Partitioned Group Password-Based Authenticated Key Exchange

Group Password-Based Authenticated Key Exchange (GPAKE) allows a group of users to establish a secret key, as long as all of them share the same password. However, in existing GPAKE protocols as soon as one user runs the protocol with a non-matching password, all the others abort and no key is established. In this paper we seek for a more flexible, yet secure, GPAKE and put forward the notion of partitioned GPAKE. Partitioned GPAKE tolerates users that run the protocol on different passwords. Through a protocol run, any subgroup of users that indeed share a password, establish a session key, factoring out the 'noise' of inputs by users holding different passwords. At the same time any two keys, each established by a different subgroup of users, are pair-wise independent if the corresponding subgroups hold different passwords. We also introduce the notion of password-privacy for partitioned GPAKE, which is a kind of affiliation hiding property, ensuring that an adversary should not be able to tell whether any given set of users share a password. Finally, we propose an efficient instantiation of partitioned GPAKE building on an unforgeable symmetric encryption scheme and a PAKE by Bellare et al. Our proposal is proven secure in the random oracle/ideal cipher model, and requires only two communication rounds.