Cubic Curves, Finite Geometry and Cryptography View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2011-09

AUTHORS

A. A. Bruen, J. W. P. Hirschfeld, D. L. Wehlau

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 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. More... »

PAGES

265-278

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10440-011-9620-z

DOI

http://dx.doi.org/10.1007/s10440-011-9620-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1040030583


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