Paper 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 isogeny versions of the decisional and gap Diffie-Hellman assumptions, respectively. We also propose a new approach for invalidating the Galbraith-Vercauteren-type attack for the gap problem.

Note: This is the full version of a paper appearing in ICISC 2018, the 21st Annual International Conference on Information Security and Cryptology, November 28-30, 2018, Seoul, Korea.