HECATE: Performance-Aware Scale Optimization for Homomorphic Encryption Compiler

Despite the benefit of Fully Homomorphic Encryption (FHE) that supports encrypted computation, writing an efficient FHE application is challenging due to magnitude scale management. Each FHE operation increases scales of ciphertext and leaving the scales high harms performance of the following FHE operations. Thus, rescaling ciphertext is inevitable to optimize an FHE application, but since FHE requires programmers to match the rescaling levels of operands of each FHE operation, programmers should rescale ciphertext reflecting the entire FHE application. Although recently proposed FHE compilers reduce the programming burden by automatically manipulating ciphertext scales, they fail to fully optimize the FHE application because they greedily rescale the ciphertext without considering their performance impacts throughout the entire application. This work proposes HECATE, a new FHE compiler framework that optimizes scales of ciphertext reflecting their rescaling levels and performance impact. With a new type system that embeds the scale and rescaling level, and a new rescaling operation called downscale, HECATE makes various scale management plans, analyzes their expected performance, and finds the optimal rescaling points throughout the entire FHE application. This work implements HECATE on top of the MLIR framework with a Python frontend and shows that HECATE achieves 27% speedup over the state-of-The-Art approach for various FHE applications.