2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114009We 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.Number Theory11Y16; 14G50text