Cubic curves, finite geometry and cryptography

Hirschfeld, J, Bruen, A and Wehlau, D (2011) Cubic curves, finite geometry and cryptography. Acta Applicandae Mathematicae, 115 (3). pp. 265-278. ISSN 1572-9036

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: James Hirschfeld
Date Deposited: 06 Feb 2012 19:32
Last Modified: 09 Jul 2012 14:26
URI: http://sro.sussex.ac.uk/id/eprint/21188
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