Cryptology ePrint Archive: Report 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. We first define a family of trapdoor one-way functions for which the computation of the inverse is based on an attack by Petit (ASIACRYPT 2017) on the problem of computing an isogeny between two supersingular elliptic curves, given the images of torsion points by this isogeny. We use this method as a decryption mechanism to build first a OW-CPA scheme, then we make use of generic transformations to obtain IND-CCA security in the quantum random oracle model, both for a PKE scheme and a KEM. Compared to alternative schemes based on SIDH, our protocols have the advantage of relying on arguably harder problems.

Category / Keywords: public-key cryptography / elliptic curves, isogenies, encryption,

Date: received 6 Nov 2019

Contact author: cyprien delpechdesaintguilhem at kuleuven be, kutasp@gmail com, christophe f petit@gmail com, javiersilvavelon@gmail com

Available format(s): PDF | BibTeX Citation

Version: 20191107:102044 (All versions of this report)

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