Point-Counting Method for Embarrassingly Parallel Evaluation in Secure Computation

In this paper we propose an embarrassingly parallel method for use in secure computation. The method can be used for a special class of functions over fixed-point real numbers namely, for functions f for which there exist functions g and h such that g(f(x), x) = h(x) and g(·, x) is monotonous. These functions include f(x) = 1 x , f(x) = √ x and f(x) = 1 √ x , but also any functions that can be represented as finding a root of a polynomial with secret coefficients and with a sufficiently low rank. The method can also be applied for other functions — such as the logarithm function. The method relies on counting techniques rather than evaluation of series, allowing the result to be obtained using less rounds of computations with the price of more communication in one round. Since the complexity of oblivious computing methods (like secret-shared multi-party computations (SMC)) is largely determined by the round complexity, this approach has a potential to give better performance/precision ratio compared to series-based approaches. We have implemented the method for several functions and benchmarked them using Sharemind SMC engine.