Criptografia usando curvas hiperelípticas

Abstract

In this work we present some properties of the hyperelliptical curves and their Jacobians, aiming at the implementation of criptossystems of public key. Also we show the algorithm of Cantor to add points in the Jacobian manifold, which is important for the effectiveness of criptossystems, and an algorithm to attack the problem of the discrete logarithms on these groups. The untractability of this problem is essential for the security of criptossystems.