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.
|Title of host publication||Advances in Cryptology – ASIACRYPT 2021|
|Subtitle of host publication||27th International Conference on the Theory and Application of Cryptology and Information Security, 2021, Proceedings, Part 4|
|Editors||Mehdi Tibouchi, Huaxiong Wang|
|Number of pages||30|
|Publication status||Published - 1 Dec 2021|
|Event||27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021 - Virtual, Online|
Duration: 6 Dec 2021 → 10 Dec 2021
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||27th International Conference on Theory and Application of Cryptology and Information Security, ASIACRYPT 2021|
|Period||6/12/21 → 10/12/21|
Bibliographical noteFunding 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.
© 2021, International Association for Cryptologic Research.
- public-key cryptography
- elliptic curves
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)