Supersingular Isogeny Diffie-Hellman Authenticated Key Exchange
Supersingular Isogeny Diffie-Hellman Authenticated Key Exchange
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.