Multiparty Computation from Somewhat Homomorphic Encryption

We propose a general multiparty computation protocol secure against an active adversary corrupting up to n−1 of the n players. The protocol may be used to compute securely arithmetic circuits over any finite field Fpk . Our protocol consists of a preprocessing phase that is both independent of the function to be computed and of the inputs, and a much more efficient online phase where the actual computation takes place. The online phase is unconditionally secure and has total computational (and communication) complexity linear in n, the number of players, where earlier work was quadratic in n. Moreover, the work done by each player is only a small constant factor larger than what one would need to compute the circuit in the clear. We show this is optimal for computation in large fields. In practice, for 3 players, a secure 64-bit multiplication can be done in 0.05 ms. Our preprocessing is based on a somewhat homomorphic cryptosystem. We extend a scheme by Brakerski et al., so that ...

• Type: Journal
• Year: 2012
• Where: CRYPTO
• Authors: Ivan Damgård, Valerio Pastro, Nigel P. Smart, Sarah Zakarias
• Keywords: Arithmetic Circuits, Communication Complexity, CRYPTO 2012, Cryptology, Preprocessing Phase