Criptografia usando curvas hiperelipticas

AUTOR(ES)

Alonso Sepulveda Castellanos

DATA DE PUBLICAÇÃO

2004

RESUMO

In 1989, Koblitz introduced by the first time the hyperelliptic cryptosystems, which based their security on the resolution of the discrete logarithm problem on the Jacobian of a hyperelliptic curve. In this article, Koblitz generalized the algorithm to add points in the Jacobian presented by Cantor in 1987. At this dissertation, we study properties of the hyperelliptic curves and its Jacobians, looking at the implementation of public-key cryptosystems. AIso, we present Cantor s algorithm to add points in the Jacobian (This is important to the efficiency of the cryptosystem) and we show an algorithm to attack the discrete logarithm problem on theses groups (The intractability of this problem is essential for the security of the cryptosystem)

ASSUNTO(S)

criptografia logaritmos curvas algebricas

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