Cryptophia's Short Combiner for Collision-Resistant Hash Functions

A combiner for collision-resistant hash functions takes two functions as input and implements a hash function with the guarantee that it is collision-resistant if one of the functions is. It has been shown that such a combiner cannot have short output (Pietrzak, Crypto 2008); that is, its output length is lower bounded by roughly 2n if the ingoing functions output n-bit hash values. In this paper, we present two novel definitions for hash function combiners that allow to bypass the lower bound: the first is an extended semi-black-box definition. The second is a new game-based, fully black-box definition which allows to better analyze combiners in idealized settings such as the random-oracle model or indifferentiability framework (Maurer, Renner, and Holenstein, TCC 2004). We then present a new combiner which is robust for pseudorandom functions (in the traditional sense), which does not increase the output length of its underlying functions and which is collision-resistant in the indifferentiability setting. Our combiner is particularly relevant in practical scenarios, where security proofs are often given in idealized models, and our combiner, in the same idealized model, yields strong security guarantees while remaining short.