Hardware circuitry may evaluate minimal perfect hash functions mapping keys to addresses in lookup tables. The circuitry may include primary hash function sub-circuits that apply linear hash functions to input key values (using carry-free arithmetic) to produce primary hash values. Each sub-circuit may multiply bit vectors representing key values by a bit matrix and add a constant bit vector to the result. The circuitry may include a secondary hash function sub-circuit that generates secondary hash values by aggregating values associated with multiple primary hash values using signed, unsigned, or modular integer addition, or bit-wise XOR operations. Secondary hash values may be usable to access data values in the lookup table that are associated with particular input key values. The circuitry may determine the validity of input keys and may alter the configuration or contents of the lookup tables. The hash function sub-circuits may include programmable hash tables.