Provably Secure Password-Authenticated Key Exchange Based on SIDH

Abstract

Password-authenticated key exchange (PAKE) schemes are cryptographic schemes for securely establishing a shared session key between a client and a server communicating over an insecure channel by using a low-entropy password. In this paper, we propose a PAKE based on SIDH, where the password is used to derive a torsion points obfuscator independent of ephemeral keys. We analyze its security and prove that it is secure in the Bellare-Pointcheval-Rogaway (BPR) model, assuming the hardness of the supersingular isogeny computational Diffie-Hellman (SI-CDH) problem.