Not sure if you are still interested, but perhaps this helps someone else:

You are looking for perturbations of the image that are as close as possible to the original image (otherwise your perturbation may actually be a different class and would probably also mean that the perturbation is clearly visible for humans). You can imagine your original image as a coordinate in a multidimensional space. And now you want to find a closeby coordinate that increases the loss. L_p is the L_p norm and defines how you measure the distance between those coordinates (common values for p are 2 (L2-norm) and p=inf (L-inf norm)).

If you'd visualize the L2 case in 3D you'd see that the border in which your perturbations should lie is defined by a sphere (cube for L-inf). Since you consider perturbations on the surface of the sphere, and inside (because the <= constraint) what you have geometrically is a ball.

Hope that helps!