Public Verifiability in the Covert Model (Almost) for Free

The covert security model (Aumann and Lindell, TCC 2007) offers an important security/efficiency trade-off: a covert player may arbitrarily cheat, but is caught with a certain fixed probability. This permits more efficient protocols than the malicious setting while still giving meaningful security guarantees. However, one drawback is that cheating cannot be proven to a third party, which prevents the use of covert protocols in many practical settings. Recently, Asharov and Orlandi (ASIACRYPT 2012) enhanced the covert model by allowing the honest player to generate a proof of cheating, checkable by any third party. Their model, which we call the PVC (publicly verifiable covert) model, offers a very compelling trade-off. Asharov and Orlandi (AO) propose a practical protocol in the PVC model, which, however, relies on a specific expensive oblivious transfer (OT) protocol incompatible with OT extension. In this work, we improve the performance of the PVC model by constructing a PVC-compatible OT extension as well as making several practical improvements to the AO protocol. As compared to the state-of-the-art OT extension-based two-party covert protocol, our PVC protocol adds relatively little: four signatures and an ≈ 67% wider OT extension matrix. This is a significant improvement over the AO protocol, which requires public-key-based OTs per input bit. We present detailed estimates showing (up to orders of magnitude) concrete performance improvements over the AO protocol and a recent malicious protocol.