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Cubic curves, finite geometry and cryptography

journal contribution
posted on 2023-06-07, 23:19 authored by J Hirschfeld, A Bruen, D Wehlau
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 used also in a new way to construct sets of points having various combinatorial and geometric properties that are of particular interest in finite Desarguesian planes.

History

Publication status

  • Published

Journal

Acta Applicandae Mathematicae

ISSN

1572-9036

Publisher

Springer Verlag

Issue

3

Volume

115

Page range

265-278

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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