An algorithm for solving the discrete log problem on hyperelliptic curves

Pierrick Gaudry (1)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We present an index-calculus algorithm for the computation of discrete logarithms in the Jacobian of hyperelliptic curves defined over finite fields. The complexity predicts that it is faster than the Rho method for genus greater than 4. To demonstrate the efficiency of our approach, we describe our breaking of a cryptosystem based on a curve of genus 6 recently proposed by Koblitz.

Domaines: Cryptographie et sécurité [cs.CR]

Pierrick Gaudry. An algorithm for solving the discrete log problem on hyperelliptic curves. Eurocrypt, 2000, Bruges, Belgium. pp.19-34, ⟨10.1007/3-540-45539-6_2⟩. ⟨inria-00512401⟩