Hard Homogeneous Spaces from the Class Field Theory of Imaginary Hyperelliptic Function Fields. (arXiv:2203.06970v2 [cs.SC] UPDATED)

We explore algorithmic aspects of a free and 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. Our
proof-of-concept C++/NTL implementation only requires a fraction of a second on
a standard computer. …

class hard theory