The Emergence of Picard Jacobians in Cryptography

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

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