Private simultaneous messages protocols with applications

We study the Private Simultaneous Messages (PSM) model which is a variant of the model proposed in [16]. In the PSM model there are n players P₁, ..., P_n, each player P_i holding a secret input x_i (say, a bit), and all having access to a common random string. Each player sends a single message to a special player, Carol, depending on its own input and the random string (and independently of all other messages). Based on these messages, Carol should be able to compute f(x₁, ..., x_n) (for some predetermined function f) but should learn no additional information on the values of x₁, ..., x_n. Our results go in two directions. First, we present efficient PSM protocols, which improve the efficiency of previous solutions, and extend their scope to several function classes for which no such solutions were known before. These classes include most of the important linear algebraic functions; as a result, we get efficient constant-round private protocols (in the standard model) for these classes. Second, we present reductions that allow transforming PSM protocols into solutions for some other problems, thereby demonstrating the power of this model. An interesting reduction of this sort shows how to construct, based on a standard (₁²)-OT (Oblivious Transfer) primitive, generalized-OT (GOT) primitives that, we believe, might be useful for the design of cryptographic protocols.