Addressing the challenge of balancing security and efficiency when deploying machine learning systems in untrusted environments, such as federated learning, remains a critical concern. A promising strategy to tackle this issue involves optimizing the performance of fully homomorphic encryption (HE). Recent research highlights the efficacy of advanced caching techniques, such as Rache, in significantly enhancing the performance of HE schemes without compromising security. However, Rache is constrained by an inherent limitation: its performance overhead is heavily influenced by the characteristics of plaintext models, specifically exhibiting a caching time complexity of $\mathcal{O}(N)$, where $N$ represents the number of cached pivots based on specific radixes. This caching overhead becomes impractical for handling large-scale data. In this study, we introduce a novel \textit{constant-time} caching technique that is independent of any parameters. The core concept involves applying scalar multiplication to a single cached ciphertext, followed by the introduction of a completely new and constant-time randomness. Leveraging the inherent characteristics of constant-time construction, we coin the term ``Smuche'' for this innovative caching technique, which stands for Scalar-multiplicative Caching of Homomorphic Encryption. We implemented Smuche from scratch and conducted comparative evaluations against two baseline schemes, Rache and CKKS. Our experimental results underscore the effectiveness of Smuche in addressing the identified limitations and optimizing the performance of homomorphic encryption in practical scenarios.

翻译：在不可信环境（如联邦学习）中部署机器学习系统时，平衡安全性与效率始终是核心挑战。一种有前景的解决方案是通过优化全同态加密（HE）性能来应对该问题。近期研究表明，Rache等高级缓存技术能在不牺牲安全性的前提下显著提升HE方案的性能。然而，Rache存在固有缺陷：其性能开销严重受明文模型特征影响，具体表现为基于特定基数的缓存时间复杂度为$\mathcal{O}(N)$（其中$N$为缓存枢轴数量）。这种缓存开销在处理大规模数据时变得不可实际。本研究提出了一种与任何参数无关的新型\textit{常数时间}缓存技术，核心思想是对单个缓存密文执行标量乘法运算，随后引入全新的常数时间随机性。基于常数时间构造的固有特性，我们将该创新缓存技术命名为"Smuche"（同态加密的标量乘法缓存）。我们从头实现了Smuche，并与Rache和CKKS两种基线方案进行了对比评估。实验结果证明了Smuche在解决上述局限性及优化实际场景中同态加密性能方面的有效性。