Sen. Res. fellow Jan Villemson (Cybernetica AS)
Prof. Dominique Unruh (Institute of Computer Science, UT)
Assoc. Prof. Claudio Orlandi (Aarhus University, Denmark),
Assoc. Prof. Octavian Catrina (Polytechnic University of Bucharest, Romania).
Nowadays data and its analysis are ubiquitous and very useful. Due to this popularity, different combinations of how these two can relate to each other proliferate. We focus on the cases where the owners of the data and those who compute on them don't coincide either partially or totally. Examples are medicinal data where the owners want secrecy but where doing statistics on them collectively is useful, or outsourcing computation. The discipline that studies these cases is called secure computation. This field has been mostly working on integer and bit data types, as they are easier to work on, and due to it being possible to reduce the other cases to integer and bit manipulations. However, using these reductions bluntly will give inefficient results. Thus this thesis studies secure computation on real numbers and presents three methods for improving efficiency. The first method concerns with fixed-point and floating-point numbers. Fixed-point numbers are simple in construction, but can lack precision and flexibility. Floating-point numbers, on the other hand, are precise and flexible, but are rather complicated in nature, which in secure setting translates to expensive operations. The first method thus combines those two number types for greater efficiency.
The second method is based on the fact that in the concrete paradigm we use, it does not matter timewise whether we perform one or million operations in parallel. Thus we attempt to
perform many instances of a fast operation in parallel in order to evaluate a more complicated
Thirdly we introduce a new real number type. We use pairs of integers (a,b) to represent the real number a – φb where φ = 1.618... is the golden ratio. This number type allows us to perform addition and multiplication relatively quicky and also achieves reasonable granularity.