The notion of Best-of-Both-Worlds introduced in the work of Ishai et al. (CRYPTO 2006) investigated whether an MPC protocol can simultaneously provide two incomparable security guarantees: guaranteed output delivery against an honest majority and security with abort against a dishonest majority and provided tight upper and lower bounds in the presence of computationally bounded, i.e., PPT adversaries. Another line of works starting from the work of Chaum (CRYPTO 1989) considered protocols that simultaneously achieved security against an unbounded adversary corrupting a minority of the parties and security against arbitrary corruption by a PPT adversary. In this work, we generalize previous work to investigate a fundamental challenge of designing an MPC in a multiverse where security is specified with respect to (1) GOD, (2) fairness, (3) security w.r.t. unbounded adversaries, and (4) security with abort. The work of Lucas et al. (PODC 2010) resolved this question when considering threshold adversaries; however, the case of general adversary structures remains open. Our main result completely characterizes when a protocol can simultaneously achieve all properties. Namely, given adversary structures $$\mathcal{Z}_{\textsf{GOD}}, \mathcal{Z}_{\textsf{fair}},\mathcal{Z}_{\textsf{S}}$$ and $$\mathcal{Z}_{\textsf{C}}$$ , we provide tight upper and lower bounds for when an MPC protocol can provide GOD, fairness, and security with abort respectively for unbounded and PPT adversaries w.r.t. these adversary structures.
The notion of Best-of-Both-Worlds introduced in the work of Ishai et al. (CRYPTO 2006) investigated whether an MPC protocol can simultaneously provide two incomparable security guarantees: guaranteed output delivery against an honest majority and security with abort against a dishonest majority and provided tight upper and lower bounds in the presence of computationally bounded, i.e., PPT adversaries. Another line of works starting from the work of Chaum (CRYPTO 1989) considered protocols that simultaneously achieved security against an unbounded adversary corrupting a minority of the parties and security against arbitrary corruption by a PPT adversary. In this work, we generalize previous work to investigate a fundamental challenge of designing an MPC in a multiverse where security is specified with respect to (1) GOD, (2) fairness, (3) security w.r.t. unbounded adversaries, and (4) security with abort. The work of Lucas et al. (PODC 2010) resolved this question when considering threshold adversaries; however, the case of general adversary structures remains open. Our main result completely characterizes when a protocol can simultaneously achieve all properties. Namely, given adversary structures ZGOD,Zfair,ZS and ZC , we provide tight upper and lower bounds for when an MPC protocol can provide GOD, fairness, and security with abort respectively for unbounded and PPT adversaries w.r.t. these adversary structures.
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.
Secure Multiparty Computation (MPC) is an expression encompassing cryptographic techniques that allow mutually distrustful parties to jointly perform computations over private data, ensuring correctness and preserving privacy despite malicious behavior. Guaranteed output is the strongest security goal for MPC: protocols with this property always deliver results. This is in contrast with weaker notions that allow malicious aborts. The seminal works of Ben-Or, Goldwasser, and Wigderson (STOC’88) and Rabin and Ben-Or (STOC’89) showed interactive protocols to compute any function with guaranteed output and perfect security if fewer than one third of parties are corrupted, or with statistical security (with a small error probability) if fewer than half are corrupted. These results hold when the set of participants is fixed throughout the execution. Ostrovsky and Yung’s proactive model (PODC’91) relaxes this assumption by allowing the set of corrupted parties to evolve over time, better capturing the dynamics of long-lived computations, where machines may be periodically compromised and recovered. The recent YOSO (You Only Speak Once) and fluid MPC models (CRYPTO’21) push this ambitious modelling even further by allowing for fully dynamic participation, with parties joining and leaving the computation at will. In this setting, known protocols with guaranteed output fall short of optimal resilience or rely on non-standard communication and adversarial assumptions. Matching the classical BGW and Rabin–Ben-Or bounds in these settings remained an open problem. We resolve these questions within the Layered MPC abstraction of David et al. (CRYPTO’23), in which the interaction pattern of a protocol is restricted to be a layered graph, meaning parties are partitioned into a sequence of disjoint sets (layers) and can send private and broadcast messages to parties in immediately subsequent layers. We match the BGW and Rabin and Ben-Or bounds in this model, fully characterizing the feasibility landscape of Layered MPC with guaranteed output. As a stepping stone towards our statistically secure protocol, we construct a more efficient and conceptually simpler computationally secure protocol relying on linear non-interactive commitments. Our results yield optimally-resilient and maximally-proactive MPC protocols with guaranteed output for both perfect and statistical security.
