Hash function mapping design utilizing probability distribution for pre-image resistance

Hash functions are often used to protect the integrity of information. In general, the design of hash functions should satisfy three standards: pre-image resistance, second pre-image resistance and collision resistance. The design of hash functions in the literature assumes that the messages to be transmitted are equally probable. In this paper, we focus on the pre-image resistance and investigate the problem of mapping design for hash function utilizing the unequal occurrence probabilities of the messages. We first present a necessary condition for the optimal mapping and then introduce a heuristic algorithm. Simulation experiments are carried out to evaluate the performance of the proposed new design. It is shown that the probability of successful attack can be significantly reduced compared with the conventional design. Our algorithm can be useful in scenarios where the attacker has limited ability or time to estimate the probability distribution of the messages. To our best knowledge, this work is the first attempt of making use of the message distribution in designing hash functions for information security.