Using the BCH construction to generate robust linear hash functions

Providing a single hash function for use across multiple applications is challenging due to the fact that different applications require different sizes of hashed values. An application-independent hash function must be robust in the sense that it must maintain good characteristics independent of the number of output bits which are used. In this paper we show how the BCH construction can be used to construct a single n→m bit linear hash function with the property that that the n→m´ bit subhash functions obtained by discarding the upper m - m´ output bits all have provably good collision avoidance properties. We apply this technique to the construction of a 256→128 bit hash function. We find that of the 256→m´ subhashes, over 78% have optimal minimum collision distances and all but one have a minimum collision distance within 2 of optimal.