With the emergence of privacy leaks in federated learning, secure aggregation protocols that mainly adopt either homomorphic encryption or threshold secret sharing have been widely developed for federated learning to protect the privacy of the local training data of each client. However, these existing protocols suffer from many shortcomings, such as the dependence on a trusted third party, the vulnerability to clients being corrupted, low efficiency, the trade-off between security and fault tolerance, etc. To solve these disadvantages, we propose an efficient and multi-private key secure aggregation scheme for federated learning. Specifically, we skillfully modify the variant ElGamal encryption technique to achieve homomorphic addition operation, which has two important advantages: 1) The server and each client can freely select public and private keys without introducing a trust third party and 2) Compared to the variant ElGamal encryption, the plaintext space is relatively large, which is more suitable for the deep model. Besides, for the high dimensional deep model parameter, we introduce a super-increasing sequence to compress multi-dimensional data into 1-D, which can greatly reduce encryption and decryption times as well as communication for ciphertext transmission. Detailed security analyses show that our proposed scheme achieves the semantic security of both individual local gradients and the aggregated result while achieving optimal robustness in tolerating both client collusion and dropped clients. Extensive simulations demonstrate that the accuracy of our scheme is almost the same as the non-private approach, while the efficiency of our scheme is much better than the state-of-the-art homomorphic encryption-based secure aggregation schemes. More importantly, the efficiency advantages of our scheme will become increasingly prominent as the number of model parameters increases.

翻译：随着联邦学习中隐私泄露问题的出现，主要采用同态加密或阈值秘密共享的安全聚合协议已被广泛开发，以保护各客户端本地训练数据的隐私。然而，这些现有协议存在诸多缺陷，例如依赖可信第三方、易受客户端被破坏的影响、效率低下、安全性与容错性之间的权衡等。为解决这些不足，我们提出了一种高效且支持多私钥的联邦学习安全聚合方案。具体而言，我们巧妙地修改了变体ElGamal加密技术以实现同态加法运算，该技术具有两个重要优势：1）服务器和每个客户端可以自由选择公钥和私钥，而无需引入可信第三方；2）与变体ElGamal加密相比，其明文空间相对较大，更适用于深度模型。此外，针对高维深度模型参数，我们引入超递增序列将多维数据压缩为一维，这可以极大地减少加密解密次数以及密文传输的通信开销。详细的安全分析表明，我们提出的方案在实现个体局部梯度和聚合结果的语义安全的同时，在容忍客户端共谋和掉线客户端方面达到了最优的鲁棒性。大量仿真实验证明，我们方案的准确性几乎与非隐私保护方法相同，而效率远优于当前最先进的基于同态加密的安全聚合方案。更重要的是，随着模型参数数量的增加，我们方案的效率优势将愈发显著。