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Paper 2019/1291

SÉTA: Supersingular Encryption from Torsion Attacks

Cyprien Delpech de Saint Guilhem and Péter Kutas and Christophe Petit and Javier Silva

Abstract

We present SÉTA, a new family of public-key encryption schemes with post-quantum security based on isogenies of supersingular elliptic curves. At the heart of this construction is a new family of trapdoor one-way functions, where the inversion algorithm uses Petit's 2017 attack to compute an isogeny between two supersingular elliptic curves given images of torsion points. We use this method as a decryption mechanism to first build a OW-CPA scheme; then we prove further properties of the OW-CPA scheme to obtain IND-CCA security in the quantum random oracle model using generic transformations, both for a PKE scheme and a KEM. We compare our protocols with the NIST proposal SIKE from both security and efficiency points of view, and we discuss how further work, including on cryptanalysis, may affect this comparison.

Metadata
Available format(s)
PDF
Category
Public-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
elliptic curvesisogeniesencryption
Contact author(s)
cyprien delpechdesaintguilhem @ kuleuven be
kutasp @ gmail com
christophe f petit @ gmail com
javiersilvavelon @ gmail com
History
2021-09-20: last of 3 revisions
2019-11-07: received
See all versions
Short URL
https://ia.cr/2019/1291
License
Creative Commons Attribution
CC BY
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