Paper 2019/1291 Original: eprint.iacr.org/2019/1291 ↗
SÉTA: Supersingular Encryption from Torsion Attacks
Abstract
We present Séta, 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.
Metadata
- Available format(s)
PDF- Category
- Public-key cryptography
- Publication info
- Preprint.
- History
- 2021-09-20: last updated
- 2019-11-07: published
- Short URL
- https://ia.cr/2019/1291
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2019/1291,
author = {Luca De Feo and Cyprien Delpech de Saint Guilhem and Tako Boris Fouotsa and Péter Kutas and Antonin Leroux and Christophe Petit and Javier Silva and Benjamin Wesolowski},
title = {SÉTA: Supersingular Encryption from Torsion Attacks},
howpublished = {Cryptology {ePrint} Archive, Paper 2019/1291},
year = {2019},
url = {https://eprint.iacr.org/2019/1291}
}