Computing a Group Action from the Class Field Theory of Imaginary Hyperelliptic Function Fields
arxiv(2022)
摘要
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
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 𝔽_q[X]-modules, which is solvable in polynomial time thanks to an algorithm by
Wesolowski. We give asymptotic complexity bounds for all algorithms presented
in this paper.
更多查看译文
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要