Systems and methods for implementing low-latency lookup circuits using sparse hash functions

A lookup circuit evaluates hash functions that map keys to addresses in lookup tables. The circuit may include multiple hash function sub-circuits, each of which applies a respective hash function to an input key value, producing a hash value. Each hash function sub-circuit may multiply bit vectors representing key values by a sparse bit matrix and may add a constant bit vector to the results. The hash function sub-circuits may be constructed using odd-parity circuits that accept as inputs subsets of the bits of the bit vectors representing the key values. The sparse bit matrices may be chosen or generated so that there are at least twice as many 0-bits per row as 1-bits or there is an upper bound on the number of 1-bits per row. Using sparse bit matrices in the hash function sub-circuits may allow the lookup circuit to perform lookup operations with very low latency.