PPO-DFK: A Privacy-Preserving Optimization of Distributed Fractional Knapsack with Application in Secure Footballer Configurations

In the optimized footballer configurations, the team coach selects the players to participate in the game based on the training status of all players. As the number of excellent players increases, the costs and budget owned by the club boss need to be considered. Obviously, the players' costs are considered as private and sensitive and the training status are also sensitive. Therefore, the private information might be revealed in the process of data sharing and processing in this distributed manner. Considering the privacy-revealing issues in the above-mentioned scenario, this article proposes a privacy-preserving optimization for distributed fractional knapsack (PPO-DFK) problem, in which it achieves the secure footballer configurations, i.e., it is able to win the game but the sum of cost does not exceed the budget, without revealing either the expenditure/money owned by the club boss or the players' training status owned by the team coach. In the proposed PPO-DFK scheme, it employs a novel transformation approach (TA), a secure comparison protocol and a secure sorting protocol as the building blocks to ensure the privacy protection of distributed optimization procedure, then it uses the greedy algorithm to find an efficient solution. The security of proposed PPO-DFK scheme is strictly analyzed and its effectiveness is demonstrated by the experimental results on concrete examples.