To attach the ends to the sphere:
Select the 4 curves.
Create a transform constraint.
Parent the constraint to the torus and move it to the center of the torus.
To move the curves to the desired connection point on the torus:
Select the curves.
Display->start position
Select the end cvs and move while holding the 'l' (length lock) key.
Now if you display the current position and playback while moving the torus and/or the controller the curves will stay attached at both ends. Note that it is a much harder setup if you want to dynamically control the motion of the torus with the controller. (you might need to use rigid bodies with chains of pin constraints)
Duncan