An algorithm for solving the discrete log problem on hyperelliptic curves. (English) Zbl 1082.94517
Preneel, Bart (ed.), Advances in cryptology - EUROCRYPT 2000. 19th international conference on the theory and application of cryptographic techniques, Bruges, Belgium, May 14–18, 2000. Proceedings. Berlin: Springer (ISBN 3-540-67517-5). Lect. Notes Comput. Sci. 1807, 19-34 (2000).
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.
For the entire collection see [Zbl 0939.00052].
For the entire collection see [Zbl 0939.00052].
