A perfect hash function PHF is an injection F from a set W of M objects into the set consisting of the first N nonnegative integers where N ⩾ M. If N = M, then F is a minimal perfect hash function, MPHF. PHFs are useful for the compact storage and fast retrieval of frequently used objects such as reserved words in a programming language or commonly employed words in a natural language. The mincycle algorithm for finding PHFs executes with an expected time complexity that is polynomial in M and has been used successfully on sets of cardinality up to 512. Given three pseudorandom functions h 0 , h 1 , and h 2 , the mincycle algorithm searches for a function g such that F(w) = (h 0 (w) + g ° h 1 (w) + g ° h 2 (w)) mod N is a PHF.