AI 中文总结
该研究提出Trimming机制，通过引入辅助裁剪模链，在RNS-CKKS中解耦乘法深度与模链，以解决其深度瓶颈，为完全解耦架构提供支持。
AI 中文摘要
近期关于Grafting的研究将缩放因子与密文模化解耦，实现了RNS-CKKS中更灵活的精度管理，但乘法深度仍受模链结构的根本限制。本文提出Trimming，一种新型细粒度层级管理机制，通过有理层级在RNS-CKKS中解耦乘法深度与模链，核心思路是引入由更小的NTT友好型模因子构成的辅助裁剪模链，支持部分模转换而非直接丢弃整个模因子。通过用细粒度模因子细化替代传统离散层级缩减，Trimming提供了超越传统基于整数的模链表示的有理层级抽象，在保留与现有RNS-CKKS算术兼容性的同时，实现了更灵活的深度管理与自适应模转换。与解决精度瓶颈的Grafting类似，Trimming针对RNS-CKKS的深度瓶颈，为实现完全解耦的RNS-CKKS架构作出贡献，该框架将通过具体实现与实验评估进一步验证，以探究其在实际同态加密应用中的实际性能与计算开销。
英文摘要
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.
CommentsThe current Trimming idea may not be feasible, as there may be bugs or errors in the implementation
