CISPA
Browse
1-1-15.pdf (826.45 kB)

Simple Two-Message OT in the Explicit Isogeny Model

Download (826.45 kB)
journal contribution
posted on 2024-05-22, 12:24 authored by Emmanuela Orsini, Riccardo ZanottoRiccardo Zanotto
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.

History

Primary Research Area

  • Algorithmic Foundations and Cryptography

Journal

Communications in Cryptology

Publisher

International Association for Cryptologic Research

Open Access Type

  • Hybrid

Sub Type

  • Article

BibTeX

@article{Orsini:Zanotto:2024, title = "Simple Two-Message OT in the Explicit Isogeny Model", author = "Orsini, Emmanuela" AND "Zanotto, Riccardo", year = 2024, month = 4, journal = "Communications in Cryptology", publisher = "International Association for Cryptologic Research", issn = "3006-5496", doi = "10.62056/a39qgy4e-" }

Usage metrics

    Categories

    No categories selected

    Licence

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC