Welcome to the resource topic for 2023/696
Title:
Universal Hashing Based on Field Multiplication and (Near-)MDS Matrices
Authors: Koustabh Ghosh, Jonathan Fuchs, Parisa Amiri Eliasi, Joan Daemen
Abstract:In this paper we propose a new construction for building universal hash functions, a specific instance called multi-265, and provide proofs for their universality.
Our construction follows the key-then-hash parallel paradigm.
In a first step it adds a variable length input message to a secret key and splits the result in blocks.
Then it applies a fixed-length public function to each block and adds their results to form the output.
The innovation presented in this work lies in the public function: we introduce the multiply-transform-multiply-construction that makes use of field multiplication and linear transformations.
We prove upper bounds for the universality of key-then-hash parallel hash functions making use of a public function with our construction provided the linear transformation are maximum-distance-separable (MDS).
We additionally propose a concrete instantiation of our construction multi-265, where the underlying public function uses a near-MDS linear transformation and prove it to be 2^{-154}-universal.
We also make the reference code for multi-265 available.
ePrint: https://eprint.iacr.org/2023/696
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