CVFL: A Chain-like and Verifiable Federated Learning Scheme with Computational Efficiency Based on Lagrange Interpolation Functions

Data privacy and security concerns have attracted significant attention, leading to the frequent occurrence of data silos in deep learning. To address this issue, federated learning (FL) has emerged. However, simple federated learning frameworks still face two security risks during the training process. Firstly, sharing local gradients instead of private datasets among users does not completely eliminate the possibility of data leakage. Secondly, malicious servers could obtain inaccurate aggregation parameters by forging or simplifying the aggregation process, ultimately leading to model training failures. To address these issues and achieve high-performance training models, we have designed a verifiable federated learning scheme called CVFL, where users exist in a serial manner to resist inference attacks and further protect the privacy of user dataset information through serial encryption. We ensure the secure aggregation of models through a verification protocol based on Lagrange interpolation functions. The serial transmission of local gradients effectively reduces the communication burden on cloud servers, and our verification protocol avoids the computational overhead caused by a large number of encryption and decryption operations without sacrificing model accuracy. Experimental results on the MNIST dataset demonstrate that, after 10 epochs of training with 100 users, our solution achieves a model accuracy of 90.63% for MLP architecture under IID data distribution and 87.47% under non-IID data distribution. For CNN architecture, our solution achieves a model accuracy of 96.72% under IID data distribution and 93.53% under non-IID data distribution. Experimental evaluations corroborate the practical performance of the presented scheme with high accuracy and efficiency.