Index calculus algorithm for non-planar curves

In this paper, we develop a variation of the index calculus algorithm using non-planar models of non-hyperelliptic curves of genus g. Using canonical model of degree 2g- 2in the projective space of dimension g- 1, intersections with hyperplanes and following similar ideas to those of Diem (who used intersections with lines on planar models), we obtain an upper bound of O (q(2- 2/g-1+ epsilon)) for the computation of discrete logarithms for all non-hyperelliptic curves of genus gdefined over the finite field F-q. This asymptotic cost is essentially the same as Diem's, but our algorithm offers several advantages over Diem's, including a constant speed-up. (c) 2023 Elsevier Inc. All rights reserved.