While homomorphic encryption (HE) has garnered significant research interest in cloud-based outsourced databases due to its algebraic properties over ciphertexts, the computational overhead associated with HE has hindered its widespread adoption in production database systems. Recently, a caching technique called Radix-based additive caching of homomorphic encryption (Rache) was proposed in SIGMOD'23. The primary objective of this paper is to address the performance overhead resulting from the expensive randomization process in Rache. To achieve this, we propose a novel encryption algorithm called $ASEnc$, which replaces the computationally intensive full scan of radixes with the caching of a polynomial number of radix-powers during an offline stage. This design significantly reduces the performance impact caused by randomization. Furthermore, this paper aims to extend Rache's capabilities to support floating-point numbers. To accomplish this, we introduce a new encryption algorithm named $FSEnc$, leveraging efficient constant multiplication available in state-of-the-art fully homomorphic encryption (FHE) schemes. Notably, $FSEnc$ offers the flexibility to cache the coefficients instead of the radixes themselves, which may result in a large number of cached ciphertexts. However, we manage this efficiently by streaming the dynamically cached ciphertexts through a vector of circular buffers. We demonstrate that both encryption algorithms guarantee semantic security (IND-CPA). To validate their performance, we implement both algorithms as loadable functions in MySQL 8.0 and deploy the system prototype on a 96-core server hosted in the Chameleon Cloud. Experimental results showcase that $ASEnc$ outperforms Rache by 2.3--3.3$\times$, while $FSEnc$ surpasses the state-of-the-art floating-point FHE CKKS by 1.8--5.6$\times$.

翻译：同态加密（HE）因其在密文上的代数性质而在基于云的外包数据库领域引起了广泛的研究兴趣，但与同态加密相关的计算开销阻碍了其在生产数据库系统中的广泛应用。近期，SIGMOD'23提出了一种名为基于基数加性缓存的同态加密（Rache）的缓存技术。本文的主要目标是解决Rache中因昂贵的随机化过程导致的性能开销问题。为此，我们提出了一种名为$ASEnc$的新型加密算法，该算法通过在离线阶段缓存多项式数量的基数幂次来替代计算密集型的完整基数扫描，从而显著减少了随机化带来的性能影响。此外，本文旨在扩展Rache对浮点数的支持能力。为实现这一目标，我们引入了一种名为$FSEnc$的新型加密算法，该算法利用现有最先进的全同态加密（FHE）方案中的高效常数乘法。值得注意的是，$FSEnc$提供了一种灵活性，可以缓存系数而非基数本身，这可能导致大量缓存的密文。然而，我们通过将动态缓存的密文流经一组环形缓冲区来高效管理这一问题。我们证明了两种加密算法均能保证语义安全性（IND-CPA）。为验证其性能，我们将两种算法作为可加载函数在MySQL 8.0中实现，并将系统原型部署在Chameleon云中的96核服务器上。实验结果表明，$ASEnc$的性能比Rache提升2.3-3.3倍，而$FSEnc$的性能比最先进的浮点FHE方案CKKS提升1.8-5.6倍。