  We consider the problems of secret sharing and multiparty computation,
assuming that agents prefer to get the secret (resp., function value) to not
getting it, and secondarily, prefer that as few as possible of the other agents
get it. We show that, under these assumptions, neither secret sharing nor
multiparty function computation is possible using a mechanism that has a fixed
running time. However, we show that both are possible using randomized
mechanisms with constant expected running time.
