In most password-based authentication protocols, the server owns a value, the so-called verifier, that depends on the registered password. This verifier is often a one-way function of the password. Despite this protection, an unauthorized person who gets access to the verifier can mount a brute-force attack to recover the password. If the entropy of the password is low, which is often the case in practice, such an attack might be successful. Motivated by the growing need to face databases compromises, we propose a two-factor password-based authentication protocol where no information about the password leak from the server's side nor from the client's side, and where the password is not sent to the server when the user authenticates. During the registration, a user gets a value, called the token, while the server records the verifier. Our security model ensures that brute-force attacks are impossible if the server is compromised. Moreover, only on-line attempts are possible if a token is stolen. The solutions that we describe fit well into scenarios where the token is stored on a mobile phone. We provide constructions, proven secure in the random-oracle model, under standard assumptions.
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