7. Conclusion
In this paper, we studied the security vulnerabilities of the OFT scheme. Firstly, we summarized the main conclusions on this subject and analyzed the conflicts found in other conclusions. Based on this analysis, we identified the exact node secrets which malicious users can obtain by collusion. Additionally, we provided proof for our own conclusion. Secondly, we proposed two improved OFT schemes named ROFT and NOFT. Compared with OFT, ROFT and NOFT do not incur extra communication overhead on the group manager. They can make the OFT scheme collusion attack resilient. More importantly, in ROFT and NOFT, the group manager has lower communication overhead and computational cost than in other schemes.