关键词: 联邦学习（FL）, 隐私保护, 对手检测, 同态加密, 阈值密钥共享

Abstract: The homomorphic encryption-threshold secret sharing (HE-SS) joint encryption algorithm is proposed to address the issues of data privacy preservation and malicious adversary detection in federated learning. Based on the interpolation principle of mapping message vectors to plaintext polynomials, a set of threshold secret sharing keys outside the encoding slots of the homomorphic encryption complex plane unit circle is established. The gradient information is implicitly transformed into ciphertext fragments and collaborative computation on the server is enabled, establishing a resilient aggregation protocol. Linear homomorphism is maintained in multi-party ciphertext operations by the algorithm, allowing for vector similarity discrimination without disclosing privacy. The inherent contradiction between privacy preservation and malicious detection in multi-party computation problems is resolved, and anonymous malicious node identification is achieved in specific environments. In a federated learning environment with both inference attacks and Byzantine attacks, test results demonstrate that sensitive client raw information is effectively protected and the existing mainstream defense solutions are outperformed in terms of global model convergence and accuracy by the HE-SS algorithm.

Key words: federal learning(FL), privacy preserving, adversary detection, homomorphic encryption, threshold secret sharing