Tweaking cryptographic primitives with moderate state space by direct manipulation

Cryptographic primitives such as hash chains or pseudo-random number generators (PRNGs) work for some time without input. State space in embedded applications is often moderate because of resource restrictions, so that state repetitions might occur too soon and may compromise security. We investigate the question whether it is possible to change the transition function of such a primitive only for a very small number of states and still achieve a notable increase in cycle length. We present a greedy algorithm that searches those states, and give an implementation that only marginally increases the effort per state transition. We evaluate the algorithm with a chaotic PRNG and hash chains based on MD5 and SHA-3 with promising results.