CHEHAB: Automatic Compiler Code Optimization for Fully Homomorphic Encryption

Fully Homomorphic Encryption (FHE) enables computations to be performed directly on encrypted data without requiring decryption, providing strong privacy guarantees. However, FHE remains computationally expensive, and writing efficient FHE programs is a complex, error-prone, and time-consuming task that demands significant cryptographic expertise. Programmers are often unaware of available optimizations, and applying them manually requires substantial effort. In this paper, we present CHEHAB, a compiler that automatically vectorizes scalar code, optimizes it, and generates highly efficient FHE programs. CHEHAB supports both structured and unstructured code and takes as input programs written in a domain-specific language embedded in C++. It relies on a Term Rewriting System (TRS) based on equality saturation to simplify and transform programs. CHEHAB targets two key challenges in FHE compilation: (1) automatic vectorization of scalar code, and (2) reduction of instruction execution latency and ciphertext noise growth. By leveraging equality saturation, CHEHAB explores a large optimization space to reduce instruction count and circuit depth while improving vector utilization. Experimental evaluation on a set of representative kernels shows that CHEHAB outperforms Coyote, a state-of-the-art vectorizing compiler for FHE. On average, CHEHAB generates code that is 7.38× faster at runtime, incurs 2.49× less accumulated noise, and achieves 251× faster compilation time. CHEHAB is released as an open-source compiler to support reproducibility and further research in FHE compilation.