Secure multiparty computation (MPC) enables a set of parties to securely carry out a joint computation of their private inputs without revealing anything but the output. Protocols for semi-honest adversaries guarantee security as long as the corrupted parties run the specified protocol and ensure that nothing is leaked in the transcript. In contrast, protocols for malicious adversaries guarantee security in the presence of arbitrary adversaries who can run any attack strategy. Security for malicious adversaries is typically what is needed in practice (and is always preferred), but comes at a significant cost. In this paper, we present the first protocol for a two-thirds honest majority that achieves security in the presence of malicious adversariesat essentially the exact same cost as the best known protocols for semi-honest adversaries. Our construction is not a general transformation and thus it is possible that better semi-honest protocols will be constructed which do not support our transformation. Nevertheless, for the current state-of-the-art for many parties (based on Shamir sharing), our protocol invokes the best semi-honest multiplication protocol exactly once per multiplication gate (plus some additional local computation that is negligible to the overall cost). Concretely, the best version of our protocol requires each party to send on average of just 2 2/3 elements per multiplication gate (when the number of multiplication gates is at least the number of parties). This is four times faster than the previous-best protocol of Barak et al. (ACM CCS 2018) for small fields, and twice as fast as the previous-best protocol of Chida et al. (CRYPTO 2018) for large fields.
Abstract. At STOC ’87, Goldreich et al. presented two protocols for secure multi-party computation (MPC) among n parties: The first protocol provides passive security against t < n corrupted parties. The second protocolprovidesevenactive security,butonlyagainstt < n/2corrupted parties. Although these protocols provide security against the provably highest possible number of corruptions, each of them has its limitation: The first protocol is rendered completely insecure in presence of a single active corruption, and the second protocol is rendered completely insecure in presence of ⌈n/2 ⌉ passive corruptions. At Crypto 2006, Ishai et al. combined these two protocols into a single protocol which provides passive security against t < n corruptions and active security against t < n/2 corruptions. This protocol unifies the security guarantees of the passive world and the active world (“best of both worlds”). However, the corruption threshold t < n can be tolerated only when all corruptions are passive. With a single active corruption,
We consider the situation where a large number n of players want to securely compute a large function f with security against an adaptive, malicious adversary which might corrupt t<cn of the parties for some given c∈[0,1) . In other words, only some arbitrarily small constant fraction of the parties are assumed to be honest. For any fixed c, we consider the asymptotic complexity as n and the size of f grows. We are in particular interested in the computational overhead, defined as the total computational complexity of all parties divided by the size of f. We show that it is possible to achieve poly-logarithmic computational overhead for all c<1 . Prior to our result it was only known how to get poly-logarithmic overhead for c<21 . We therefore significantly extend the area where we can do secure multiparty computation with poly-logarithmic overhead. Since we allow that more than half the parties are corrupted, we can only get security with abort, i.e., the adversary might make the protocol abort before all parties learn their outputs. We can, however, for all c make a protocol for which there exists d>0 such that if at most dn parties are actually corrupted in a given execution, then the protocol will not abort. Our result is solely of theoretical interest. In its current form, it has not practical implications whatsoever.
In this work, we study perfectly-secure multi-party computation (MPC) against general (non-threshold) adversaries. Known protocols in a synchronous network are secure against Q(3) adversary structures, while in an asynchronous network, known protocols are secure against Q(4) adversary structures. A natural question is whether there exists a single protocol which remains secure against Q(3) and Q(4) adversary structures in a synchronous and in an asynchronous network respectively, where the parties are not aware of the network type. We design the first such best-of-both-worlds protocol against general adversaries. Our result generalizes the result of Appan, Chandramouli and Choudhury (PODC 2022), which presents a best-of-both-worlds perfectly-secure protocol against threshold adversaries. To design our protocol, we present two important building blocks which are of independent interest. The first building block is a best-of-both-worlds perfectly-secure Byzantine agreement (BA) protocol for Q(3) adversary structures, which remains secure both in a synchronous, as well as an asynchronous network. The second building block is a best-of-both-worlds perfectly-secure verifiable secret-sharing (VSS) protocol, which remains secure against Q(3) and Q(4) adversary structures in a synchronous network and an asynchronous network respectively.