On Sun, Nov 17, 2013 at 05:25:10AM -0800, absinthe wrote: > Hi everyone, > > I'd like to know if there is any implementation in Sage for inverting > multiplication over elliptic curves. To clarify the question as many might > misunderstand the problem with discrete log... > Let's assume that we have a curve E, but we don't know the number of points > of E. Moreover, for given k, P we know that P=kQ and we want to find Q. If > k=2 then we have the point halving problem which can be done efficiently (I > don't know though if there is a Sage implementation for that). Are you aware > of any algorithm for general k? > > Thanks >
Have tried point.division_points(k) ? e.g: sage: E=EllipticCurve(QQ,[1,1,13,0,0]);P=E([0,0]);k=3;Q= k * P;pts=Q.division_points(k);pts [(0 : 0 : 1)] Type "P.division_points?" for help. Note that you can get more than one point. In this case over QQ P.height() might give you the correct solution, over GF(p) many points are discrete log IMHO. -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/groups/opt_out.
