A Survey on Algebraic Curve Cryptosystems

Abstract

This paper is a survey on the state-of-the-art of cryptosystems based on the discrete logarithm over algebraic curves on finite fields. The issue on security of these systems against various attacks are firstly considered. Then fast addition algorithms and efficient point counting algorithms for Jacobian varieties of algebraic curves are discussed. These algorithms, although are necessary for construction of algebraic curve cryptosystems, had not been available until very recently. This paper also surveys the known results and the recent advances of related number theoretic algorithms and new developments in construction of algebraic curve cryptosystems.