fast path for Vélu isogenies with a single kernel generator #36805
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GiacomoPope
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Feb 2, 2024
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Tried to find something to suggest to change, but the PR is good and clean.
This is an obvious thing to implement as most calls only include a single point rather than a list so this will be a "free speed boost" for most people.
Good addition to the isogeny code.
vbraun
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Feb 7, 2024
…enerator
The current implementation of Vélu's formulas always assumes that the
kernel subgroup is given by an arbitrary set of generators: The
important special case of a single generator is handled using the same
code as the general case.
In this patch we add a fast path to handle a single generator, which can
yield big speedups. Example:
```sage
sage: E = EllipticCurve(GF(2^127-1), [1,1,1,1,1])
sage: P = E.lift_x(73833238617088645877502541346296796686)
sage: P.set_order(2543)
sage: %timeit E.isogeny(P)
```
Sage 10.2:
```
63.6 ms ± 588 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
```
With this patch:
```
33.3 ms ± 98.8 µs per loop (mean ± std. dev. of 7 runs, 10 loops each)
```
URL: sagemath#36805
Reported by: Lorenz Panny
Reviewer(s): Giacomo Pope
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The current implementation of Vélu's formulas always assumes that the kernel subgroup is given by an arbitrary set of generators: The important special case of a single generator is handled using the same code as the general case.
In this patch we add a fast path to handle a single generator, which can yield big speedups. Example:
Sage 10.2:
With this patch: