On Communication-Efficient Asynchronous MPC with Adaptive Security

Secure multi-party computation (MPC) allows a set of $n$ parties to jointly compute an arbitrary computation over their private inputs. Two main variants have been considered in the literature according to the underlying communication model. Synchronous MPC protocols proceed in rounds, and rely on the fact that the communication network provides strong delivery guarantees within each round. Asynchronous MPC protocols achieve security guarantees even when the network delay is arbitrary. While the problem of MPC has largely been studied in both variants with respect to both feasibility and efficiency results, there is still a substantial gap when it comes to communication complexity of adaptively secure protocols. Concretely, while adaptively secure synchronous MPC protocols with linear communication are known for a long time, the best asynchronous protocol communicates $\mathcal{O}(n^4 \kappa)$ bits per multiplication. In this paper, we make progress towards closing this gap by providing two protocols. First, we present an adaptively secure asynchronous protocol with optimal resilience $t<n/3$ and $\mathcal{O}(n^2 \kappa)$ bits of communication per multiplication, improving over the state of the art protocols in this setting by a quadratic factor in the number of parties. The protocol has cryptographic security and follows the CDN approach [Eurocrypt\u2701], based on additive threshold homomorphic encryption. Second, we show an optimization of the above protocol that tolerates up to $t<(1-\epsilon)n/3$ corruptions and communicates \mathcal{O}(n\cdot \poly(\kappa)) bits per multiplication under stronger assumptions

Asynchronous Multi-Party Quantum Computation

Multi-party quantum computation (MPQC) allows a set of parties to securely compute a quantum circuit over private quantum data. Current MPQC protocols rely on the fact that the network is synchronous, i.e., messages sent are guaranteed to be delivered within a known fixed delay upper bound, and unfortunately completely break down even when only a single message arrives late. Motivated by real-world networks, the seminal work of Ben-Or, Canetti and Goldreich (STOC\u2793) initiated the study of multi-party computation for classical circuits over asynchronous networks, where the network delay can be arbitrary. In this work, we begin the study of asynchronous multi-party quantum computation (AMPQC) protocols, where the circuit to compute is quantum. Our results completely characterize the optimal achievable corruption threshold: we present an n-party AMPQC protocol secure up to t < n/4 corruptions, and an impossibility result when t ? n/4 parties are corrupted. Remarkably, this characterization differs from the analogous classical setting, where the optimal corruption threshold is t < n/3

Efficient MPC with a Mixed Adversary

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.ISSN:1868-896

Asynchronous Multiparty Computation: Theory and Implementation

We propose an asynchronous protocol for general multiparty computation with perfect security and communication complexity O(n^2 |C| k) where n is the number of parties, |C| is the size of the arithmetic circuit being computed, and k is the size of elements in the underlying field. The protocol guarantees termination if the adversary allows a preprocessing phase to terminate, in which no information is released. The communication complexity of this protocol is the same as that of a passively secure solution up to a constant factor. It is secure against an adaptive and active adversary corrupting less than n/3 players. We also present a software framework for implementation of asynchronous protocols called VIFF (Virtual Ideal Functionality Framework), which allows automatic parallelization of primitive operations such as secure multiplications, without having to resort to complicated multithreading. Benchmarking of a VIFF implementation of our protocol confirms that it is applicable to practical non-trivial secure computations. VIFF can be downloaded from http://viff.dk/

The Bottleneck Complexity of Secure Multiparty Computation

In this work, we initiate the study of bottleneck complexity as a new communication efficiency measure for secure multiparty computation (MPC). Roughly, the bottleneck complexity of an MPC protocol is defined as the maximum communication complexity required by any party within the protocol execution. We observe that even without security, bottleneck communication complexity is an interesting measure of communication complexity for (distributed) functions and propose it as a fundamental area to explore. While achieving O(n) bottleneck complexity (where n is the number of parties) is straightforward, we show that: (1) achieving sublinear bottleneck complexity is not always possible, even when no security is required. (2) On the other hand, several useful classes of functions do have o(n) bottleneck complexity, when no security is required. Our main positive result is a compiler that transforms any (possibly insecure) efficient protocol with fixed communication-pattern for computing any functionality into a secure MPC protocol while preserving the bottleneck complexity of the underlying protocol (up to security parameter overhead). Given our compiler, an efficient protocol for any function f with sublinear bottleneck complexity can be transformed into an MPC protocol for f with the same bottleneck complexity. Along the way, we build cryptographic primitives - incremental fully-homomorphic encryption, succinct non-interactive arguments of knowledge with ID-based simulation-extractability property and verifiable protocol execution - that may be of independent interest

