A new Private Mutual Authentication scheme with group discovery

If users from the same group would like to securely distinguish each other and negotiate a session key, the Private Mutual Authentication (PMA) protocol is a good choice. During the interaction, no group information will be leaked to non-members, so as to protect the users’ private affiliations. In practical applications, users generally belong to multiple groups and would like to discover other members who are also authorized by more common groups. To solve such group discovery problem efficiently, we propose a new private mutual authentication scheme denoted by PMA-GD in this paper. The key idea of PMA-GD is derived from Authorized Private Set Intersection (APSI) based on Identity-Based Encryption(IBE), which achieves linear complexity in essence. In PMA-GD, two participants distinguish each other secretly only if the authentication policy is satisfied, which requires that the intersection of groups in common is non-empty or reaches a threshold value. Our proposal is designed on the basis of Bilinear Diffie–Hellman (BDH) problem, so it is provably secure in the Random Oracle Model(ROM). Compared with previous work, the performance analysis demonstrates that PMA-GD is still competitive and applicable for scenarios with limited resources.