COMBINE: COMpilation and Backend-INdependent vEctorization for Multi-Party Computation

Recent years have witnessed significant advances in programming technology for multi-party computation (MPC), bringing MPC closer to practice and wider applicability. Typical MPC programming frameworks focus on either front-end language design (e.g., Wysteria, Viaduct, SPDZ), or back-end protocol design and implementation (e.g., ABY, MOTION, MP-SPDZ). We propose a methodology for an MPC compilation toolchain, which by mimicking the compilation methodology of classical compilers enables middle-end (i.e., machine-independent) optimizations, yielding significant improvements. We advance an intermediate language, which we call MPC-IR that can be viewed as the analogue of (enriched) Static Single Assignment (SSA) form. MPC-IR enables backend-independent optimizations in a close analogy to machine-independent optimizations in classical compilers. To demonstrate our approach, we focus on a specific backend-independent optimization, SIMD-vectorization: We devise a novel classical-compiler-inspired automatic SIMD-vectorization on MPC-IR. To demonstrate backend independence and quality of our optimization, we evaluate our approach with two mainstream backend frameworks that support multiple types of MPC protocols, namely MOTION and MP-SPDZ, and show significant improvements across the board.