Some embodiments provide a physical forwarding element that hashes portions of packet headers using several novel hashing techniques. The techniques include a novel set of finishing operations that improve the quality of resulting hashes by increasing their distribution and improving their apparent-randomness. In addition, the finishing operations virtually guarantee that different length inputs will hash to different results, even when padded to be the same initial values. The techniques also include efficient handling of remainder sections when distributing sections of a hash input across multiple processing units. The remainders are hashed into various previously generated hashes based on how many remainders result. These hashing techniques are useful for many network applications.