The basic idea of a Bloom filter is that you represent each item in the filter by setting k bits, and you set and query these bits using k hash functions. The b

The basic idea of a Bloom filter is that you represent each item in the filter by setting k bits, and you set and query these bits using k hash functions. The bits need to be independent and uniformly distributed, so the hash functions need to output suitably random values for the same input. Even fast hash functions like Murmur add overhead, though, and the lower the desired false positive rate, the more hash functions you need (x hash functions for 2^-x false positive rate). The conclusion of the paper is roughly that you can create new hash functions by recombining the outputs of two initial hash functions without compromising the statistical integrity of the filter, and this makes querying the filter a lot faster. To be clear, even the two initial hash functions can be halves or quarters of a single hash function with an output larger than the filter needs, e.g. a filter that needs 64-bit hashes can run entirely on Murmur-128 using its bottom and top halves as the two hash functions.