We introduce and study the notion of non-interactive secure multiparty computation
(NIMPC). An NIMPC protocol for a function f (x 1,…, xn) is specified by a joint probability
distribution R=(R 1,…, R n) and local encoding functions Enc i (xi, ri), 1≤ i≤ n. Given
correlated randomness (r 1,…, rn)∈ RR, each party P i, using its input xi and its randomness
ri, computes the message mi= Enc i (xi, ri). The messages m 1,…, mn can be used to decode
f (x 1,…, xn). For a set T⊆ n, the protocol is said to be T-robust if revealing the messages …

Non-interactive secure multiparty computation (NIMPC) is a variant of secure computation
which allows each of n players to send only a single message depending on his input and
correlated randomness. Abelian programs, which can realize any symmetric function, are
defined as functions on the sum of the players' inputs over an abelian group and provide
useful functionalities for real-world applications. We improve and extend the previous results
in the following ways: We present NIMPC protocols for abelian programs that improve the …