Index Calculus Attack for Hyperelliptic Curves of Small Genus

  • Nicolas Thériault
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2894)


We present a variation of the index calculus attack by Gaudry which can be used to solve the discrete logarithm problem in the Jacobian of hyperelliptic curves. The new algorithm has a running time which is better than the original index calculus attack and the Rho method (and other square-root algorithms) for curves of genus ≥ 3. We also describe another improvement for curves of genus ≥ 4 (slightly slower, but less dependent on memory space) initially mentioned by Harley and used in a number of papers, but never analyzed in details.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Nicolas Thériault
    • 1
  1. 1.University of Toronto 

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