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Simple Oblivious Transfer Protocols Compatible with Supersingular Isogenies

  • Vanessa VitseEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11627)

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.

Keywords

Oblivious transfer Diffie–Hellman key exchange Supersingular isogeny Post-quantum cryptography 

Notes

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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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Univ. Grenoble Alpes, CNRS, Institut FourierGrenobleFrance

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