Paper 2018/886

An Isogeny-Based Password-Authenticated Key Establishment Protocol

Oleg Taraskin and Vladimir Soukharev and David Jao and Jason LeGrow

Abstract

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 present the first quantum-resistant password-authenticated key exchange scheme based on supersingular elliptic curve isogenies. The scheme is built upon supersingular isogeny Diffie-Hellman, and uses the password to generate functions which obscure the auxiliary points used in the computation. We include a detailed security proof based on a number of reasonable computational problems on supersingular elliptic curves.