The Security Power of the Ballot Box Patterns in Pitch Periods

We show that any function f can be securely evaluated by a protocol with ballots and a ballot box. That is, n mutually suspicious players, each player i possessing a secret input xi, can use ballots and ballot boxes to jointly evaluate f(x1, . . . , xn) = (y1, . . . , yn), so that (no matter how many players may collude and deviate from their prescribed instructions, and no matter how long they compute!) each player i learns exactly yi with the same privacy and correctness as if all players privately handed their secret inputs to a trusted party, who privately evaluates f and privately returns yi to each player i. Our protocol is (1) efficient, (2) enjoys perfect privacy, (3) guarantees perfect correctness, (4) is universally composable in the sense of [DoMi00] and [Can01], and (5) is always collusion-free in the sense of [LMS05], even for games with secret actions.