### Semi-Commutative Masking: A Framework for Isogeny-based Protocols, with an Application to Fully Secure Two-Round Isogeny-based OT

Cyprien Delpech de Saint Guilhem, Emmanuela Orsini, Christophe Petit, and Nigel P. Smart

##### Abstract

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 discuss two instantiations: the first is based on commutative group actions and captures both the action of exponentiation in the discrete logarithm setting and the action of the class group of commutative endomorphism rings of elliptic curves, in the style of the CSIDH key-exchange protocol; the second is based on the semi-commutative action of isogenies of supersingular elliptic curves, in the style of the SIDH key-exchange protocol. We then construct two oblivious transfer protocols using this new structure and prove that these UC-securely realise the oblivious transfer functionality in the random-oracle-hybrid model against passive adversaries with static corruptions. Moreover, by starting from one of these two protocols and using the compiler introduced by Döttling et al. (Eurocrypt 2020), we achieve the first fully UC-secure two-round OT protocol based on supersingular isogenies.

Available format(s)
Category
Public-key cryptography
Publication info
Published elsewhere. MAJOR revision.International Conference on Cryptology And Network Security (CANS) 2020
Keywords
oblivious transferUC securitygroup actionsupersingular isogenies
Contact author(s)
cyprien delpechdesaintguilhem @ kuleuven be
emmanuela orsini @ kuleuven be
christophe f petit @ gmail com
nigel smart @ kuleuven be
History
2020-10-19: last of 2 revisions
See all versions
Short URL
https://ia.cr/2018/648

CC BY

BibTeX

@misc{cryptoeprint:2018/648,
author = {Cyprien Delpech de Saint Guilhem and Emmanuela Orsini and Christophe Petit and Nigel P.  Smart},
title = {Semi-Commutative Masking: A Framework for Isogeny-based Protocols, with an Application to Fully Secure Two-Round Isogeny-based OT},
howpublished = {Cryptology ePrint Archive, Paper 2018/648},
year = {2018},
note = {\url{https://eprint.iacr.org/2018/648}},
url = {https://eprint.iacr.org/2018/648}
}

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