Paper 2020/916

Black-Box Transformations from Passive to Covert Security with Public Verifiability

Ivan Damgård, Claudio Orlandi, and Mark Simkin

Abstract

In the context of secure computation, protocols with security against covert adversaries ensure that any misbehavior by malicious parties will be detected by the honest parties with some constant probability. As such, these protocols provide better security guarantees than passively secure protocols and, moreover, are easier to construct than protocols with full security against active adversaries. Protocols that, upon detecting a cheating attempt, allow the honest parties to compute a certificate that enables third parties to verify whether an accused party misbehaved or not are called publicly verifiable. In this work, we present the first generic compilers for constructing two-party protocols with covert security and public verifiability from protocols with passive security. We present two separate compilers, which are both fully blackbox in the underlying protocols they use. Both of them only incur a constant multiplicative factor in terms of bandwidth overhead and a constant additive factor in terms of round complexity on top of the passively secure protocols they use. The first compiler applies to all two-party protocols that have no private inputs. This class of protocols covers the important class of preprocessing protocols that are used to setup correlated randomness among parties. We use our compiler to obtain the first secret-sharing based two-party protocol with covert security and public verifiability. Notably, the produced protocol achieves public verifiability essentially for free when compared with the best known previous solutions based on secret-sharing that did not provide public verifiability Our second compiler constructs protocols with covert security and public verifiability for arbitrary functionalities from passively secure protocols. It uses our first compiler to perform a setup phase, which is independent of the parties' inputs as well as the protocol they would like to execute. Finally, we show how to extend our techniques to obtain multiparty computation protocols with covert security and public verifiability against arbitrary constant fractions of corruptions.