On probabilities of hash value matches

Hash functions are used in authentication and cryptography, as well as for the efficient storage and retrieval of data using hashed keys. Hash functions are susceptible to undesirable collisions. To design or choose an appropriate hash function for an application, it is essential to estimate the probabilities with which these collisions can occur. In this paper we consider two problems: one of evaluating the probability of no collision at all and one of finding a bound for the probability of a collision with a particular hash value. The quality of these estimates under various values of the parameters is also discussed.