Scalable and Unconditionally Secure Multiparty Computation

We present a multiparty computation protocol that is unconditionally secure against adaptive and active adversaries, with communication complexity O(Cn)k + O(Dn)k + poly(nκ), where C is the number of gates in the circuit, n is the number of parties, k is the bitlength of the elements of the field over which the computation is carried out, D is the multiplicative depth of the circuit, and κ is the security parameter. The corruption threshold is t < n/3. For passive security the corruption threshold is t < n/2 and the communication complexity is O(nC)k. These are the first unconditionally secure protocols where the part of the communication complexity that depends on the circuit size is linear in n. We also present a protocol with threshold t < n/2 and complexity O(Cn)k+poly(nκ) based on a complexity assumption which, however, only has to hold during the execution of the protocol – that is, the protocol has so called everlasting security.