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. 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.

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

Date: received 6 Nov 2019, last revised 11 Feb 2020

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: 20200211:152159 (All versions of this report)

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