Cryptology ePrint Archive: Report 2018/730

Supersingular Isogeny Diffie-Hellman Authenticated Key Exchange

Atsushi Fujioka and Katsuyuki Takashima and Shintaro Terada and Kazuki Yoneyama

Abstract: We propose two authenticated key exchange protocols from supersingular isogenies. Our protocols are the first post-quantum one-round Diffie-Hellman type authenticated key exchange ones in the following points: one is secure under the quantum random oracle model and the other resists against maximum exposure where a non-trivial combination of secret keys is revealed. The security of the former and the latter is proven under an isogeny version of the decisional and gap Diffie-Hellman assumption, respectively. We also propose a new approach for invalidating the Galbraith-Vercauteren attack for the gap problem.

Category / Keywords: public-key cryptography / one-round authenticated key exchange, supersingular isogeny decisional Diffie-Hellman assumption, supersingular isogeny gap Diffie-Hellman assumption, CK model, CK^+ model, quantum adversary, random oracle model

Date: received 7 Aug 2018

Contact author: Takashima Katsuyuki at aj MitsubishiElectric co jp

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Version: 20180809:150921 (All versions of this report)

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