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Séta: Supersingular Encryption from Torsion Attacks

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 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.
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https://hal.inria.fr/hal-03471926
Contributor : Antonin Leroux Connect in order to contact the contributor
Submitted on : Thursday, December 9, 2021 - 8:33:01 AM
Last modification on : Sunday, June 26, 2022 - 3:23:50 AM

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Luca de Feo, Cyprien Delpech de Saint Guilhem, Tako Boris Fouotsa, Péter Kutas, Antonin Leroux, et al.. Séta: Supersingular Encryption from Torsion Attacks. Advances in Cryptology – ASIACRYPT 2021, 13093, Springer International Publishing, pp.249-278, 2021, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-92068-5_9⟩. ⟨hal-03471926⟩

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