CipherAPR: Accelerating RNS-CKKS Encrypted Inference via Importance-Guided and Level-Aware Mixed-Degree Polynomial Design

Fully Homomorphic Encryption (FHE) enables Machine Learning as a Service (MLaaS) providers to perform inference over encrypted data, preserving user privacy. In the RNS-CKKS FHE scheme, however, ReLU activations must be replaced with polynomials. High-degree polynomial approximations preserve accuracy but consume more ciphertext levels, triggering costly bootstrapping operations. Existing mixed-degree methods reduce the bootstrapping count by assigning different polynomial degrees across layers. However, recent FHE compiler research shows that reducing the bootstrapping count alone is insufficient to fully accelerate inference, because bootstrapping placement and the level budget restored after each operation also significantly affect performance. Incorporating such execution-side factors into mixed-degree design substantially enlarges the search space, making straightforward extensions of existing methods computationally infeasible. We propose CipherAPR, an importance-guided framework for level-aware mixed-degree polynomial design. CipherAPR introduces the Low-Magnitude Activation Ratio (LMAR) to prioritize degree updates on accuracy-sensitive layers, combines Domain-Adaptive Approximation (DAAP) with Multi-Objective Coefficient Tuning (MOCT) to produce reusable polynomial approximations that consume fewer ciphertext levels, and applies ciphertext-level utilization (CLU) to filter configurations with poor restored-level utilization. Lightweight latency and accuracy estimators further accelerate offline candidate screening. Experiments on ResNet and VGG show that CipherAPR achieves a 1.09×–1.39× speedup over AutoFHE with comparable accuracy.