International Association
for Cryptologic Research

Universal hash functions play a prominent role in the design of message authentication codes and the like. Whereas it is known how to build highly efficient sequential universal hash functions, parallel non-algebraic universal hash function designs are always built on top of a PRP. In such case, one employs a relatively strong primitive to obtain a function with a relatively weak security model. In this work, we present EliHash, a construction of a parallel universal hash function from non-compressing universal hash functions, and we back it up with supporting security analysis. We use this construction to design EliMAC, a message authentication code similar to LightMAC. We consider a heuristic instantiation of EliMAC with roundreduced AES, and argue that this instantiation of EliMAC is much more efficient than LightMAC, it is around 21% faster, and additionally allows for precomputation of the keys, albeit with a stronger assumption on the AES primitive than in LightMAC. These observations are backed up with an implementation of our scheme.

The current paper studies the probability of differential characteristics for an unkeyed (or with a fixed key) construction. Most notably, it focuses on the gap between two probabilities of differential characteristics: probability with independent S-box assumption, pind, and exact probability, pexact. It turns out that pexact is larger than pind in Feistel network with some S-box based inner function. The mechanism of this gap is then theoretically analyzed. The gap is derived from interaction of S-boxes in three rounds, and the gap depends on the size and choice of the S-box. In particular the gap can never be zero when the S-box is bigger than six bits. To demonstrate the power of this improvement, a related-key differential characteristic is proposed against a lightweight block cipher RoadRunneR. For the 128-bit key version, pind of 2−48 is improved to pexact of 2−43. For the 80-bit key version, pind of 2−68 is improved to pexact of 2−62. The analysis is further extended to SPN with an almost-MDS binary matrix in the core primitive of the authenticated encryption scheme Minalpher: pind of 2−128 is improved to pexact of 2−96, which allows to extend the attack by two rounds.

Cryptographic modes built on top of a blockcipher usually rely on the assumption that this primitive behaves like a pseudorandom permutation (PRP). For many of these modes, including counter mode and GCM, stronger security guarantees could be derived if they were based on a PRF design. We propose a heuristic method of transforming a dedicated blockcipher design into a dedicated PRF design. Intuitively, the method consists of evaluating the blockcipher once, with one or more intermediate state values fed-forward. It shows strong resemblance with the optimally secure EDMD construction by Mennink and Neves (CRYPTO 2017), but the use of internal state values make their security analysis formally inapplicable. In support of its security, we give the rationale of relying on the EDMD function (as opposed to alternatives), and present analysis of simplified versions of our conversion method applied to the AES. We conjecture that our main proposal AES-PRF, AES with a feed-forward of the middle state, achieves close to optimal security. We apply the design to GCM and GCM-SIV, and demonstrate how it entails significant security improvements. We furthermore demonstrate how the technique extends to tweakable blockciphers and allows for security improvements in, for instance, PMAC1.

BLAKE2 is a hash function introduced at ACNS 2013, which has been adopted in many constructions and applications. It is a successor to the SHA-3 finalist BLAKE, which received a significant amount of security analysis. Nevertheless, BLAKE2 introduces sufficient changes so that not all results from BLAKE carry over, meaning new analysis is necessary. To date, all known cryptanalysis done on BLAKE2 has focused on its underlying building blocks, with little focus placed on understanding BLAKE2’s generic security. We prove that BLAKE2’s compression function is indifferentiable from a random function in a weakly ideal cipher model, which was not the case for BLAKE. This implies that there are no generic attacks against any of the modes that BLAKE2 uses.