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Annual International Conference on the Theory and Applications of Cryptographic Techniques

EUROCRYPT 2021: Advances in Cryptology – EUROCRYPT 2021 pp 213–241Cite as

Compact, Efficient and UC-Secure Isogeny-Based Oblivious Transfer

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12696))

Abstract

Oblivious transfer (OT) is an essential cryptographic tool that can serve as a building block for almost all secure multiparty functionalities. The strongest security notion against malicious adversaries is universal composability (UC-secure). An important goal is to have post-quantum OT protocols. One area of interest for post-quantum cryptography is isogeny-based crypto. Isogeny-based cryptography has some similarities to Diffie-Hellman, but lacks some algebraic properties that are needed for discrete-log-based OT protocols. Hence it is not always possible to directly adapt existing protocols to the isogeny setting.

We propose the first practical isogeny-based UC-secure oblivious transfer protocol in the presence of malicious adversaries. Our scheme uses the CSIDH framework and does not have an analogue in the Diffie-Hellman setting. The scheme consists of a constant number of isogeny computations. The underlying computational assumption is a problem that we call the computational reciprocal CSIDH problem, and that we prove polynomial-time equivalent to the computational CSIDH problem.

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Acknowledgments

We sincerely thank the anonymous reviewers of EUROCRYPT 2021 for their patience and valuable comments that helped to substantially improve the presentation of this work. We are also grateful to Wouter Castryck for sharing his knowledge of isogenies and Yehuda Lindell for sharing his knowledge of MPC. This research is partially funded by the Ministry for Business, Innvovation and Employment in New Zealand.

This work was supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT and by CyberSecurity Research Flanders with reference number VR20192203. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the ERC or of Cyber Security Research Flanders.

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Authors and Affiliations

  1. University of Auckland, Auckland, New Zealand

    Yi-Fu Lai & Steven D. Galbraith

  2. imec-COSIC, KU Leuven, Leuven, Belgium

    Cyprien Delpech de Saint Guilhem

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  1. Yi-Fu Lai
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  2. Steven D. Galbraith
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Correspondence to Yi-Fu Lai .

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  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Lai, YF., Galbraith, S.D., Delpech de Saint Guilhem, C. (2021). Compact, Efficient and UC-Secure Isogeny-Based Oblivious Transfer. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12696. Springer, Cham. https://doi.org/10.1007/978-3-030-77870-5_8

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  • DOI: https://doi.org/10.1007/978-3-030-77870-5_8

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