Jorge Estrada-Sarlabous; Jean-Pierre Cherdieu; Ernesto Reinaldo-Barreiro;
Rolf-Peter Holzapfel
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976), 21
MSC 2000
-
14H45 Special curves and curves of low genus
Abstract
In
this paper we present a new family of Jacobian Varieties defined over finite
fields that provides many elements whose group structure is suitable for
cryptosystems based on the intractability of the discrete logarithm problem.
Their security against several know attacks and the efficiency (and effectiveness)
of the most important algorithms of the corresponding cryptosystems are
discussed.
Keywords:Picard
Curves, Jacobian Varieties, Addition Law, Discrete Logarithm, Complex Multiplication