how to join random points to form a curve along a surface

hi all.
i have a problem in getting my defination to work for me.
i have started with a circle and dividing it into a number of points..these points are then translated in the plane perpendicular to the circle in a random distance...which again are translated, rather moved/copied in a random distance...thus i have a series of random points...
in essence i have a number of points on say a lofted cylinder...

the problem :
when i join these points with a curve i do get the curves but these curves follow a random path i:e they also move withing the cylinder..
what i need is the curve to move only along the surface of the cylinder..thus from the first point to the next it should only be following the plane of the cylinder.....and not inside the cylinder as in my definition/attached image.
the same goes for random lines too i guess.

would love some help on this problem
regards
samir