Adaptively Secure Multi-Party Computation with Dishonest Majority

Adaptively secure multiparty computation is an essential and fundamental notion in cryptography. In this work we focus on the basic question of constructing a multiparty computation protocol secure against a malicious, adaptive adversary in the stand-alone setting without assuming an honest majority, in the plain model. It has been believed that this question can be resolved by composing known protocols from the literature. We show that in fact, this belief is fundamentally mistaken. In particular, we show: Round inefficiency is unavoidable when using black-box simulation: There does not exist any o( n logn ) round protocol that adaptively securely realizes a (natural) n-party functionality with a black-box simulator. Note that most previously known protocols in the adaptive security setting relied on black-box simulators. A constant round protocol using non-black-box simulation: We construct a constant round adaptively secure multiparty computation protocol in a setting without honest majority that makes crucial use of non-black box techniques. Taken together, these results give the first resolution to the question of adaptively secure multiparty computation protocols with a malicious dishonest majority in the plain model, open since the first formal treatment of adaptive security for multiparty computation in 1996. ⋆ Research supported in part from a DARPA/ONR PROCEED award, NSF grants 1136174, 1118096, 1065276, 0916574 and 0830803, a Xerox Faculty Research Award, a Google Faculty Research Award, an equipment grant from Intel, and an Okawa Foundation Research Grant. This material is based upon work supported by the Defense Advanced Research Projects Agency through the U.S. Office of Naval Research under Contract N00014-11-1-0389. The views expressed are those of the author and do not reflect the official policy or position of the Department of Defense or the U.S. Government.