The round complexity of secure protocols
Donald Beaver, Silvio Micali, Phillip Rogaway · 1990
In a network of n players, each player i having private input zi, we show how the players can collaboratively evaluate a function f(zl, ..., zn) in a way that does not compromise the privacy of the players' inputs, and yet requires only a constant number of rounds of interaction.The underlying model of computation is a complete network of private channels, with broadcast, and a majority of the players must behave honestly.Our solution assumes the existence of a one-way function.share bi to player i.For some parameter t, t < n/2, we require that no t players get information about b from their pieces; and yet, b is recoverable, and is known to be recoverable, given the cooperation of the n -t good players--even if the t bad players try to obstruct b's recovery, or try to alter the recovered value.The value b which a player has effectively "committed to" is independent of the values that honest players may concurrently be committing to.After the sharing stage, a computation stage follows, in which each player, given his own shares of xl, ..., x,~, computes his own share of f(zt,..., z,~).To accomplish this, the function f to be evaluated is represented by a