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A Short Universal Hash Function from Bit Rotation, and Applications to Blockcipher Modes

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Provable Security (ProvSec 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8209))

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Abstract

In this paper we propose a new universal hash function based on bit rotation. The proposed scheme, called Circulant hash, is a variant of the classical random matrix-based hash of Carter and Wegman, called H 3, and Toeplitz hash by Krawczyk. However, Circulant hash has a smaller key space and the proved differential probability is not implied by the previous analyses on these functions.

Since Circulant hash is an almost XOR-universal hash function for balanced input/output, it may not be a perfect substitute for H 3 and Toeplitz hash. However, we show that Circulant hash is a useful tool for blockcipher modes, specifically as an alternative to Galois field constant multiplications. We provide some illustrative examples of the constructions of tweakable blockcipher and vector-input pseudorandom function using Circulant hash. Our schemes are as efficient as previous ones using GF constant multiplications, and provide some unique features.

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Authors and Affiliations

  1. NEC Corporation, 1753 Shimonumabe, Nakahara-Ku, Kawasaki, Japan

    Kazuhiko Minematsu

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  1. Kazuhiko Minematsu
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  1. Centre for Computer and Information Security Research, School of Computer Science and Software Engineering, University of Wollongong, Northfields Ave, NSW 2522, Wollongong, Australia

    Willy Susilo

  2. École Polytechnique Fédérale de Lausanne, IC LASEC, Bâtiment INF, Station 14, 1015, Lausanne, Switzerland

    Reza Reyhanitabar

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Minematsu, K. (2013). A Short Universal Hash Function from Bit Rotation, and Applications to Blockcipher Modes. In: Susilo, W., Reyhanitabar, R. (eds) Provable Security. ProvSec 2013. Lecture Notes in Computer Science, vol 8209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41227-1_13

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  • DOI: https://doi.org/10.1007/978-3-642-41227-1_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41226-4

  • Online ISBN: 978-3-642-41227-1

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