Also, not a crypto person so someone correct me if I'm wrong, But. The algorithm presented is essentially a way of determining the next 384bit number in a sequence given the last one. If that sequence contains every 384bit number before forming a cycle then it defines a mathematical permutation of the 384bit numbers.
This sort of process is used in e.g. pseudo-random number generators. Naively, you can for can keep 384bits internal state then at each step output the lowest 64bits as your pseudo-random number.
