Séta: Supersingular Encryption from Torsion Attacks
DELPECH DE SAINT GUILHEM, Cyprien
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
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Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
DELPECH DE SAINT GUILHEM, Cyprien
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]
LEROUX, Antonin
Direction générale de l'armement [Bagneux] [DGA]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
Direction générale de l'armement [Bagneux] [DGA]
Laboratoire d'informatique de l'École polytechnique [Palaiseau] [LIX]
Geometry, arithmetic, algorithms, codes and encryption [GRACE]
WESOLOWSKI, Benjamin
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]
< Reduce
Lithe and fast algorithmic number theory [LFANT]
Centre National de la Recherche Scientifique [CNRS]
Language
en
Communication dans un congrès
This item was published in
ASIACRYPT 2021 - 27th International Conference on the Theory and Application of Cryptology and Information Security, 2021-12-06, Singapour. 2021-12-01, vol. 13093, p. 249-278
Springer International Publishing
English Abstract
We present Séta, 11 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 ...Read more >
We present Séta, 11 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 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 Séta 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.Read less <
Origin
Hal imported