I am just wondering if point halving is allowed then why can't we half the point of puzzle given pub keys?
By point halving, I assume it as reversal of point doubling. Like when we double a point P to 2P and 2P to 4P, isn't point halving means calculating 2P from 4P and P from 2P? In that case, it won't take long I guess to reduce the size of bit range to a more manageable bit range, does it?