Alternative Implementations of Secure Real Numbers
Vassil S. Dimitrov, Liisi Kerik, Toomas Krips, Jaak Randmets, Jan Willemson · 2016
This paper extends the choice available for secure real number implementations with two new contributions. We will consider the numbers represented in form a-φ b where φ is the golden ratio, and in form (-1)s.2e 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.