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Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields. (arXiv:2203.06970v3 [cs.SC] UPDATED)
July 6, 2022, 1:20 a.m. | Antoine Leudière, Pierre-Jean Spaenlehauer
cs.CR updates on arXiv.org arxiv.org
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 …
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