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Index calculus with double large prime variation for curves of small genus with cyclic class group

Claus Diem
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Abstract

We present an index calculus algorithm with double large prime variation which lends itself well to a rigorous analysis. Using this algorithm we prove that for fixed genus $g \geq 2$, the discrete logarithm problem in degree 0 class groups of non-singular curves over finite fields $\mathbb{F}_q$ can be solved in an expected time of $\tilde{O}(q^{2-2/g})$, provided that the curve is given by a plane model of bounded degree and the degree 0 class group is cyclic. The result generalizes a previous result for hyperelliptic curves given by an imaginary Weierstraß equation obtained by Gaudry, Thomé, Thériault and the author.

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Claus Diem. 2006-06-23. Index calculus with double large prime variation for curves of small genus with cyclic class group. https://arxiv.org/abs/math/0606607

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