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2021•IACR Cryptology ePrint ArchiveRequires access

One-way functions and malleability oracles: Hidden shift attacks on isogeny-based protocols.

Péter Kutas, Simon-Philipp Merz, Christophe Petit, Charlotte Weitkämper

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Abstract

Supersingular isogeny Diffie-Hellman key exchange (SIDH) is a post-quantum protocol based on the presumed hardness of computing an isogeny between two supersingular elliptic curves given some additional torsion point information. Unlike other isogeny-based protocols, SIDH has been widely believed to be immune to subexponential quantum attacks because of the non-commutative structure of the endomorphism rings of supersingular curves.

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What this paper is about

Supersingular isogeny Diffie-Hellman key exchange (SIDH) is a post-quantum protocol based on the presumed hardness of computing an isogeny between two supersingular elliptic curves given some additional torsion point information. Unlike other isogeny-based protocols, SIDH has been widely believed to be immune to subexponential quantum attacks because of the non-commutative structure of the endomorphism rings of supersingular curves.

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Available abstract

Supersingular isogeny Diffie-Hellman key exchange (SIDH) is a post-quantum protocol based on the presumed hardness of computing an isogeny between two supersingular elliptic curves given some additional torsion point information. Unlike other isogeny-based protocols, SIDH has been widely believed to be immune to subexponential quantum attacks because of the non-commutative structure of the endomorphism rings of supersingular curves.

Key concepts: Isogeny, Supersingular elliptic curve, Key exchange, Diffie–Hellman key exchange, Mathematics, Post-quantum cryptography, Computer science, Discrete mathematics

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One-way functions and malleability oracles: Hidden shift attacks on isogeny-based protocols. — Research Paper | ScholarLens