The Spymasters Double-Agent Problem: Multiparty Computations Secure Unconditionally from Minorities and Cryptographically from Majorities

A multiparty-computation protocol allows each of a set of participants to provide secret input to a mutually agreed computation. Such protocols enforce two security properties: (1) secrecy of the inputs, apart from what is revealed by the output; and (2) correctness of the output, as defined by the agreed computation. All solutions, including those presented here, are based on two kinds of assumptions: (a) public-key cryptography; and (b) limited collusion in a setting where pairs of participants can exchange messages with secret and authenticated content. Some of the previous solutions relied totally on assumption (a), the others totally on (b).