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Simple Oblivious Transfer Protocols Compatible with Supersingular Isogenies

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Progress in Cryptology – AFRICACRYPT 2019 (AFRICACRYPT 2019)

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Abstract

The key exchange protocol of Diffie and Hellman, which can be defined for any group, has the special feature of using only exponentiations. In particular, it can also be instantiated in Kummer varieties, which are not groups, and in the post-quantum isogeny-based setting.

In this article, we propose a new simple oblivious transfer (OT) protocol, based on Diffie–Hellman key exchange, that only uses exponentiations; we also revisit the older Wu–Zhang–Wang scheme. Both protocols can be directly instantiated on fast Kummer varieties; more importantly, they can also be transposed in the isogeny setting. The semantic security of our proposals relies on the hardness of non-standard versions of the (supersingular) DH problem, that are investigated within this article. To the best of our knowledge, these protocols are the simplest discrete-log based OT schemes using only exponentiations, and the first isogeny-based OT schemes.

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Acknowledgments

This work has been supported in part by the European Union’s H2020 Programme under grant agreement number ERC-669891. The author would like to thank Luca de Feo, Charles Bouillaguet, Damien Vergnaud and Antoine Joux for their helpful discussions, and anonymous referees for their relevant remarks and for pointing us the article of Wu, Zhang and Wang.

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Authors and Affiliations

  1. Univ. Grenoble Alpes, CNRS, Institut Fourier, 38000, Grenoble, France

    Vanessa Vitse

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  1. Vanessa Vitse
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Correspondence to Vanessa Vitse .

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Editors and Affiliations

  1. Technical University of Darmstadt, Darmstadt, Germany

    Johannes Buchmann

  2. Université de Caen, Caen, France

    Abderrahmane Nitaj

  3. Al Akhawayn University, Ifrane, Morocco

    Tajjeeddine Rachidi

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Vitse, V. (2019). Simple Oblivious Transfer Protocols Compatible with Supersingular Isogenies. In: Buchmann, J., Nitaj, A., Rachidi, T. (eds) Progress in Cryptology – AFRICACRYPT 2019. AFRICACRYPT 2019. Lecture Notes in Computer Science(), vol 11627. Springer, Cham. https://doi.org/10.1007/978-3-030-23696-0_4

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  • DOI: https://doi.org/10.1007/978-3-030-23696-0_4

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  • Online ISBN: 978-3-030-23696-0

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