Provably Secure Password-Authenticated Key Exchange Using Diffie-Hellman

When designing password-authenticated key exchange protocols (as opposed to key exchange protocols authenticated using cryptographically secure keys), one must not allow any information to be leaked that would allow verification of the password (a weak shared key), since an attacker who obtains this information may be able to run an off-line dictionary attack to determine the correct password. We present a new protocol called PAK which is the first Diffie-Hellman-based passwordauthenticated key exchange protocol to provide a formal proof of security (in the random oracle model) against both passive and active adversaries. In addition to the PAK protocol that provides mutual explicit authentication, we also show a more efficient protocol called PPK that is provably secure in the implicit-authentication model. We then extend PAK to a protocol called PAK-X, in which one side (the client) stores a plaintext version of the password, while the other side (the server) only stores a verifier for the password. We formally prove security of PAK-X, even when the server is compromised. Our formal model for passwordauthenticated key exchange is new, and may be of independent interest.