If size is a prime, repeated multiplication on a generator element (any element) will work if you compute `mod p`. But it's not going to have nice random properties for the most part. It's just a "permutation".
The reason it works is because the subgroup order generated by the element has to be divisible in the group order. There's only 1 and p. So unless it's trivial (i.e., the element 1), it's going to be p and thus it generates the whole group in p steps.
From memory you don't need size to be a prime, what you need is that it is coprime with your step.
Thus, the easiest solution is to take a step-size that is prime and different from you size (that works for any size). Given the index of the current element, the next index would be `(current_index + step) % size`.
The reason it works is because the subgroup order generated by the element has to be divisible in the group order. There's only 1 and p. So unless it's trivial (i.e., the element 1), it's going to be p and thus it generates the whole group in p steps.