As a newly emerging distributed machine learning technology, federated learning has unique advantages in the era of big data. We explore how to motivate participants to experience auctions more actively and safely. It is also essential to ensure that the final participant who wins the right to participate can guarantee relatively high-quality data or computational performance. Therefore, a secure, necessary and effective mechanism is needed through strict theoretical proof and experimental verification. The traditional auction theory is mainly oriented to price, not giving quality issues as much consideration. Hence, it is challenging to discover the optimal mechanism and solve the privacy problem when considering multi-dimensional auctions. Therefore, we (1) propose a multi-dimensional information security mechanism, (2) propose an optimal mechanism that satisfies the Pareto optimality and incentive compatibility named the SecMDGM and (3) verify that for the aggregation model based on vertical data, this mechanism can improve the performance by 2.73 times compared to that of random selection. These are all important, and they complement each other instead of being independent or in tandem. Due to security issues, it can be ensured that the optimal multi-dimensional auction has practical significance and can be used in verification experiments.
Keywords: auction theory; federated learning; game theory; mechanism design; partial homomorphic encryption.