DE FEO, Luca; DELPECH DE SAINT GUILHEM, Cyprien; FOUOTSA, Tako Boris; KUTAS, Péter; LEROUX, Antonin; PETIT, Christophe; SILVA, Javier; WESOLOWSKI, Benjamin

doi:10.1007/978-3-030-92068-5_9

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DE FEO, Luca
Lithe and fast algorithmic number theory [LFANT]

DELPECH DE SAINT GUILHEM, Cyprien
Catholic University of Leuven = Katholieke Universiteit Leuven [KU Leuven]

FOUOTSA, Tako Boris
Università degli Studi Roma Tre = Roma Tre University [ROMA TRE]

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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

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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.< Réduire

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Séta: Supersingular Encryption from Torsion Attacks

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