### 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, and Benjamin Wesolowski

##### 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.

Available format(s)
Category
Public-key cryptography
Publication info
Keywords
elliptic curvesisogeniesencryption
Contact author(s)
asiacrypt21 @ defeo lu
cyprien delpechdesaintguilhem @ kuleuven be
takoboris fouotsa @ uniroma3 it
kutasp @ gmail com
antonin leroux @ polytechnique org
christophe f petit @ gmail com
javiersilvavelon @ gmail com
History
2021-09-20: last of 3 revisions
See all versions
Short URL
https://ia.cr/2019/1291

CC BY

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},
note = {\url{https://eprint.iacr.org/2019/1291}},
url = {https://eprint.iacr.org/2019/1291}
}

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