The notion of covert security for secure two-party computation serves as a compromise between the traditional semi-honest and malicious security definitions. Roughly, covert security ensures that cheating behavior is detected by the honest party with reasonable probability (say, 1/2). It provides more realistic guarantees than semi-honest security with significantly less overhead than is required by malicious security.
The notion of covert security for secure two-party computation serves as a compromise between the traditional semi-honest and malicious security definitions. Roughly, covert security ensures that cheating behavior is detected by the honest party with reasonable probability (say, 1/2). It provides more realistic guarantees than semi-honest security with significantly less overhead than is required by malicious security.
We introduce the notion of covert security with public verifiability, building on the covert security model introduced by Aumann and Lindell (TCC 2007). Protocols that satisfy covert security guarantee that the honest parties involved in the protocol will notice any cheating attempt with some constant probability ɛ. The idea behind the model is that the fear of being caught cheating will be enough of a deterrent to prevent any cheating attempt. However, in the basic covert security model, the honest parties are not able to persuade any third party (say, a judge) that a cheating occurred. We propose (and formally define) an extension of the model where, when an honest party detects cheating, it also receives a certificate that can be published and used to persuade other parties, without revealing any information about the honest party’s input. In addition, malicious parties cannot create fake certificates in the attempt of framing innocents. Finally, we construct a secure two-party computation protocol for any functionality f that satisfies our definition, and our protocol is almost as efficient as the one of Aumann and Lindell. We believe that the fear of a public humiliation or even legal consequences vastly exceeds the
Multiparty computation protocols (MPC) are said to be secure against covert adversaries if the honest parties are guaranteed to detect any misbehavior by the malicious parties with a constant probability. Protocols that, upon detecting a cheating attempt, additionally allow the honest parties to compute certificates, which enable third parties to be convinced of the malicious behavior of the accused parties, are called publicly verifiable. In this work, we make several contributions to the domain of MPC with security against covert adversaries. We identify a subtle flaw in a protocol of Goyal, Mohassel, and Smith (Eurocrypt 2008), meaning that their protocol does not allow to identify a cheating party, and show how to fix their original construction to obtain security against covert adversaries. We present generic compilers that transform arbitrary passively secure preprocessing protocols, i.e. protocols where the parties have no private inputs, into protocols that are secure against covert adversaries and publicly verifiable. Using our compiler, we construct the first efficient variants of the BMR and the SPDZ protocols that are secure and publicly verifiable against a covert adversary that corrupts all but one party, and also construct variants with covert security and identifiable abort. We observe that an existing impossibility result by Ishai, Ostrovsky, and Seyalioglu (TCC 2012) can be used to show that there exist certain functionalities that cannot be realized by parties, that have oracle-access to broadcast and arbitrary two-party functionalities, with information-theoretic security against a covert adversary.
We introduce covert two-party computation, a stronger notion of security than standard secure two-party computation. Like standard secure two-party computation, covert two-party computation allows Alice and Bob, with secret inputs xA and xB respectively, to compute a function f(xA,xB) without leaking any additional information about their inputs. In addition, covert two-party computation guarantees that even the existence of a computation is hidden from all protocol participants unless the value of the function mandates otherwise. This allows the construction of protocols that return f(xA,xB) only when it equals a certain value of interest (such as "Yes, we are romantically interested in each other") but for which neither party can determine whether the other even ran the protocol whenever f(xA,xB) is not a value of interest. Since existing techniques for secure function evaluation always reveal that both parties participate in the computation, covert computation requires the introduction of new techniques based on provably secure steganography. We introduce security definitions for covert two-party computation and show that this surprising notion can be achieved by a protocol given the Decisional Diffie-Hellman assumption in the "honest but curious" model. Using this protocol as a subroutine, we present another protocol which is fair and secure against malicious adversaries in the Random Oracle Model --- unlike most other protocols against malicious adversaries, this protocol does not rely on zero-knowledge proofs (or similar cut-and-choose techniques), because they inherently reveal that a computation took place. We remark that all our protocols are of comparable efficiency to protocols for standard secure two-party computation.
We address the problem of efficiently verifying a commitment in a two-party computation. This addresses the scenario where a party P1 commits to a value x to be used in a subsequent secure computation with another party P2 that wants to receive assurance that P1 did not cheat, i.e. that x was indeed the value inputted into the secure computation. Our constructions operate in the publicly verifiable covert (PVC) security model, which is a relaxation of the malicious model of MPC, appropriate in settings where P1 faces a reputational harm if caught cheating.
In the secure two-party computation (2PC), an adversary is often categorized as semi-honest or malicious, depending on whether it follows the protocol specifications. Covert security (Aumann and Lindell, 2010) first looks into the “middle ground”, such that an active adversary who cheats will be caught with a predefined probability. Other security notions, such as publicly auditable security (Baum et al., 2014) and (robust) accountability family (Küsters et al., 2010; Graf et al., 2023; Rivinius et al., 2022), achieve public verifiability as a stronger security guarantee by relying on heavy offline and online constructions with zero knowledge proofs and (or) a bulletin board functionality. In this work, we propose a new security notion called honorific security, where an external arbiter can identify the cheater without a bulletin board. Specifically, we delay and outsource the verification steps to the arbiter, so that the original online computation is thus accelerated. We show that a maliciously secure garbled circuit (GC) (Yao, 1986) protocol can be constructed with only slightly more overhead than a passively secure protocol. Our construction performs up to 2.37 times and 13.30 times as fast as the state-of-the-art protocols with covert and malicious security, respectively.
Adversaries in cryptography have traditionally been modeled as either semi-honest or malicious. Over the years, however, several works have investigated the design of cryptographic protocols against rational adversaries. The most well-known example are covert adversaries in secure computation (Aumann & Lindell, TCC '07) which are adversaries that wish to deviate from the protocol but without being detected. Protocols secure against such covert adversaries guarantee that deviations are detected with probability at least - which is known as the deterrence factor.