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$\times$.

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