Four Round Secure Computation Without Setup

We construct a 4-round multi-party computation protocol in the plain model for any functionality, secure against a malicious adversary. Our protocol relies on the sub-exponential hardness of the Learning with Errors (LWE) problem with slightly super-polynomial noise ratio, and on the existence of adaptively secure commitments. Our round complexity matches a lower bound of Garg et al. (EUROCRYPT ’16), and outperforms the state of the art of 6-rounds based on similar assumptions to ours, and 5-rounds relying on indistinguishability obfuscation and other strong assumptions. To do this, we construct an LWE based multi-key FHE scheme with a very simple one-round distributed setup procedure (vs. the trusted setup required in previous LWE based constructions). This lets us construct a 3-round semi-malicious protocol without setup using the approach of Mukherjee and Wichs (EUROCRYPT ’16). Finally, subexponential hardness and adaptive commitments are used to “compile” the protocol into the fully malicious setting. ∗Supported by the Israel Science Foundation (Grant No. 468/14), Alon Young Faculty Fellowship and Binational Science Foundation (Grant No. 712307). †Supported by the Defense Advanced Research Projects Agency (DARPA) and Army Research Office(ARO) under Contract No. W911NF-15-C-0236. ‡Supported by the National Science Foundation under Grant No. 1617676, IBM under Agreement 4915013672, the Packard Foundation under Grant 2015-63124, and the Danish National Research Foundation and the National Science Foundation of China (under the grant 61361136003) for the Sino-Danish Center for the Theory of Interactive Computation. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsors.