Public Verifiability in the Covert Model (Almost) for Free

Abstract. The covert security model (Aumann and Lindell, TCC 2007) offers an extremely important security/efficiency trade-off: a covert player may arbitrarily cheat, but will be caught with a certain fixed probability, called the deterrence factor. This permits much more efficient protocols than the malicious setting while still giving meaningful security guarantees. However, one drawback is that cheating cannot be proven, which prevents the use of covert protocols in many practical settings. In ASI-ACRYPT 2012, Asharov and Orlandi (AO) enhanced the covert model by allowing the honest player to generate a proof of cheating, checkable by any third party. Their model, which we here abbreviate PVC (publicly verifiable covert), offers a very compelling trade-off. Asharov and Orlandi 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 greatly improve the performance of the PVC model by constructing a PVC-compatible OT extension as well as making several important practical improvements to the AO protocol. We work in the random oracle model, which is slightly stronger than what is needed for standard OT extension and free-XOR. Our construction is truly efficient. 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 the best known malicious protocol.