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Title:
On the security of keyed hashing based on an unkeyed block function
Authors: Jonathan Fuchs, Yann Rotella, Joan Daemen
Abstract:In this paper we study the security of two constructions for variable-length universal hash functions by means of their universality. Both constructions make use of a fixed-length unkeyed function that we call a block function. One construction is serial and is an idealization of the compression phase of Pelican-MAC. The other construction is parallel and is an idealization of the compression phase of Farfalle.
Both are instances of a class of functions we call semi-group accumulators.
We prove that the universality of these constructions is fully determined by the differential probability of block function differentials and, if not a permutation, the relative frequency of block function outputs. We show that both block function parallelization and serialization have equal security (against forgery) in the Wegman-Carter(-Shoup) construction. However, for the block functions we target, parallelization can provide
significantly better security than serialization in the Protected Hash (PH) construction. Moreover, below a certain data limit, PH provides better security than WC(S) for the block function parallelization, despite the fact that it does not require a nonce.
We show evidence of this effect by taking Xoodoo[3] as the block function .
ePrint: https://eprint.iacr.org/2022/1172
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