Simpler Session-Key Generation from Short Random Passwords

Abstract

Goldreich and Lindell (CRYPTO ’01) recently presented the first protocol for password-authenticated key exchange in the standard model (with no common reference string or set-up assumptions other than the shared password). However, their protocol uses several heavy tools and has a complicated analysis. We present a simplification of the Goldreich–Lindell (GL) protocol and analysis for the special case when the dictionary is of the form \(\mathcal{D}=\{0,1\}^{d}\) i.e., the password is a short string chosen uniformly at random (in the spirit of an ATM PIN number). The security bound achieved by our protocol is somewhat worse than the GL protocol. Roughly speaking, our protocol guarantees that the adversary can “break” the scheme with probability at most \(O(\mathrm{poly}(n)/|\mathcal{D}|)^{\Omega(1)}\) , whereas the GL protocol guarantees a bound of \(O(1/|\mathcal{D}|)\) . We also present an alternative, more natural definition of security than the “augmented definition” of Goldreich and Lindell, and prove that the two definitions are equivalent.