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Cryptographic Hash Functions and Expander Graphs: The End of the Story?

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The New Codebreakers

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9100))

Abstract

Cayley hash functions are a family of cryptographic hash functions constructed from the Cayley graphs of non-Abelian finite groups. Their security relies on the hardness of mathematical problems related to long-standing conjectures in graph and group theory. We recall the Cayley hash design and known results on the underlying problems. We then describe related open problems, including the cryptanalysis of relevant parameters as well as new applications to cryptography and outside, assuming either that the problem is “hard” or easy.

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Acknowledgements

Part of this work was done while Christophe Petit was visiting the Computer Science Department at University College London and the Number Theory Group at the University of Oxford, under an FRS-FNRS Research Collaborator grant at Universit catholique de Louvain. He is grateful to Jens Groth (UCL) and Alan Lauder (Oxford) for the fruitful work he could do there. The research leading to these results has also received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 307937 and the Engineering and Physical Sciences Research Council grant EP/J009520/1.

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Authors and Affiliations

  1. Information Security Group, University College London, London, UK

    Christophe Petit & Jean-Jacques Quisquater

  2. Crypto Group, Université Catholique de Louvain, Louvain-la-Neuve, Belgium

    Christophe Petit & Jean-Jacques Quisquater

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  1. Christophe Petit
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  2. Jean-Jacques Quisquater
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Correspondence to Jean-Jacques Quisquater .

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Editors and Affiliations

  1. Université du Luxembourg , Luxembourg, Luxembourg

    Peter Y. A. Ryan

  2. Ecole normale supérieure , Paris, France

    David Naccache

  3. Université Catholique de Louvain , Louvain-la-Neuve, Belgium

    Jean-Jacques Quisquater

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Petit, C., Quisquater, JJ. (2016). Cryptographic Hash Functions and Expander Graphs: The End of the Story?. In: Ryan, P., Naccache, D., Quisquater, JJ. (eds) The New Codebreakers. Lecture Notes in Computer Science(), vol 9100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49301-4_19

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  • DOI: https://doi.org/10.1007/978-3-662-49301-4_19

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