  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$\times$.
