GROSE: Optimal group size estimation for broadcast proxy re-encryption

Abstract

In this paper, we propose GROSE —a scheme to determine the optimal group size of the receiver in Broadcast Proxy Re-encryption. GROSE uses the Rubinstein–Ståhl bargaining approach, so that both the sender and the receiver are mutually benefited and the total payoff increases. Proxy re-encryption is an important scheme to send cloud data securely to another user. For secured sharing of data to more than one users, the concept of broadcast proxy re-encryption was introduced. However, it poses an overhead on the receiver, if the receiver group is large, as each of the receivers in the group has to calculate the additional expensive algebraic operations, which linearly increases with the number of users in the receiver group. We model the problem using a bargaining perspective, and address it as the Rubinstein–Ståhl bargaining game for finite version of the game and then extend it to the infinite horizon version of it. We define the payoff of the sender and the receiver, and discuss how the payoff depends on different factors. Finally, we implement GROSE and compare it with the previously proposed schemes to depict the efficiency of GROSE. It is observed that GROSE is more efficient than the traditional proxy re-encryption and broadcast proxy re-encryption schemes.