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A new multi-linear universal hash family

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Abstract

A new universal hash family is described which generalises a previously known multi-linear hash family. Messages are sequences over a finite field \({\mathbb{F}_q}\) while keys are sequences over an extension field \({\mathbb{F}_{q^n}}\). A linear map \({\psi}\) from \({\mathbb{F}_{q^n}}\) to itself is used to compute the output digest. Of special interest is the case q = 2. For this case, we show that there is an efficient way to implement \({\psi}\) using a tower field representation of \({\mathbb{F}_{q^n}}\). From a practical point of view, the focus of our constructions is small hardware and other resource constrained applications. For such platforms, our constructions compare favourably to previous work.

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  1. Applied Statistics Unit, Indian Statistical Institute, 203, B.T. Road, Kolkata, 700108, India

    Palash Sarkar

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  1. Palash Sarkar
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Correspondence to Palash Sarkar.

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Communicated by V. Rijmen.

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Sarkar, P. A new multi-linear universal hash family. Des. Codes Cryptogr. 69, 351–367 (2013). https://doi.org/10.1007/s10623-012-9672-8

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  • DOI: https://doi.org/10.1007/s10623-012-9672-8

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