Trimming: Decoupling Multiplicative Depth from Modulus Chains in RNS-CKKS via Rational Levels

Computer Science > Cryptography and Security [Submitted on 1 Aug 2026] Trimming: Decoupling Multiplicative Depth from Modulus Chains in RNS-CKKS via Rational Levels John Chiang Recent work on Grafting decouples scale factors from ciphertext moduli, enabling more flexible precision management in RNS-CKKS. However, the multiplicative depth remains fundamentally constrained by the modulus chain structure. In this paper, we propose \emph{Trimming}, a novel fine-grained level management mechanism that decouples multiplicative depth from modulus chains in RNS-CKKS via rational levels. The key idea is to introduce an auxiliary trimming modulus chain composed of smaller NTT-friendly modulus factors, which enables partial modulus transitions instead of directly discarding an entire modulus factor. By replacing conventional discrete level reductions with fine-grained modulus factor refinement, Trimming provides a rational-level abstraction beyond the traditional integer-based modulus chain representation. Our approach preserves the compatibility with existing RNS-CKKS arithmetic while enabling more flexible depth management and adaptive modulus transitions. Similar to Grafting, which addresses the precision bottleneck, Trimming targets the depth bottleneck in RNS-CKKS and contributes toward a fully decoupled RNS-CKKS architecture. The proposed framework will be further validated through concrete implementation and experimental evaluation to investigate its practical performance and computational overhead in real-world homomorphic encryption applications. Subjects: Cryptography and Security (cs.CR) Cite as: arXiv:2608.00375 [cs.CR]   (or arXiv:2608.00375v1 [cs.CR] for this version)   https://doi.org/10.48550/arXiv.2608.00375 Focus to learn more Submission history From: John Chiang [view email] [v1] Sat, 1 Aug 2026 01:11:41 UTC (86 KB) Access Paper: HTML (experimental) view license Current browse context: cs.CR < prev   |   next > new | recent | 2026-08 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?)