Efficient Arithmetic-and-Comparison Homomorphic Encryption with Space Switching

Computer Science > Cryptography and Security [Submitted on 21 Apr 2026] Efficient Arithmetic-and-Comparison Homomorphic Encryption with Space Switching Erwin Eko Wahyudi, Yan Solihin, Qian Lou Fully homomorphic encryption (FHE) enables computation on encrypted data without decryption, making it central to privacy-preserving applications. However, no existing scheme efficiently supports both arithmetic and comparison operations in a unified framework. Prior approaches such as scheme switching and polynomial approximation face serious limitations: switching incurs prohibitive overhead for large inputs, while approximation methods introduce errors near critical points, restricting use in accuracy-sensitive tasks. We propose space switching method to integrate arithmetic and comparison computation seamlessly within FV-style schemes. Our approach identifies that the two types of operations require different plaintext spaces and introduces two procedures: a reduction step to transition from the number space \mathbb{Z}_{p^r} to the digit space \mathbb{Z}_{p}, and a modulus-raising step to map results back to \mathbb{Z}_{p^r}. This design enables continuous evaluation of arithmetic and comparison within the same scheme. Experiments show that our method achieves up to 17\times faster performance than scheme switching and 15\times faster than direct comparison on database workloads, demonstrating its practicality for real-world privacy-preserving computation. Code and artifacts are available at this https URL. Comments: Accepted by IEEE Symposium on Security and Privacy 2026 Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2604.19890 [cs.CR]   (or arXiv:2604.19890v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2604.19890 Focus to learn more Submission history From: Qian Lou [view email] [v1] Tue, 21 Apr 2026 18:12:37 UTC (289 KB) Access Paper: view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-04 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)