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Fast algorithms for computing isogenies between elliptic curves
Abstract
We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree ( different from the characteristic) in time quasi-linear with respect to . This is based in particular on fast algorithms for power series expansion of the Weierstrass -function and related functions- info:eu-repo/semantics/report
- Reports
- Fast algorithms
- elliptic curves
- finite fields
- isogenies
- Schoof-Elkies-Atkin algorithm
- Newton iteration
- ACM: G.: Mathematics of Computing/G.4: MATHEMATICAL SOFTWARE/G.4.0: Algorithm design and analysis
- [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC]
- [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS]
- [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
- [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]