Non-Interactive Secure Multiparty Computation

We introduce and study the notion of non-interactive secure multiparty computation (NIMPC). An NIMPC protocol for a function f(x1,…,x n ) is specified by a joint probability distribution R = (R1,…,R n ) and local encoding functions Enc i (x i ,r i ), 1 ≤ i ≤ n. Given correlated randomness (r1,…,r n ) ∈ R R, each party P i , using its input x i and its randomness r i , computes the message m i = Enc i (x i ,r i ). The messages m1,…,m n can be used to decode f(x1,…,x n ). For a set T ⊆ [n], the protocol is said to be T-robust if revealing the messages \((\mathrm{Enc}_i(x_i,r_i))_{i\not\in T}\) together with the randomness (r i )i ∈ T gives the same information about \((x_i)_{i\not\in T}\) as an oracle access to the function f restricted to these input values. Namely, a coalition T can learn no more than the restriction of f fixing the inputs of uncorrupted parties, which, in this non-interactive setting, one cannot hope to hide. For 0 ≤ t ≤ n, the protocol is t-robust if it is T-robust for every T of size at most t and it is fully robust if it is n-robust. A 0-robust NIMPC protocol for f coincides with a protocol in the private simultaneous messages model of Feige et al. (STOC 1994).