Adaptively Secure UC Constant Round Multi-Party Computation Protocols

We present a universally composable multiparty computation protocol that is adaptively secure against corruption of n − 1 of the n players. The protocol has a constant number of rounds and communication complexity that depends only on the number of inputs and outputs (and not on the size of the circuit to be computed securely). Such protocols were already known for honest majority. However, adaptive security and constant round was known to be impossible in the stand-alone model and with black-box proofs of security. Here, we solve the problem in the UC model using a set-up assumption. Our protocol is secure assuming LWE is hard and achieved by building a special type of crypto system we call equivocal FHE from LWE. We also build adaptively secure and constant round UC commitment and zero-knowledge proofs (of knowledge) based on LWE.