We consider the task of designing secure computation protocols in an unstable network where honest parties can drop out at any time, according to a schedule provided by the adversary. This type of setting, where even honest parties are prone to failures, is more realistic than traditional models, and has therefore gained a lot of attention recently. Our model, Phoenix, enables a new approach to secure multiparty computation with dropouts, allowing parties to drop out and re-enter the computation on an adversarially-chosen schedule and without assuming that these parties receive the messages that were sent to them while being offline - features that are not available in the existing models of Sleepy MPC (Guo et al., CRYPTO '19), Fluid MPC (Choudhuri et al., CRYPTO '21 ) and YOSO (Gentry et al. CRYPTO '21). Phoenix does assume an upper bound on the number of rounds that an honest party can be off-line - otherwise protocols in this setting cannot guarantee termination within a bounded number of rounds; however, if one settles for a weaker notion, namely guaranteed output delivery only for honest parties who stay on-line long enough, this requirement is not necessary. In this work, we study the settings of perfect, statistical and computational security and design MPC protocols in each of these scenarios. We assume that the intersection of online-and-honest parties from one round to the next is at least 2t+1, t+1 and 1 respectively, where t is the number of (actively) corrupt parties. We show the intersection requirements to be optimal. Our (positive) results are obtained in a way that may be of independent interest: we implement a traditional stable network on top of the unstable one, which allows us to plug in any MPC protocol on top. This approach adds a necessary overhead to the round count of the protocols, which is related to the maximal number of rounds an honest party can be offline. We also present a novel, perfectly secure MPC protocol in the preprocessing model that avoids this overhead by following a more "direct" approach rather than first building a stable network and then using existing protocols. We introduce our network model in the UC-framework, show that the composition theorem still holds, and prove the security of our protocols within this setting.
We consider the task of designing secure computation protocols in an unstable network where honest parties can drop out at any time, according to a schedule provided by the adversary. This type of setting, where even honest parties are prone to failures, is more realistic than traditional models, and has therefore gained a lot of attention recently. Our model, Phoenix, enables a new approach to secure multiparty computation with dropouts, allowing parties to drop out and re-enter the computation on an adversarially-chosen schedule and without assuming that these parties receive the messages that were sent to them while being offline - features that are not available in the existing models of Sleepy MPC (Guo et al., CRYPTO '19), Fluid MPC (Choudhuri et al., CRYPTO '21 ) and YOSO (Gentry et al. CRYPTO '21). Phoenix does assume an upper bound on the number of rounds that an honest party can be off-line - otherwise protocols in this setting cannot guarantee termination within a bounded number of rounds; however, if one settles for a weaker notion, namely guaranteed output delivery only for honest parties who stay on-line long enough, this requirement is not necessary. In this work, we study the settings of perfect, statistical and computational security and design MPC protocols in each of these scenarios. We assume that the intersection of online-and-honest parties from one round to the next is at least 2t+1, t+1 and 1 respectively, where t is the number of (actively) corrupt parties. We show the intersection requirements to be optimal. Our (positive) results are obtained in a way that may be of independent interest: we implement a traditional stable network on top of the unstable one, which allows us to plug in any MPC protocol on top. This approach adds a necessary overhead to the round count of the protocols, which is related to the maximal number of rounds an honest party can be offline. We also present a novel, perfectly secure MPC protocol in the preprocessing model that avoids this overhead by following a more "direct" approach rather than first building a stable network and then using existing protocols. We introduce our network model in the UC-framework, show that the composition theorem still holds, and prove the security of our protocols within this setting.
Abstract. Existing communication models for multiparty computation (MPC) either assume that all messages are delivered eventually or any message can be lost. Under the former assumption, MPC protocols guaranteeing output delivery are known. However, this assumption may not hold in some network settings like the Internet where messages can be lost due to denial of service attack or heavy network congestion. On the other hand, the latter assumption may be too conservative. Known MPC protocols developed under this assumption have an undesirable feature: output delivery is not guaranteed even only one party suffers message loss. In this work, we propose a communication model which makes an intermediate assumption on message delivery. In our model, there is a common global clock and three types of parties: (i) Corrupted parties (ii) Honest parties with connection problems (where message delivery is never guaranteed) (iii) Honest parties that can normally communicate but may lose a small fraction of messages at each round due to transient network problems. We define secure MPC under this model. Output delivery is guaranteed to type (ii) parties that do not abort and type (iii) parties. Let n be the total number of parties, ef and ec be upper bounds on the number of corrupted parties and type (ii) parties respectively. We construct a secure MPC protocol for n> 4ef + 3ec. Protocols for broadcast and verifiable secret sharing are constructed along the way. 1
The Fluid multiparty computation (MPC) model, introduced in (Choudhuri et al. CRYPTO 2021), addresses dynamic scenarios where participants can join or leave computations between rounds. Communication complexity initially stood at Ω ( n 2 ) elements per gate, where n is the number of parties in a committee online at a time. This held for both statistical security (honest majority) and computational security (dishonest majority) in (Choudhuri et al. CRYPTO'21) and (Rachuri and Scholl, CRYPTO'22), respectively. The work of (Bienstock et al. CRYPTO'23) improved communication to O ( n ) elements per gate. However, it's important to note that the perfectly secure setting with one-third corruptions per committee has only recently been addressed in the work of (David et al. CRYPTO'23). Notably, their contribution marked a significant advancement in the Fluid MPC literature by introducing guaranteed output delivery. However, this achievement comes at the cost of prohibitively expensive communication, which scales to Ω ( n 9 ) elements per gate. In this work, we study the realm of perfectly secure Fluid MPC under one-third active corruptions. Our primary focus lies in proposing efficient protocols that embrace the concept of security with abort. Towards this, we design a protocol for perfectly secure Fluid MPC that requires only linear communication of O ( n ) elements per gate, matching the communication of the non-Fluid setting. Our results show that, as in the case of computational and statistical security, perfect security with abort for Fluid MPC comes “for free” (asymptotically linear in n ) with respect to traditional non-Fluid MPC, marking a substantial leap forward in large scale dynamic computations, such as Fluid MPC.
