Mitigating server breaches in password-based authentication: Secure and efficient solutions

Password-Authenticated Key Exchange allows users to generate a strong cryptographic key based on a shared “human-memorable” password without requiring a public-key infrastructure. It is one of the most widely used and fundamental cryptographic primitives. Unfortunately, mass password theft from organizations is continually in the news and, even if passwords are salted and hashed, brute force breaking of password hashing is usually very successful in practice. In this paper, we propose two efficient protocols where the password database is somehow shared among two servers (or more), and authentication requires a distributed computation involving the client and the servers. In this scenario, even if a server compromise is doable, the secret exposure is not valuable to the adversary since it reveals only a share of the password database and does not permit to brute force guess a password without further interactions with the parties for each guess. Our protocols rely on smooth projective hash functions and are proven secure under classical assumption in the standard model (i.e. do not require idealized assumption, such as random oracles).