Simple Two-Round OT in the Explicit Isogeny Model

Emmanuela Orsini; Riccardo Zanotto

Paper 2023/269

Simple Two-Round OT in the Explicit Isogeny Model

Emmanuela Orsini

, Bocconi University, imec-COSIC, KU Leuven

Riccardo Zanotto

, CISPA Helmholtz Center for Information Security

Abstract

In this work we apply the Type-Safe (TS) generic group model, recently introduced by Zhandry (2022), to the more general setting of group actions and extend it to the universal composability (UC) framework of Canetti (2000). We then relax this resulting model, that we call UC-TS, to define an algebraic action framework (UC-AA), where the adversaries can behave algebraically, similarly to the algebraic group model (AGM), but for group actions. Finally, we instantiate UC-AA with isogeny-based assumptions, obtaining the Explicit-Isogeny model, UC-EI, and show that, under certain assumptions, UC-EI is less restricting that UC-AGM. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure protocol described by Lai et al. (2021), hence providing the first concretely efficient two-round isogeny-based OT protocol in the random oracle model against malicious adversaries.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Isogenies Group Actions Oblivious Transfer CSIDH
Contact author(s): emmanuela orsini @ unibocconi it
riccardo zanotto @ cispa de
History: 2023-02-24: revised; 2023-02-23: received; See all versions
Short URL: https://ia.cr/2023/269
License: CC BY

BibTeX

@misc{cryptoeprint:2023/269,
      author = {Emmanuela Orsini and Riccardo Zanotto},
      title = {Simple Two-Round OT in the Explicit Isogeny Model},
      howpublished = {Cryptology ePrint Archive, Paper 2023/269},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/269}},
      url = {https://eprint.iacr.org/2023/269}
}