Homomorphic encryption (HE) has found extensive utilization in federated learning (FL) systems, capitalizing on its dual advantages: (i) ensuring the confidentiality of shared models contributed by participating entities, and (ii) enabling algebraic operations directly on ciphertexts representing encrypted models. Particularly, the approximate fully homomorphic encryption (FHE) scheme, known as CKKS, has emerged as the de facto encryption scheme, notably supporting decimal numbers. While recent research predominantly focuses on enhancing CKKS's encryption rate and evaluation speed in the context of FL, the search operation has been relatively disregarded due to the tendency of some applications to discard intermediate encrypted models. Yet, emerging studies emphasize the importance of managing and searching intermediate models for specific applications like large-scale scientific computing, necessitating robust data provenance and auditing support. To address this, our paper introduces an innovative approach that efficiently searches for a target encrypted value, incurring only a logarithmic number of network interactions. The proposed method capitalizes on CKKS's additive and multiplicative properties on encrypted models, propagating equality comparisons between values through a balanced binary tree structure to ultimately reach a single aggregate. A comprehensive analysis of the proposed algorithm underscores its potential to significantly broaden FL's applicability and impact.

翻译：同态加密（HE）在联邦学习（FL）系统中得到了广泛应用，这得益于其双重优势：（i）确保参与实体贡献的共享模型的机密性，（ii）支持直接在表示加密模型的密文上执行代数运算。特别是，被称为CKKS的近似全同态加密（FHE）方案已成为事实上的加密方案，尤其支持十进制数运算。尽管近期研究主要聚焦于提升CKKS在FL背景下的加密速率和评估速度，但由于某些应用倾向于丢弃中间加密模型，搜索操作相对被忽视。然而，新兴研究强调，对于大规模科学计算等特定应用，管理和搜索中间模型具有重要意义，这需要稳健的数据溯源和审计支持。为解决这一问题，本文提出一种创新方法，能够高效搜索目标加密值，仅需对数级别的网络交互。所提方法利用CKKS在加密模型上的加法和乘法特性，通过平衡二叉树结构传播数值间的相等比较，最终汇聚至单一聚合结果。对所提算法的全面分析表明，其具有显著拓展FL应用范围及影响力的潜力。