Communications in Cryptology IACR CiC

Simple Two-Message OT in the Explicit Isogeny Model

Authors

Emmanuela Orsini, Riccardo Zanotto
Emmanuela Orsini ORCID
Bocconi University, Milan, Italy
emmanuela dot orsini at unibocconi dot it
Riccardo Zanotto ORCID
CISPA Helmholtz Center for Information Security, Saarbrücken, Germany
riccardo dot zanotto at cispa dot de
Keywords: Oblivious Transfer Isogenies CSIDH Group Action Model

Abstract

In this work we study algebraic and generic models for group actions, and extend them to the universal composability (UC) framework of Canetti (FOCS 2001). We revisit the constructions of Duman et al. (PKC 2023) integrating the type-safe model by Zhandry (Crypto 2022), adapted to the group action setting, and formally define an algebraic action model (AAM). This model restricts the power of the adversary in a similar fashion to the algebraic group model (AGM). By imposing algebraic behaviour to the adversary and environment of the UC framework, we construct the UC-AAM. Finally, we instantiate UC-AAM with isogeny-based assumptions, in particular the CSIDH action with twists, obtaining the explicit isogeny model, UC-EI; we observe that, under certain assumptions, this model is "closer" to standard UC than the UC-AGM, even though there still exists an important separation. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure oblivious transfer protocol described by Lai et al. (Eurocrypt 2021), hence providing the first concretely efficient two-message isogeny-based OT protocol in the random oracle model against malicious adversaries.

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DOI: https://doi.org/10.62056/a39qgy4e-
History
Submitted: 2024-01-09
Accepted: 2024-03-05
Published: 2024-04-09
How to cite

Emmanuela Orsini and Riccardo Zanotto, Simple Two-Message OT in the Explicit Isogeny Model. IACR Communications in Cryptology, vol. 1, no. 1, Apr 09, 2024, doi: 10.62056/a39qgy4e-.

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