This paper gives a survey on cryptographic hash functions. It gives an overview of all types of hash functions and reviews design principals and possible methods of attacks. It also focuses on keyed hash functions and provides the applications, requirements, and constructions of keyed hash functions.

Black box cryptanalysis applies to hash algorithms consisting of many small boxes, connected by a known graph structure, so that the boxes can be evaluated forward and backwards by given oracles. We study attacks that work for any choice of the black boxes, i.e. we scrutinize the given graph structure. For example we analyze the graph of the fast Fourier transform (FFT). We present optimal black box inversions of FFT--compression functions and black box constructions of collisions. This determines the minimal depth of FFT-- compression networks for collision--resistant hashing. We propose the concept of multipermutation, which is a pair of orthogonal latin squares, as a new cryptographic primitive that generalizes the boxes of the FFT. Our examples of multipermutations are based on the operations circul

We propose SWIFFT, a collection of compression functions that are highly parallelizable and admit very efficient implementations on modern microprocessors. The main technique underlying our functions is a novel use of the Fast Fourier Transform (FFT) to achieve “diffusion, ” together with a linear combination to achieve compression and “confusion. ” We provide a detailed security analysis of concrete instantiations, and give a high-performance software implementation that exploits the inherent parallelism of the FFT algorithm. The throughput of our implementation is competitive with that of SHA-256, with additional parallelism yet to be exploited. Our functions are set apart from prior proposals (having comparable efficiency) by a supporting asymptotic security proof: it can be formally proved that finding a collision in a randomly-chosen function from the family (with noticeable probability) is at least as hard as finding short vectors in cyclic/ideal lattices in the worst case.

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 “diffusion ” 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

1.4 Simple XOR

We analyse the security of a cryptographic primitive on the basis of the geometry of its computation graph. We assume the computation graph of the primitive to be given whereas the boxes sitting on the vertices of this graph are unknown and random, i.e. they are black boxes. We formalize and study a family of attacks which generalize exhaustive search and the birthday paradox. We establish complexity lower bounds for this family and we apply it to compression functions based on the FFT network.