Cubic Curves, Finite Geometry and Cryptography

Details Cubic Curves, Finite Geometry and Cryptography Cubic Curves, Finite Geometry and Cryptography

2011-07-21

arxiv.org/abs/1107.4387v1

Mathematics

Number Theory

This is a version of our article to appear in Acta Applicandae Mathematicae. In this version, we have corrected a sentence in

Scientific paper

10.1007/s10440-011-9620-z

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.

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