Prefer to use composite isogeny in more cases #40224
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Note: make sure to review the dependency before this pull request.
The advantage of this pull request is that
.isogeny()
finishes quickly when the curve order is highly composite, even if you forget to passalgorithm="factored"
. Example (from doctest):The reason why this is never slower than the existing code is the following. Currently when the kernel generator
P
has unknown order, it usesEllipticCurveIsogeny
, which in turn uses__init_from_kernel_point
, as you can see it takes time linear in the order ofP
.The new code takes time
O(√(order of P))
which is negligible compared to that. (Maybe with some extra log factor.)📝 Checklist
⌛ Dependencies
#40223