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On Building Hash Functions from Multivariate Quadratic Equations

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Information Security and Privacy (ACISP 2007)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4586))

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Abstract

Recent advances in hash functions cryptanalysis provide a strong impetus to explore new designs. This paper describes a new hash function mq-hash that depends for its security on the difficulty of solving randomly drawn systems of multivariate equations over a finite field. While provably achieving pre-image resistance for a hash function based on multivariate equations is relatively easy, naïve constructions using multivariate equations are susceptible to collision attacks. In this paper, therefore, we describe a mechanism—also using multivariate quadratic polynomials—yielding the collision-free property we seek while retaining provable pre-image resistance. Therefore, mq-hash offers an intriguing companion proposal to the provably collision-free hash function vsh.

This work has been supported in part by the French government through the SAPHIR and MAC projects.

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Authors and Affiliations

  1. France Telecom R&D, Issy-les-Moulineaux, France

    Olivier Billet, Matt J. B. Robshaw & Thomas Peyrin

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  1. Olivier Billet
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  2. Matt J. B. Robshaw
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  3. Thomas Peyrin
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Josef Pieprzyk Hossein Ghodosi Ed Dawson

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Billet, O., Robshaw, M.J.B., Peyrin, T. (2007). On Building Hash Functions from Multivariate Quadratic Equations. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds) Information Security and Privacy. ACISP 2007. Lecture Notes in Computer Science, vol 4586. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73458-1_7

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  • DOI: https://doi.org/10.1007/978-3-540-73458-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73457-4

  • Online ISBN: 978-3-540-73458-1

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