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Analysis of Multivariate Hash Functions

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Information Security and Cryptology - ICISC 2007 (ICISC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4817))

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Abstract

We analyse the security of new hash functions whose compression function is explicitly defined as a sequence of multivariate equations. First we prove non-universality of certain proposals with sparse equations, and deduce trivial collisions holding with high probability. Then we introduce a method inspired from coding theory for solving underdefined systems with a low density of non-linear monomials, and apply it to find collisions in certain functions. We also study the security of message authentication codes HMAC and NMAC built on multivariate hash functions, and demonstrate that families of low-degree functions over GF(2) are neither pseudo-random nor unpredictable.

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Authors and Affiliations

  1. FHNW, 5210 Windisch, Switzerland

    Jean-Philippe Aumasson & Willi Meier

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  1. Jean-Philippe Aumasson
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  2. Willi Meier
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Kil-Hyun Nam Gwangsoo Rhee

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Aumasson, JP., Meier, W. (2007). Analysis of Multivariate Hash Functions. In: Nam, KH., Rhee, G. (eds) Information Security and Cryptology - ICISC 2007. ICISC 2007. Lecture Notes in Computer Science, vol 4817. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76788-6_25

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  • DOI: https://doi.org/10.1007/978-3-540-76788-6_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-76787-9

  • Online ISBN: 978-3-540-76788-6

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