Séta: supersingular encryption from torsion attacks

Luca De Feo*, Cyprien Delpech de Saint Guilhem, Tako Boris Fouotsa, Péter Kutas, Antonin Leroux, Christophe Petit, Javier Silva, Benjamin Wesolowski

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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We present Séta (To be pronounced [ʃe:tɒ] meaning “walk” in Hungarian.), 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.

Original languageEnglish
Title of host publicationAdvances in Cryptology – ASIACRYPT 2021
Subtitle of host publication27th International Conference on the Theory and Application of Cryptology and Information Security, 2021, Proceedings, Part 4
EditorsMehdi Tibouchi, Huaxiong Wang
Number of pages30
ISBN (Electronic)9783030920685
ISBN (Print)9783030920678
Publication statusPublished - 1 Dec 2021
Event27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021 - Virtual, Online
Duration: 6 Dec 202110 Dec 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13093 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021
CityVirtual, Online

Bibliographical note

Funding Information:
Acknowledgments. We would like to thank the anonymous reviewers for their remarks and suggestions. Péter Kutas and Christophe Petit’s work was supported by EPSRC grant EP/S01361X/1. Péter Kutas was also supported by the Ministry of Innovation and Technology and the National Research, Development and Innovation Office within the Quantum Information National Laboratory of Hungary. Cyprien Delpech de Saint Guilhem’s work was supported by ERC Advanced Grant ERC-2015-AdG-IMPaCT, by DARPA under contract No. HR001120C0085, and by CyberSecurity Research Flanders with reference number VR20192203.

Publisher Copyright:
© 2021, International Association for Cryptologic Research.


  • public-key cryptography
  • elliptic curves
  • isogenies
  • Encryption

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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