Alternative Implementations of Secure Real Numbers

This paper extends the choice available for secure real number implementations with two new contributions. We will consider the numbers represented in form a -ϕb where ϕ is the golden ratio, and in form (-1) s • 2 e where e is a fixed-point number. We develop basic arithmetic operations together with some frequently used elementary functions. All the operations are implemented and benchmarked on Sharemind secure multi-party computation framework. It turns out that the new proposals provide viable alternatives to standard floating-and fixed-point implementations from the performance/error viewpoint in various settings. However, the optimal choice still depends on the exact requirements of the numerical algorithm to be implemented.