That's definitely a bug since (2^63)*P is instantaneous as one would
expect from 63 doublings.

I thought that I knew the actual code for group operations on elliptic
curves, but when I do P.__mul__?? and see that it ends with

return coercion_model.bin_op(left, right, mul)

then I rather lose heart -- there is some clever magic here (the file
sage/schemes/elliptic_curves/ell_point.py implements addition and
negation but not multiplcation which is handled by some very general
thing somewhere).  Just not quite clever enough.

As a stopgap, of course -((2^63)*P) works fine.

John

On 23 February 2015 at 16:27, William Stein <[email protected]> wrote:
> Hi,
>
> A user reports (and I confirm) that if P is pretty much any point on
> an elliptic curve over a finite field, then
>
>    (-2^63)*P
>
> hangs forever.  For example,
>
> E = EllipticCurve(GF(5),[0,1])
> P = E.random_element()
> (-2^63)*P   # hangs
>
> --
> William (http://wstein.org)
>
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