Secure floating point arithmetic and private satellite collision analysis

In this paper, we show that it is possible and, indeed, feasible to use secure multiparty computation (SMC) for calculating the probability of a collision between two satellites. For this purpose, we first describe basic floating point arithmetic operators (addition and multiplication) for multiparty computations. The operators are implemented on the $${\textsc {Sharemind}}$$SHAREMIND SMC engine. We discuss the implementation details, provide methods for evaluating example elementary functions (inverse, square root, exponentiation of $$e$$e, error function). Using these primitives, we implement a satellite conjunction analysis algorithm and give benchmark results for the primitives as well as the conjunction analysis itself.