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

par de Saint Guilhem, Cyprien Delpech;Orsini, Emmanuela;Petit, Christophe ;Smart, Nigel N.P.
Référence Lecture notes in computer science, 12579 LNCS, page (235-258)
Publication Publié, 2020-03-01

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Résumé :

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.