Cubic Curves, Finite Geometry and Cryptography

被引：0

作者：

A. A. Bruen

J. W. P. Hirschfeld

D. L. Wehlau

机构：

[1] University of Calgary,Department of Electrical and Computer Engineering

[2] University of Sussex,Department of Mathematics

[3] Royal Military College,Department of Mathematics and Computer Science

来源：

Acta Applicandae Mathematicae | 2011年 / 115卷

关键词：

Cubic curves; Group law; Non-singularity; Elliptic curve cryptography; Finite geometries;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Some geometry on non-singular cubic curves, mainly over finite fields, is surveyed. Such a curve has 9,3,1 or 0 points of inflexion, and cubic curves are classified accordingly. The group structure and the possible numbers of rational points are also surveyed. A possible strengthening of the security of elliptic curve cryptography is proposed using a ‘shared secret’ related to the group law. Cubic curves are also used in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.

引用

页码：265 / 278

页数：13

共 10 条

[1] Alderson T.L.(2007)Maximum distance separable codes and arcs in projective spaces J. Comb. Theory, Ser. A 114 1101-1117
[2] Bruen A.A.(1984)Arcs and multiple blocking sets Comb. Symp. Math. 28 15-29
[3] Silverman R.(2002)Geometry and group structures of some cubics Forum Geom. 2 135-146
[4] Bruen A.A.(1987)A note on elliptic curves over a finite field Math. Comput. 49 201-304
[5] Lang F.(1987)Nonsingular plane cubic curves over finite fields J. Comb. Theory, Ser. A 46 183-211
[6] Rück H.(1987)On the completeness of certain plane arcs Eur. J. Comb. 8 453-456
[7] Schoof R.(1988)A note on elliptic curves over finite fields Bull. Soc. Math. Fr. 116 455-458
[8] Voloch J.F.(1969)Abelian varieties over finite fields Ann. Sci. Ecole Norm. Super. 4 521-560
[9] Voloch J.F.(undefined)undefined undefined undefined undefined-undefined
[10] Waterhouse W.C.(undefined)undefined undefined undefined undefined-undefined

← 1 →