#6384: [with patch, needs review] elliptic curve -- isogeny function is not
robust
-- it doesn't check validity of its input
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Reporter: was | Owner: shumow
Type: defect | Status: new
Priority: major | Milestone: sage-4.1.2
Component: elliptic curves | Keywords: elliptic curves, isogeny,
Reviewer: | Author:
Merged: |
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Comment(by cremona):
I have just read through the above discussions. I think that by far the
most common way people will create isgenies from kernels will be either
from a kernel polynomial (in which case there definitely should be a
check, as Chris implemented, that the polynomial given does define a valid
subgroup), or by giving a point generating a cyclic kernel. So I'm with
Chris on this one. It is very easy to convert a pint P of order n to a
list of points in the subgroup generated by P, just use
list(multiples(P,n)) --multiples() returned an iterator. It will be
very rare for non-cyclic isogenies to be needed, with the single exception
of the multiplication-by-m map which we can already create using the
division_polynomial(m).
I don't think that backward compatibility is an important issue here,
though I can see that it might be for Dan, since the isogeny code is so
new, to the extent that I still consider it to be "beta" code, as I have
not had a chance to use it much.
Dan, I cannot imagine it to be at all common for a user to have the points
of a subgroup but not know the generator(s), so I think your comment about
the complexity here is not a very serious one.
I will now spend some time testing the patch; if I don't find any
problems I'll give this a positive review.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6384#comment:14>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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