Semi-commutative masking: A framework for isogeny-based protocols, with an application to fully secure two-round isogeny-based OT

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Colleges, School and Institutes

External organisations

  • KU Leuven
  • University of Bristol
  • Département d’informatique
  • Université Libre de Bruxelles


We define semi-commutative invertible masking structures which aim to capture the methodology of exponentiation-only protocol design (such as discrete logarithm and isogeny-based cryptography). We give an instantiation based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then construct an oblivious transfer protocol using this new structure and prove that it UC-securely realises the oblivious transfer functionality in the random-oracle-hybrid model against passive adversaries with static corruptions. Moreover, we show that it satisfies the security properties required by the compiler of Döttling et al. (Eurocrypt 2020), achieving the first fully UC-secure two-round OT protocol based on supersingular isogenies.

Bibliographic note

Funding Information: Acknowledgements. This work has been supported in part by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by CyberSecurity Research Flanders with reference number VR20192203, by the Defense Advanced Research Projects Agency (DARPA) and Space and Naval Warfare Systems Center, Pacific (SSC Pacific) under contracts No. N66001-15-C-4070 and No. HR001120C0085, by the FWO under an Odysseus project GOH9718N and by EPSRC grant EP/S01361X/1 Publisher Copyright: © Springer Nature Switzerland AG 2020.


Original languageEnglish
Title of host publicationCryptology and Network Security - 19th International Conference, CANS 2020, Vienna, Austria, December 14–16, 2020, Proceedings
EditorsStephan Krenn, Haya Shulman, Serge Vaudenay
Publication statusPublished - 2020
Event19th International Conference on Cryptology and Network Security, CANS 2020 - Vienna, Austria
Duration: 14 Dec 202016 Dec 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12579 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Cryptology and Network Security, CANS 2020