Monte Carlo execution time estimation for Privacy-preserving Distributed Function Evaluation protocols

Recent developments in Machine Learning and Deep Learning depend heavily on cloud computing and specialized hardware, such as GPUs and TPUs. This forces those using those models to trust private data to cloud servers. Such scenario has prompted a large interest on Homomorphic Cryptography and Secure Multi-Party Computation protocols that allow the use of cloud computing power in a privacy-preserving manner. When comparing the efficiency of such protocols, most works in literature resort to complexity analysis that gives asymptotic higher-bounding limits of computational cost when input size tends to infinite. These limits may be very different from the actual cost or execution time, when performing such computations over small, or average-sized datasets. We argue that Monte Carlo methods can render better computational cost and time estimates, fostering better design and implementation decisions for complex systems, such as Privacy-Preserving Machine Learning Frameworks.