Provably Secure Password-Authenticated Key Exchange Using Diffie-Hellman

Abstract

Abstract. 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.

Efficient Password-Authenticated Key Exchange Using Human-Memorable Passwords

“…More recently, two formal models for password-authenticated key exchange have been proposed: one by Bellare, Pointcheval, and Rogaway [3], based on [4,6] with extensions suggested by [21]; and a second by Boyko, MacKenzie, and Patel [10], following [2] with extensions given in [28]. While both models have their advantages, we choose to work in the first model and review the appropriate definitions in Section 2.…”

“…Only recently have formal validations of security for specific protocols appeared [3,10,22]. However, these validations are not proofs in the standard model; [3] relies on ideal ciphers, while [10,22] rely on random oracles.…”

“…The setting arising most often in practice -in which (human) users are only capable of storing "human-memorable" passwords (password-authenticated key exchange) -remains much less studied, though many heuristic protocols exist. Indeed, only recently have formal definitions of security for this setting appeared [3,10,22,17].…”

“…Many heuristic protocols have been proposed to solve this important problem. Only recently have formal validations of security (namely, proofs in the idealized random oracle and ideal cipher models) been given for specific constructions [3,10,22].Very recently, a construction based on general assumptions, secure in the standard model with human-memorable passwords, has been proposed by Goldreich and Lindell [17]. Their protocol requires no public parameters; unfortunately, it requires techniques from general multi-party computation which make it impractical.…”

“…Many heuristic protocols have been proposed to solve this important problem. Only recently have formal validations of security (namely, proofs in the idealized random oracle and ideal cipher models) been given for specific constructions [3,10,22].…”