Abstract. Secure multi-party computation (MPC) allows a set P of n players to evaluate a function f in presence of an adversary who corrupts a subset of the players. In this paper we consider active, general adversaries, characterized by a so-called adversary structure Z which enumerates all possible subsets of corrupted players. In particular for small sets of players general adversaries better capture real-world requirements than classical threshold adversaries. Protocols for general adversaries are “efficient ” in the sense that they require |Z | O(1) bits of communication. However, as |Z | is usually very large (even exponential in n), the exact exponent is very relevant. In the setting with perfect security, the most efficient protocol known to date communicates O(|Z | 3) bits; we present a protocol for this setting which communicates O(|Z | 2) bits. In the setting with statistical security, O(|Z | 3) bits of communication is needed in general (whereas for a very restricted subclass of adversary structures, a protocol with communication O(|Z | 2) bits is known); we present a protocol for this setting (without limitations) which communicates O(|Z | 1) bits.
Abstract. Secure multi-party computation (MPC) allows a set P of n players to evaluate a function f in presence of an adversary who corrupts a subset of the players. In this paper we consider active, general adversaries, characterized by a so-called adversary structure Z which enumerates all possible subsets of corrupted players. In particular for small sets of players general adversaries better capture real-world requirements than classical threshold adversaries. Protocols for general adversaries are “efficient ” in the sense that they require |Z | O(1) bits of communication. However, as |Z | is usually very large (even exponential in n), the exact exponent is very relevant. In the setting with perfect security, the most efficient protocol known to date communicates O(|Z | 3) bits; we present a protocol for this setting which communicates O(|Z | 2) bits. In the setting with statistical security, O(|Z | 3) bits of communication is needed in general (whereas for a very restricted subclass of adversary structures, a protocol with communication O(|Z | 2) bits is known); we present a protocol for this setting (without limitations) which communicates O(|Z | 1) bits.
In this paper, we design secure multi-party computation (MPC) protocols in the asynchronous communication setting with optimal resilience. Our protocols are secure against a computationally-unbounded malicious adversary, characterized by an adversary structure Z, which enumerates all possible subsets of potentially corrupt parties. Our protocols incur a communication of O(∣Z∣2) and O(∣Z∣) bits per multiplication for perfect and statistical security respectively. These are the first protocols with this communication complexity, as such protocols were known only in the synchronous communication setting (Hirt and Tschudi, ASIACRYPT 2013).
Over the past 20 years, the efficiency of secure multi-party protocols has been greatly improved. While the seminal protocols from the late 80’s require a communication of Ω(n⁶) field elements per multiplication among n parties, recent protocols offer linear communication complexity. This means that each party needs to communicate a constant number of field elements per multiplication, independent of n. However, these efficient protocols only offer active security, which implies that at most t<n/3 (perfect security), respectively t<n/2 (statistical or computational security) parties may be corrupted. Higher corruption thresholds (i.e., t≥ n/2) can only be achieved with degraded security (unfair abort), where one single corrupted party can prevent honest parties from learning their outputs. The aforementioned upper bounds (t<n/3 and t<n/2) have been circumvented by considering mixed adversaries (Fitzi et al., Crypto' 98), i.e., adversaries that corrupt, at the same time, some parties actively, some parties passively, and some parties in the fail-stop manner. It is possible, for example, to achieve perfect security even if 2/3 of the parties are faulty (three quarters of which may abort in the middle of the protocol, and a quarter may even arbitrarily misbehave). This setting is much better suited to many applications, where the crash of a party is more likely than a coordinated active attack. Surprisingly, since the presentation of the feasibility result for the mixed setting, no progress has been made in terms of efficiency: the state-of-the-art protocol still requires a communication of Ω(n⁶) field elements per multiplication. In this paper, we present a perfectly-secure MPC protocol for the mixed setting with essentially the same efficiency as the best MPC protocols for the active-only setting. For the first time, this allows to tolerate faulty majorities, while still providing optimal efficiency. As a special case, this also results in the first fully-secure MPC protocol secure against any number of crashing parties, with optimal (i.e., linear in n) communication. We provide simulation-based proofs of our construction.
Abstract. A multiparty computation (MPC) protocol allows a set of players to compute a function of their inputs while keeping the inputs private and at the same time securing the correctness of the output. Most MPC protocols assume that the adversary can corrupt up to a fixed fraction of the number of players. Hirt and Maurer initiated the study of MPC under more general corruption patterns, in which the adversary is allowed to corrupt any set of players in some pre-defined collection of sets [6]. In this paper we consider this important direction of research and present significantly improved communication complexity of MPC protocols for general adversary structures. More specifically, ours is the first unconditionally secure protocol that achieves linear communication in the size of Monotone Span Program representing the adversary structure in the malicious setting against any Q2 adversary structure, whereas all previous protocols were at least cubic.
