Performance-aware Scale Analysis with Reserve for Homomorphic Encryption

Thanks to the computation ability on encrypted data and the efficient fixed-point execution, the RNS-CKKS fully homomorphic encryption (FHE) scheme is a promising solution for privacy-preserving machine learning services. However, writing an efficient RNS-CKKS program is challenging due to its manual scale management requirement. Each cipher-text has a scale value with its maximum scale capacity. Since each RNS-CKKS multiplication increases the scale, programmers should properly rescale a ciphertext by reducing the scale and capacity together. Existing compilers reduce the programming burden by automatically analyzing and managing the scales of ciphertexts, but they either conservatively rescale ciphertexts and thus give up further optimization opportunities, or require time-consuming scale management space exploration. This work proposes a new performance-aware static scale analysis for an RNS-CKKS program, which generates an efficient scale management plan without expensive space exploration. This work analyzes the scale budget, called "reserve", of each ciphertext in a backward manner from the end of a program and redistributes the budgets to the ciphertexts, thus enabling performance-aware scale management. This work also designs a new type system for the proposed scale analysis and ensures the correctness of the analysis result. This work achieves 41.8% performance improvement over EVA that uses conservative static scale analysis. It also shows similar performance improvement to exploration-based Hecate yet with 15526x faster scale management time.