Unconditionally Secure Multiparty Computation and Secret Sharing

We suggest protocols for secure computation of the sum, product, and some other functions of three or more elements of an arbitrary constructible ring, without using any one-way functions. A new input that we offer here is that, in contrast with other proposals, we conceal “intermediate results” of a computation, i.e., we do not let any party accumulate functions of other parties’ private numbers that would allow him to recover those numbers. Other applications of our method include voting/rating over insecure channels and a rather elegant and efficient solution of the “two millionaires problem”. Finally, we propose a secret sharing scheme where an advantage over Shamir’s and other known secret sharing schemes is that nobody, including the dealer, ends up knowing the shares (of the secret) owned by any particular player.