Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields - Inria - Institut national de recherche en sciences et technologies du numérique
Article Dans Une Revue Journal of Symbolic Computation Année : 2024

Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields

Résumé

We explore algorithmic aspects of a simply transitive commutative group action coming from the class field theory of imaginary hyperelliptic function fields. Namely, the Jacobian of an imaginary hyperelliptic curve defined over $\mathbb F_q$ acts on a subset of isomorphism classes of Drinfeld modules. We describe an algorithm to compute the group action efficiently. This is a function field analog of the Couveignes-Rostovtsev-Stolbunov group action. We report on an explicit computation done with our proof-of-concept C++/NTL implementation; it took a fraction of a second on a standard computer. We prove that the problem of inverting the group action reduces to the problem of finding isogenies of fixed τ-degree between Drinfeld $\mathbb F_q[X]$-modules, which is solvable in polynomial time thanks to an algorithm by Wesolowski.

Dates et versions

hal-03633990 , version 1 (07-04-2022)

Identifiants

Citer

Pierre-Jean Spaenlehauer, Antoine Leudière. Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields. Journal of Symbolic Computation, 2024, 125, ⟨10.1016/j.jsc.2024.102311⟩. ⟨hal-03633990⟩
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