A Compiler from Array Programs to Vectorized Homomorphic Encryption

Abstract: Homomorphic encryption (HE) is a practical approach to secure computation over encrypted data. However, writing programs with efficient HE implementations remains the purview of experts. A difficult barrier for programmability is that efficiency requires operations to be vectorized in inobvious ways, forcing efficient HE programs to manipulate ciphertexts with complex data layouts and to interleave computations with data movement primitives. We present Viaduct-HE, a compiler generates efficient vectorized HE programs. Viaduct-HE can generate both the operations and complex data layouts required for efficient HE programs. The source language of Viaduct-HE is array-oriented, enabling the compiler to have a simple representation of possible vectorization schedules. With such a representation, the compiler searches the space of possible vectorization schedules and finds those with efficient data layouts. After finding a vectorization schedule, Viaduct-HE further optimizes HE programs through term rewriting. The compiler has extension points to customize the exploration of vectorization schedules, to customize the cost model for HE programs, and to add back ends for new HE libraries. Our evaluation of the prototype Viaduct-HE compiler shows that it produces efficient vectorized HE programs with sophisticated data layouts and optimizations comparable to those designed by experts.