Post-quantum Dropout-Resilient Aggregation for Federated Learning via Lattice-Based PRF

Machine learning has greatly improved the convenience of modern life. As the deployment scale of machine learning grows larger, the corresponding data scale also increases, leading to a large number of small and medium-sized organizations wishing to use their respective data to train models together, even though this may bring risks of violating data privacy regulations and privacy leakage. To meet this demand, federated learning was proposed, which can satisfy the needs of various organizations to expand the training data scale without directly sharing data, while avoiding violations of data privacy regulations and privacy leakage. General federated learning usually allows clients to train local models independently, and then aggregate them on a central server to build a global model in a privacy-preserving manner. There are various ways to protect privacy, such as homomorphic encryption, differential privacy, etc. Among these methods, one type of federated learning scheme is based on homomorphic pseudorandom functions. This type of scheme is relatively simple to construct, has a smaller communication scale, is more resilient to disconnections, and has high scalability. However, the security aggregation with cryptographic primitives based on classic assumptions such as DDH cannot resist quantum attacks, and since the protected gradient vectors are usually tens of thousands of dimensions, obtaining the aggregation results requires solving tens of thousands of discrete logarithms, which leads to some loss of efficiency. In this paper, we proposed a secure aggregation scheme based on HPRG over lattice, which has practical efficiency and resilience to dropout and can resist quantum attacks due to the hardness of the RLWE assumption. Moreover, our scheme only requires polynomial multiplication and addition (usually treated as vectors in implements), thus significantly improving computational efficiency.