Abstract: Abstract: Dual threats of identity authentication failure and malicious poisoning are faced by Federated Prototype Learning in open network environments: existing homomorphic signature schemes suffer from uneven spectral distribution during lattice sampling, allowing external attackers to bypass authentication by forging public keys; meanwhile, legitimate identities are exploited by internal attackers to inject malicious prototypes into the server, leading to a decline in global model accuracy and convergence instability. To address these issues, an Identity Authentication Mechanism for Federated Prototype Learning based on Spectral Metric Lattice Sampling (FedSPE) was proposed. First, an adaptive spectral lattice sampling algorithm was developed. By utilizing the spectral norm of the noise matrix as a manifold metric, the covariance matrix was dynamically regulated to precisely align with the spectral characteristics of the lattice basis. Consequently, sampling statistical bias was fundamentally eliminated, and robust homomorphic signature credentials were established. Second, an abnormal prototype detection algorithm based on local density estimation was designed to quantify the degree of distributional anomaly of prototypes within the feature space. A differentiated graded correction strategy was implemented, where "hard blocking" was executed on high-risk outliers and "weighted soft correction" was applied to medium-risk perturbations. Through this approach, the contribution of benign heterogeneous features was maximized while poisoning was rigorously prevented, thereby guaranteeing the stability of global aggregation. Experimental results demonstrate that, compared with existing work, the abnormal prototype recognition rate is increased by 12.3% and global model accuracy is improved by 4.7% through the effective blocking of illegal clients and the injection of abnormal prototypes.

Key words: Federated Prototype Learning, Homomorphic Signature, Lattice Sampling, identity authentication, Anomaly Detection

摘要： 摘 要: 联邦原型学习在开放网络环境中面临身份认证失效与恶意投毒双重威胁：现有同态签名方案在格采样过程中存在谱分布不均的缺陷，致使外部攻击者伪造公钥绕过身份认证；同时，内部攻击者利用合法身份向服务器注入恶意原型，导致全局模型精度下降且难以收敛。为解决上述问题，提出一种基于光谱计量格采样的联邦原型学习身份认证机制（FedSPE）。首先提出自适应光谱格采样算法，以噪声矩阵的光谱范数为流形度量，动态规约协方差矩阵精准匹配格基谱特性，从根源上消除采样统计偏差并确立同态签名凭证。其次，设计基于局部密度估计的异常原型检测算法，量化原型在特征空间中的分布异常度；通过实施差异化的分级矫正策略——对高风险离群点执行硬性阻断，对中风险扰动执行加权软修正——在严防投毒的同时，最大化保留良性异构特征的贡献度，保障全局聚合的稳定性。实验表明，与现有工作相比，FedSPE通过阻断非法客户端和异常原型注入，使异常原型识别率提升12.3%，全局模型精度提升4.7%。

关键词: 联邦原型学习, 同态签名, 格采样, 身份认证, 异常检测