Abstract: Federated learning offers new ideas for solving the problem of multiparty joint modeling in “data silos”.Federated support vector machines can realize cross-device support vector machine modeling without local data,but the existing research has some defects such as insufficient privacy protection in a training process and a lack of research on nonlinear federated support vector machines.To solve the above problems,this paper utilizes the stochastic Fourier feature method and CKKS homomorphic encryption system to propose a nonlinear federated support vector machine training(PPNLFedSVM) algorithm for privacy protection.Firstly,the same Gaussian kernel approximate mapping function is generated locally for each participant based on the random Fourier feature method,and the training data of each participant is explicitly mapped from the low-dimensional space to the high-dimensional space.Secondly,the model parameter security aggregation algorithm based on CKKS cryptography ensures the privacy of model parameters and their contributions during the model aggregation process.Moreover,the parameter aggregation process is optimized and adjusted according to the characteristics of CKKS cryptography to improve the efficiency of the security aggregation algorithm.Security analysis and experimental results show that the PPNLFedSVM algorithm can ensure the privacy of participant model parameters and their contributions to the training process without losing the model accuracy.

Key words: Federated learning, Privacy preserving, Homomorphic encryption, Support vector machines, Multi-party secure random seed negotiation, Random Fourier features