基于CKKS函数型Bootstrapping的融合式同态LayerNorm方案设计OA

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.