## Cryptology ePrint Archive: Report 2016/773

Alternative Implementations of Secure Real Numbers

Vassil Dimitrov and Liisi Kerik and Toomas Krips and Jaak Randmets and Jan Willemson

Abstract: This paper extends the choice available for secure real number implementations with two new contributions. We will consider the numbers represented in form $a-\varphi b$ where $\varphi$ is the golden ratio, and in form $(-1)^s\cdot2^e$ 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.

Category / Keywords: cryptographic protocols / Secure fixed- and floating-point arithmetic, privacy-preserving data analysis, secure computations

Original Publication (in the same form): Accepted to ACM CCS 2016