CubeHash

Abstract: In this paper, an improved differential cryptanalysis framework for finding collisions in hash functions is provided. Its principle is based on linearization of compression functions in order to find low weight differential characteristics as initiated by Chabaud and Joux. This is formalized and refined however in several ways: for the problem of finding a conforming message pair whose differential trail follows a linear trail, a condition function is introduced so that finding a collision is equivalent to finding a preimage of the zero vector under the condition function. Then, the dependency table concept shows how much influence every input bit of the condition function has on each output bit. Careful analysis of the dependency table reveals degrees of freedom that can be exploited in accelerated preimage reconstruction under the condition function. These concepts are applied to an in-depth collision analysis of reduced-round versions of the two SHA-3 candidates CubeHash and MD6, and are demonstrated to give by far the best currently known collision attacks on these SHA-3 candidates.

Abstract: Sponge functions were introduced by Bertoni et al. as an alternative to the classical Merkle-Damgard design. Many hash function submissions to the SHA-3 competition launched by NIST in 2007, such as CubeHash, Fugue, Hamsi, JH, Keccak and Luffa, derive from the original sponge design, and security guarantees from some of these constructions are typically based on indifferentiability results. Although indifferentiability proofs for these designs often bear significant similarities, these have so far been obtained independently for each construction. In this work, we introduce the parazoa family of hash functions as a generalization of “sponge-like” functions. Similarly to the sponge design, the parazoa family consists of compression and extraction phases. The parazoa hash functions, however, extend the sponge construction by enabling the use of a wider class of compression and extraction functions that need to satisfy certain properties. More importantly, we prove that the parazoa functions satisfy the indifferentiability notion of Maurer et al. under the assumption that the underlying permutation is ideal. Not surprisingly, our indifferentiability result confirms the bound on the original sponge function, but it also carries over to a wider spectrum of hash functions and eliminates the need for a separate indifferentiability analysis.

Abstract: Hash functions are widely used in, and form an important part of many cryptographic protocols. Currently, a public competition is underway to find a new hash algorithm(s) for inclusion in the NIST Secure Hash Standard (SHA-3). Computational efficiency of the algorithms in hardware will form one of the evaluation criteria. In this paper, we focus on five of these candidate algorithms, namely CubeHash, Grostl, LANE, Shabal and Spectral Hash. Using Xilinx Spartan-3 and Virtex-5 FPGAs, we present architectures for each of these hash functions, and explore area-speed trade-offs in each design. The efficiency of various architectures for the five hash functions is compared in terms of throughput per unit area. To the best of the authors’ knowledge, this is the first such comparison of these SHA-3 candidates in the literature.