / 272

页数：8

共 24 条

[1] Abel N.H., 1881, OEUVRES COMPLETES
[2] [Anonymous], AUSTR INF SEC C AISC
[3] Bernstein DJ, 2008, LECT NOTES COMPUT SC, V5023, P389
[4] Billet O, 2003, LECT NOTES COMPUT SC, V2643, P34
[5] SEQUENCES OF NUMBERS GENERATED BY ADDITION IN FORMAL GROUPS AND NEW PRIMALITY AND FACTORIZATION TESTS
CHUDNOVSKY, DV
CHUDNOVSKY, GV
[J]. ADVANCES IN APPLIED MATHEMATICS, 1986, 7 (04) : 385 - 434
[6] A normal form for elliptic curves
Edwards, Harold M.
[J]. BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 44 (03) : 393 - 422
[7] Feng R., 2009, MEAN VALUE FORMULA E
[8] Feng R., 2010, ELLIPTIC CURVES HUFF
[9] Giorgi P., 2009, SPIE, p7444N
[10] Hitt L., 2008, DIVISION POLYNOMIALS

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