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Paper: Séta: Supersingular Encryption from Torsion Attacks

Authors:
Péter Kutas , University of Birmingham
Christophe Petit , Université Libre de Bruxelles and University of Birmingham
Luca de Feo , IBM Research Europe, Zürich, Switzerland
Antonin Leroux , DGA, École Polytechnique
Tako Boris Fouotsa , Universita Degli Studi Roma Tre, Italy
Benjamin Wesolowski , CNRS , Univ. Bordeaux, France
Cyprien Delpech de Saint Guilhem , imec-COSIC, KU Leuven, Belgium
Javier Silva , Universitat Pompeu Fabra
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Conference: ASIACRYPT 2021
Abstract: We present Séta, a new family of public-key encryption schemes with post-quantum security based on isogenies of supersingular elliptic curves. It is constructed from a new family of trapdoor one-way functions, where the inversion algorithm uses Petit's so called \emph{torsion attacks} on SIDH to compute an isogeny between supersingular elliptic curves given an endomorphism of the starting curve and images of torsion points. We prove the OW-CPA security of S\'eta and present an IND-CCA variant using the post-quantum OAEP transformation. Several variants for key generation are explored together with their impact on the selection of parameters, such as the base prime of the scheme. We furthermore formalise an ``uber'' isogeny assumption framework which aims to generalize computational isogeny problems encountered in schemes including SIDH, CSDIH, OSIDH and ours. Finally, we carefully select parameters to achieve a balance between security and run-times and present experimental results from our implementation.
Video from ASIACRYPT 2021
BibTeX
@inproceedings{asiacrypt-2021-31453,
  title={Séta: Supersingular Encryption from Torsion Attacks},
  publisher={Springer-Verlag},
  author={Péter Kutas and Christophe Petit and Luca de Feo and Antonin Leroux and Tako Boris Fouotsa and Benjamin Wesolowski and Cyprien Delpech de Saint Guilhem and Javier Silva},
  year=2021
}