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An algorithm for solving the discrete log problem on hyperelliptic curves

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (2000) 1807 19-34
DOI: 10.1007/3-540-45539-6_2
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Abstract

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.

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Gaudry, P. (2000). An algorithm for solving the discrete log problem on hyperelliptic curves. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1807, pp. 19–34). Springer Verlag. https://doi.org/10.1007/3-540-45539-6_2

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