Universal Hashing Based on Field Multiplication and (Near-)MDS Matrices

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.