Index Calculus Attack for Hyperelliptic Curves of Small Genus
- Cite this paper as:
- Thériault N. (2003) Index Calculus Attack for Hyperelliptic Curves of Small Genus. In: Laih CS. (eds) Advances in Cryptology - ASIACRYPT 2003. ASIACRYPT 2003. Lecture Notes in Computer Science, vol 2894. Springer, Berlin, Heidelberg
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.