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Article Dans Une Revue Finite Fields and Their Applications Année : 2023

Index calculus algorithm for non-planar curves

Nicolas Thériault

Résumé

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-2 in 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)}) for the computation of discrete logarithms for all non-hyperelliptic curves of genus g defined 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.
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Dates et versions

hal-04138475 , version 1 (23-06-2023)

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Roger Oyono, Nicolas Thériault. Index calculus algorithm for non-planar curves. Finite Fields and Their Applications, 2023, 90, pp.102227. ⟨10.1016/j.ffa.2023.102227⟩. ⟨hal-04138475⟩

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