In this work, we initiate the study of network-agnostic perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries, where the corruption capacity of the adversary is specified through an adversary structure, which is a set of potentially corrupt subsets of parties. Known MPC protocols are designed either assuming a synchronous network where every sent message is guaranteed to be delivered within some known time or assuming an asynchronous network where no timing assumptions are made and every sent message is eventually delivered. Perfectly-secure MPC protocols in the synchronous network can be designed as long as the underlying adversary structure satisfies the$ {{\mathcal {Q}}}^{(3)}condition,meaningthattheunionofnothreesubsetsfromtheadversarystructurecoverstheentiresetofparties.Ontheotherhand,perfectly−secureMPCprotocolsintheasynchronousnetworkcanbedesignedonlyagainst {{\mathcal {Q}}}^{(4)}adversarystructures,meaningthattheunionofnofoursubsetsfromtheadversarystructurecoverstheentiresetofparties.AnaturalquestioniswhetherasingleMPCprotocolexists,whichremainssecureevenifthepartiesareunawareofthenetworkconditionsatexecutiontime.Thatis,ifthesynchronyissatisfiedthroughouttheprotocolexecutionthentheprotocolshouldbesecureagainstany {{\mathcal {Q}}}^{(3)}adversarystructure.However,evenifanysynchronyassumptionisviolatedduringtheexecution,theprotocolshouldstillbesecureagainstany {{\mathcal {Q}}}^{(4)}adversarystructure.Weanswertheabovequestionaffirmatively.Fixanyadversarystructure{\mathcal {Z}}_{s}and{\mathcal {Z}}_{a}satisfying {{\mathcal {Q}}}^{(3)}and {{\mathcal {Q}}}^{(4)}conditionsrespectively,suchthat{\mathcal {Z}}_{a} \subset {\mathcal {Z}} _{s}.Weshowtheexistenceofanetwork−agnosticperfectly−secureMPCprotocoltolerating{\mathcal {Z}}_{s}and{\mathcal {Z}}_{a}insynchronousandasynchronousnetworksrespectivelyaslongasthe {{\mathcal {Q}}}^{(3, 1)}conditionissatisfied,meaningthattheunionofnothreesubsetsfrom{\mathcal {Z}}_{s}andonesubsetfrom{\mathcal {Z}}_{a}$covers the entire set of parties. Our result generalizes the result of Appan, Chandramouli and Choudhury (IEEE Transactions on IT, 2023), which presents the only known perfectly-secure network-agnostic MPC protocol against threshold adversaries.
The goal of Multi-Party Computation (MPC) is to perform an arbitrary computation in a distributed, private, and fault-tolerant way. For this purpose, a fixed set of n parties runs a protocol that tolerates an adversary corrupting a subset of the participating parties, and still preserves certain security guarantees.
Most MPC protocols provide security guarantees in an all-or-nothing fashion. In this paper, we provide the first treatment of MPC with graceful degradation of both security and corruptions. First of all, our protocols provide graceful degradation of security, i.e., different security guarantees depending on the actual number of corrupted parties: the more corruptions, the weaker the security guarantee. We consider all security properties generally discussed in the literature (secrecy, correctness, robustness, fairness, and agreement on abort). Furthermore, the protocols provide graceful degradation with respect to the corruption type, by distinguishing fully honest parties, passively corrupted parties, and actively corrupted parties. Security can be maintained against more passive corruptions than is possible for active corruptions.
We focus on perfect security, and prove exact bounds for which MPC with graceful degradation of security and corruptions is possible for both threshold and general adversaries. Furthermore, we provide protocols that meet these bounds. This strictly generalizes known results on hybrid security and mixed adversaries.
Introduction In this chapter we will show how the protocols we have seen so far can be generalized to be based on general linear secret-sharing schemes. Doing this generalization has several advantages: first, it allows us to design protocols that protect against general adversary structures, a concept we explain later, and second, it allows us to consider protocols in which the field that is used in defining the secret-sharing scheme can be of size independent of the number of players. This turns out to be an advantage for the applications of multiparty computation (MPC) that we consider later but cannot be done for the protocols that we have seen so far: to use Shamir's scheme for n players based on polynomials as we have seen, the field must be of size at least n +1. For now, we will only consider the theory for linear secret sharing that we need to construct the protocols in this chapter. However, we note already that to get full mileage from the more general applications of secret sharing and MPC, we need additional theory, in particular, about the asymptotic behavior of secret-sharing schemes. This material can be found in Chapter 11. General Adversary Structures The corruption tolerance of the protocols that we have seen so far has been characterized by only a single number t , the maximal number of corruptions that can be tolerated. This is also known as the threshold-t model . One way to motivate this might be to think of corruption of a player as something that requires the adversary to invest some amount of resource, such as time or money. If the adversary has only bounded resources, there should be a limit on the corruptions he or she can do. However, characterizing this limit by only an upper bound implicitly assumes that all players are equally hard to corrupt. In reality, this may be completely false: some players may have much better security than others, so a more realistic model might be that the adversary can corrupt a small number of well-protected players or a large number of poorly protected players. However, the threshold model does not allow us to express this.