Logsum using Garbled circuits

Abstract

Secure multiparty computation allows for a set of users to evaluate a particular function over their inputs without revealing the information they possess to each other. Theoretically, this can be achieved using fully homomorphic encryption systems, but so far they remain in the realm of computational impracticability. An alternative is to consider secure function evaluation using homomorphic public-key cryptosystems or Garbled Circuits, the latter being a popular trend in recent times due to important breakthroughs. We propose a technique for computing the logsum operation using Garbled Circuits. This technique relies on replacing the logsum operation with an equivalent piecewise linear approximation, taking advantage of recent advances in efficient methods for both designing and implementing Garbled Circuits. We elaborate on how all the required blocks should be assembled in order to obtain small errors regarding the original logsum operation and very fast execution times.