The marriage proposals problem: fair and efficient solution for two-party computations

Abstract

In this paper we will present a fair and efficient solution to The Marriage Proposals Problem (i.e. two-party computation of AND). This solution uses many similar ideas with the solution to The Socialist Millionaires' Problem of [6] (we deal here with AND instead of EQUALITY and this introduces some practical small changes). Then we generalize our algorithm in three directions : first, to compute the AND with many players (not only two). Second, to compute any binary operators (boolean function of two inputs). In all these solutions we do not use Mix and Match techniques [20] but direct solutions based on the DiffieHellman assumption (whereas the solution of The Socialist Millionaires' Problem of [6], as Mix and Match techniques, requires the Decision DiffieHellman assumption). Moreover, with our solutions we have to compute less exponentiations compared with Mix and Match techniques (50 4- 4k instead of 78+4k or 96+4k, where k is the security parameter i.e. security is in l/2 k, we reduce the overall security to the Diffie-Hellman problem is difficult). Third, we will explain how to have a fair computation of any boolean function with any number of inputs (i.e. any number of players) by using Mix and Match techniques (here we will explain how to extend the scheme of [20] for fair computations). © Springer-Verlag 2004.