Towards Isogeny-Based Password-Authenticated Key Establishment

Password authenticated key establishment (PAKE) is a cryptographic primitive that allows two parties who share a low-entropy secret (a password) to securely establish cryptographic keys in the absence of public key infrastructure. We propose the first quantum-resistant password-authenticated key exchange scheme based on supersingular elliptic curve isogenies. The scheme is built upon supersingular isogeny Diffie-Hellman [15], and uses the password to generate permutations which obscure the auxiliary points. We include elements of a security proof, and discuss roadblocks to obtaining a proof in the BPR model [1]. We also include some performance results.