In this work, we consider the setting where the process of securely evaluating a multi-party functionality is divided into two phases: offline (or preprocessing ) and online . The offline phase is independent of the parties’ inputs, whereas the online phase does require the knowledge of the inputs. We consider the problem of minimizing the round of communication required in the online phase and propose a round preserving compiler that can turn a big class of multi-party computation (MPC) protocols into protocols in which only the last two rounds are input-dependent. Our compiler can be applied to a big class of MPC protocols, and in particular to all existing round-optimal MPC protocols. All our results assume no setup and are proven in the dishonest majority setting with black-box simulation. As part of our contribution, we propose a new definition we call Multi-Party Computation with Adaptive-Input Selection , which allows the distinguisher to craft the inputs the honest parties should use during the online phase, adaptively on the offline phase. This new definition is needed to argue that not only are the messages of the offline phase input-independent but also that security holds even in the stronger (and realistic) adversarial setting where the inputs may depend on some of the offline-phase protocol messages. We argue that this is the definition that any protocol should satisfy to be securely used while preprocessing part of the rounds. We are the first to study this definition in a setting where there is no setup, and the majority of the parties can be corrupted. Prior definitions have been presented in the Universal Composable framework, which is unfortunately not well suited for our setting (i.e., no setup and dishonest majority). As a corollary, we obtain the first four-round (which is optimal) MPC protocol, where the first two rounds can be preprocessed, and its security holds against adaptive-input selection.
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 multi-party computation (MPC) protocols that are resilient to a dishonest majority allow the adversary to get the output of the computation while, at the same time, forcing the honest parties to abort. Aumann and Lindell introduced the enhanced notion of security with identifiable abort , which still allows the adversary to trigger an abort but, at the same time, it enables the honest parties to agree on the identity of the party that led to the abort. More recently, in Eurocrypt 2016, Garg et al. showed that, assuming access to a simultaneous message exchange channel for all the parties, at least four rounds of communication are required to securely realize non-trivial functionalities in the plain model. Following Garg et al., a sequence of works has matched this lower bound, but none of them achieved security with identifiable abort. In this work, we close this gap and show that four rounds of communication are also sufficient to securely realize any functionality with identifiable abort using standard and generic polynomial-time assumptions. To achieve this result we introduce the new notion of bounded-rewind secure MPC that guarantees security even against an adversary that performs a mild form of reset attacks. We show how to instantiate this primitive starting from any MPC protocol and by assuming trapdoor-permutations. The notion of bounded-rewind secure MPC allows for easier parallel composition of MPC protocols with other (interactive) cryptographic primitives. Therefore, we believe that this primitive can be useful in other contexts in which it is crucial to combine multiple primitives with MPC protocols while keeping the round complexity of the final protocol low.
Secure Multi-Party Computation (MPC) with small number of parties is an interesting area of research, primarily due to its ability to model most real-life MPC applications and the simplicity and efficiency of the resulting protocols. In this work, we present efficient, constant-round 3-party (3PC) and 4-party (4PC) protocols in the honest-majority setting that achieve strong security notions of fairness (corrupted parties receive their output only if all honest parties receive output) and guaranteed output delivery (corrupted parties cannot prevent honest parties from receiving their output). Being constant-round, our constructions are suitable for Internet-like high-latency networks and are built from garbled circuits (GC). Assuming the minimal model of pairwise-private channels, we present two protocols that involve computation and communication of a single GC-- (a) a 4-round 3PC with fairness, (b) a 5-round 4PC with guaranteed output delivery. Empirically, our protocols are on par with the best known 3PC protocol of Mohassel et al. [CCS 2015] that only achieves security with selective abort, in terms of the computation time, LAN runtime, WAN runtime and communication cost. In fact, our 4PC outperforms the 3PC of Mohassel et al. significantly in terms of per-party computation and communication cost. With an extra GC, we improve the round complexity of our 4PC to four rounds. The only 4PC in our setting, given by Ishai et al. [CRYPTO 2015], involves 12 GCs. Assuming an additional broadcast channel, we present a 5-round 3PC with guaranteed output delivery that involves computation and communication of a single GC. A broadcast channel is inevitable in this setting for achieving guaranteed output delivery, owing to an impossibility result in the literature. The overall broadcast communication of our protocol is nominal and most importantly, is independent of the circuit size. This protocol too induces a nominal overhead compared to the protocol of Mohassel et al.