On Secure Two-party Computation

1.1. Secure Two-Party Computation. In essence, secure multiparty computation is the solution to the problem how to compute on private inputs from several parties when we do not trust other parties and we don’t have a central authority who can get inputs, perform computations and give outputs to those that need them. Here we will talk about secure twoparty computation, where Alice, holding xa and Bob, holding xb, wish to learn the outcome of f(xa, xb) for some function f without revealing anything else. The original example used by Yao, when he proposed the problem in 1982 in [1] is the millionaire problem, where two millionaires want to find out who is richer without the other millionaire learning how much money they have, but there are also more practical examples. Yao proposed the garbled circuits solution — we construct a circuit that evaluates the function f where gates and wires have been replaced with cryptographic primitives. This report aims to give a short overview of two recent approaches in secure two-party computation — one is based on the [2] and the other is the LEGO protocol, proposed by [3] and improved by [4]. First, we will describe how garbled circuits are usually done.