A caution on universal classes of hash functions

Abstract

Universal classes of hash functions of the form (( A × Key + B) mod P) mod Size, where A, B, and P (a prime greater than A and B) are constants and Size is the number of hash addresses, have come into common use. Theory and practical tests have shown that for random choices of the constants, excellent performance is to be expected. This paper points out that certain choices of these constants will lead to very poor performance. The paper develops a measure to evaluate hash functions; establishes the fact of poor performance in practice; explains the poor performance; and finally explains why good performance is to be expected for other choices of the constants. Theoretical results are presented which establish the universal nature of fixed-precision versions of these functions such as would be encountered with micro-computer hardware. These fixed-precision versions require restrictions on the hash functions which differ from other versions.