With the rise of practical Secure Multi-party Computation (MPC) protocols, compilers have been developed that create Boolean or Arithmetic circuits for MPC from functionality descriptions in a high-level language. Previous compilers focused on the creation of size-minimal circuits. However, many MPC protocols, such as GMW and SPDZ, have a round complexity that is dependent on the circuit's depth. When deploying these protocols in real world network settings, with network latencies in the range of tens or hundreds of milliseconds, the round complexity quickly becomes a significant performance bottleneck. In this work, we present ShallowCC, a compiler extension that creates depth minimized Boolean circuits from ANSI-C. We first introduce novel optimized building blocks that are up to 50% shallower than previous constructions. Second, we present multiple high- and low-level depth minimization techniques and implement these in the existing CBMCGC compiler. Our experiments show significant depth reductions over hand-optimized constructions (for some applications up to 2.5×), while maintaining a circuit size that is competitive with size-minimizing compilers. Evaluating exemplary functionalities in a GMW framework, we show that depth reductions lead to significant speed-ups in any real-world network setting. For an exemplary biometric matching application we report a 400× speed-up in comparison with a circuit generated from a size-minimizing compiler.
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