Provably Secure FFT Hashing

We propose a new family of collision resistant hash functions with the distinguishing feature of being provably secure. The main technique underlying our functions is a novel use of the Fast Fourier Transform to achieve ideal "diusion" properties, together with a random linear function to achieve compression and "confusion". Our functions admit fast implementation both in hardware and software, but are set apart from previous proposals (based on similar building blocks) in the literature by a supporting security proof: it can be formally proven that (asymptotically) finding collisions to our functions (for keys chosen uniformly at random) with non-negligible probability is at least as hard as solving certain lattice problems in the worst case. Our proposal and techniques are based on previous work by Micciancio (FOCS 2002, Computational Complexity 2007), Peikert and Rosen (TCC 2006) and Lyubashevsky and Micciancio (ICALP 2006).