通信学报2026，Vol.47Issue(8)：296-310,15.DOI:10.11959/j.issn.1000-436x.TXXB260263
基于CKKS函数型Bootstrapping的融合式同态LayerNorm方案设计
Design of a fused homomorphic LayerNorm scheme based on CKKS functional Bootstrapping
摘要
Abstract
To address the high multiplicative depth required for inverse square root computation in LayerNorm for CKKS-based homomorphic Transformer inference,a fused functional Bootstrapping scheme was proposed.In the Eval-Mod stage,the arcsine polynomial was replaced with a composite polynomial that directly computed the inverse square root.Pre-scaling and statistical bounds were used to constrain the input,enabling zero additional multiplicative depth within the calibrated bound.In addition,the Remez algorithm was employed to construct a degree-31 minimax approxi-mation.Experimental results show that,compared with the Goldschmidt iteration(k=3),the proposed scheme saves six levels of multiplicative depth,accelerates LayerNorm computation by 1.26 times,and reduces peak memory usage by 16.7%.BERT-Base achieves a homomorphic classification accuracy of 92.1%on the SST-2 dataset,only 0.4 percentage points lower than plaintext inference.The proposed scheme reduces the computational depth and resource overhead of homomorphic LayerNorm while maintaining classification accuracy.关键词
全同态加密/CKKS/层归一化/函数型Bootstrapping/Transformer/隐私保护推理Key words
fully homomorphic encryption/CKKS/LayerNorm/functional Bootstrapping/Transformer/privacy-preserving inference分类
信息技术与安全科学引用本文复制引用
陈智罡,宋新霞,Liqun Chen..基于CKKS函数型Bootstrapping的融合式同态LayerNorm方案设计[J].通信学报,2026,47(8):296-310,15.基金项目
国家自然科学基金资助项目(No.62571283) （No.62571283）
浙江省自然科学基金资助项目(No.LMS26F020025) （No.LMS26F020025）
宁波市自然科学基金资助项目(No.2025J185) （No.2025J185）
宁波财经学院高级别科研培育基金资助项目(No.1320263702) The National Natural Science Foundation of China(No.62571283),Zhejiang Provincial Natural Science Founda-tion of China(No.LMS26F020025),Ningbo Natural Science Foundation of China(No.2025J185),High-Level Scientific Research In-cubation Project of Ningbo University of Finance&Economics(No.1320263702) （No.1320263702）
