Affiliation-Hiding Authenticated Key Exchange (AH-AKE) protocols enable two distrusting users, being in possession of membership credentials for some group, to establish a secure session key without leaking any information about this group to non-members. In practice, users might be members of several groups, and such protocols must be able to generate session keys between users who have one or more groups in common. Finding efficient solutions for this group discovery problem has been considered an open research problem, inherent to the practical deployment of these protocols. We show how to solve the privacy-preserving group discovery problem with linear computational and communication complexity, namely O(n) complexity where n is the number of groups per user. Our generic solution is based on a new primitive - Index-Hiding Message Encoding (IHME), for which we provide definitions and an unconditionally secure construction. Additionally, we update the syntax and the security model of AH-AKE protocols to allow multiple input groups per participant and session. Furthermore, we design a concrete multi-group AH-AKE protocol by applying IHME to a state-of-the-art single-group scheme.