Preventing Collusion Attacks on the One-Way Function Tree (OFT) Scheme

The one-way function tree (OFT) scheme proposed by Balenson et al.is widely regarded as an efficient key management solution for multicast communication in large dynamic groups. Following Horng's claim that the original OFT scheme was vulnerable to a collusion attack, Ku et al.studied the collusion attack on OFT and proposed a solution to prevent the attack. The solution, however, requires to broadcast about h2+ h(his the height of the key tree) keys for every eviction operation, whereas the original OFT scheme only requires about hkeys. This modified OFT scheme thus loses a key advantage that the original OFT has over the logical key hierarchy (LKH) scheme, that is a halving in broadcast size. In this paper, we revisit collusion attacks on the OFT scheme. We generalize the examples of attacks given by Horng and Ku et al.to a generic collusion attack on OFT, and derive necessary and sufficient conditions for such an attack to exist. We then show a solution for preventing collusion attacks while minimizing the average broadcast size. Our simulation results show that the proposed solution allows OFT to outperform LKH in many cases.