Universally Composable Efficient Multiparty Computation from Threshold Homomorphic Encryption

We present a new general multiparty computation protocol for the cryptographic scenario which is universally composable — in particular, it is secure against an active and adaptive adversary, corrupting any minority of the parties. The protocol is as efficient as the best known statically secure solutions, in particular the number of bits broadcast (which dominates the complexity) is Ω (nk |C|), where n is the number of parties, k is a security parameter, and |C| is the size of a circuit doing the desired computation. Unlike previous adaptively secure protocols for the cryptographic model, our protocol does not use non-committing encryption, instead it is based on homomorphic threshold encryption, in particular the Paillier cryptosystem.