Cubic Curves, Finite Geometry and Cryptography

被引：5

作者：

Bruen, A. A. ^{[2
]}

Hirschfeld, J. W. P. ^{[3
]}

Wehlau, D. L. ^{[1
]}

机构：

[1] Royal Mil Coll Canada, Dept Math & Comp Sci, Kingston, ON K7K 7B4, Canada

[2] Univ Calgary, Dept Elect & Comp Engn, Calgary, AB T2N 1N4, Canada

[3] Univ Sussex, Dept Math, Brighton BN1 9RF, E Sussex, England

来源：

ACTA APPLICANDAE MATHEMATICAE | 2011年 / 115卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

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

D O I：

10.1007/s10440-011-9620-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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：14

共 13 条

[1] Maximum distance separable codes and arcs in projective spaces [J].

Alderson, T. L. ;

Bruen, A. A. ;

Silverman, R. .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2007, 114 (06) :1101-1117

[2]

[Anonymous], ANN SCI ECOLE NORM S

[3]

Bruen A., 2005, CRYPTOGRAPHY INFORM

[4]

BRUEN AA, 1984, COMB S MATH, V28, P15

[5]

Fulton W., 1969, Algebraic Curves

[6]

Hirschfeld J.W.P, 1998, PROJECTIVE GEOMETRIE

[7]

Hirschfeld J.W.P., 2008, Princeton Series in Applied Mathematics

[8]

Lang F., 2002, FORUM GEOM, V2, P135

[9]

RUCK H, 1987, MATH COMPUT, V49, P201

[10]

Scafati M. T., 1971, ATT CONV GEOM COMB S, P413

← 1 2 →