Federated learning is a distributed machine learning framework that allows multiple parties to collaboratively train a shared model without the need to share their original data with a central server. This approach minimizes the risk of data leakage and effectively addresses the challenge of isolated data silos. However, it necessitates multiple rounds of interactions to transmit models or gradients between the client and the server, leading to a significant communication cost and private data leakage. Consequently, some schemes compress the transmitted models or gradients through model pruning or knowledge distillation. However, they often overlook the privacy implications of compressed gradients or models, potentially resulting in privacy breaches. Additionally, they are susceptible to client disconnections, resulting in incomplete or delayed model updates. To address these challenges, this paper proposes Octopus, a robust and privacy-preserving scheme for compressed gradients in federated learning. Octopus employs Sketch to compress gradients and embeds masks for the compressed gradients, thereby safeguarding the gradients while concurrently reducing communication overhead. Moreover, we propose an anti-disconnection strategy to support model updates even in situations where some clients are disconnected. Lastly, we carry out comprehensive security and convergence analyses, along with extensive performance evaluations, demonstrating Octopus's robustness, stability, and efficiency over existing schemes.

Federated Learning (FL) is widely used in various industries because it effectively addresses the predicament of isolated data island. However, eavesdroppers is capable of inferring user privacy from the gradients or models transmitted in FL. Homomorphic Encryption (HE) can be applied in FL to protect sensitive data owing to its computability over ciphertexts. However, traditional HE as a single-key system cannot prevent dishonest users from intercepting and decrypting the ciphertexts from cooperative users in FL. Guaranteeing privacy and efficiency in this multi-user scenario is still a challenging target. In this paper, we propose a secure and efficient Federated Learning scheme (SecFed) based on multi-key HE to preserve user privacy and delegate some operations to TEE to improve efficiency while ensuring security. Specifically, we design the first TEE-based multi-key HE cryptosystem (EMK-BFV) to support privacy-preserving FL and optimize operation efficiency. Furthermore, we provide an offline protection mechanism to ensure the normal operation of system with disconnected participants. Finally, we give their security proofs and show their efficiency and superiority through comprehensive simulations and comparisons with existing schemes. SecFed offers a 3x performance improvement over TEE-based scheme and a 2x performance improvement over HE-based solution.