An End-to-End System for Large Scale P2P MPC-as-a-Service and Low-Bandwidth MPC for Weak Participants

Protocols for secure multiparty computation enable a set of parties to compute a joint function of their inputs, while preserving \emph{privacy}, \emph{correctness} and more. In theory, secure computation has broad applicability and can be used to solve many of the modern concerns around utilization of data and privacy. Huge steps have been made towards this vision in the past few years, and we now have protocols that can carry out large computations extremely efficiently, especially in the setting of an honest majority. However, in practice, there are still major barriers to widely deploying secure computation, especially in a decentralized manner. In this paper, we present the first end-to-end automated system for deploying large-scale MPC protocols between end users, called MPSaaS (for \textit{MPC system-as-a-service}). Our system enables parties to pre-enroll in an upcoming MPC computation, and then participate by either running software on a VM instance (e.g., in Amazon), or by running the protocol on a mobile app, in Javascript in their browser, or even on an IoT device. Our system includes an automation system for deploying MPC protocols, an administration component for setting up an MPC computation and inviting participants, and an end-user component for running the MPC protocol in realistic end-user environments. We demonstrate our system for a specific application of running secure polls and surveys, where the secure computation is run end-to-end with each party actually running the protocol (i.e., without relying on a set of servers to run the protocol for them). This is the first such system constructed, and is a big step forward to the goal of commoditizing MPC. One of the cryptographic difficulties that arise in this type of setting is due to the fact that end users may have low bandwidth connections, making it a challenge to run an MPC protocol with high bandwidth. We therefore present a protocol based on Beerliova-Trubiniova and Hirt (TCC 2008) with many optimizations, that has very low concrete communication, and the lowest published for small fields. Our protocol is secure as long as less than a third of the parties are \textit{malicious}, and is well suited for computing both arithmetic and Boolean circuits. We call our protocol HyperMPC and show that it has impressive performance. In particular, 150 parties can compute statistics---mean, standard deviation and regression---on 4,000,000 inputs (with a circuit of size 16,000,000 gates of which 6,000,000 are multiplication) in five minutes, and 10 parties can compute the same circuit in 30 seconds. Although our end-to-end system can be used to run any MPC protocol (and we have incorporated numerous protocols already), we demonstrate it for our new protocol that is optimized for end-users without high bandwidth

Efficient Statistical Asynchronous Verifiable Secret Sharing and Multiparty Computation with Optimal Resilience

Verifiable Secret Sharing (VSS) is a fundamental primitive used as a building block in many distributed cryptographic tasks, such as Secure Multiparty Computation (MPC) and Byzantine Agreement (BA). An important variant of VSS is Asynchronous VSS (AVSS) which is designed to work over asynchronous networks. AVSS is a two phase (Sharing, Reconstruction) protocol carried out among n parties in the presence of a computationally unbounded active adversary, who can corrupt up to t parties. We assume that every two parties in the network are directly connected by a pairwise secure channel. In this paper, we present a new statistical AVSS protocol with optimal resilience; i.e. with n = 3t+1. Our protocol privately communicates O((\ell n^3 + n^4 \log{\frac{1}{\epsilon}}) \log{\frac{1}{\epsilon}}) bits and A-casts O(n^3 \log(n)) bits to simultaneously share \ell \geq 1 elements from a finite field F, where \epsilon is the error parameter of our protocol. There are only two known statistical AVSS protocols with n = 3t+1 reported in [CR93] and [PCR09]. The AVSS protocol of [CR93] requires a private communication of O(n^9 (\log{\frac{1}{\epsilon}})^4) bits and A-cast of O(n^9 (\log{\frac{1}{\epsilon}})^2 \log(n)) bits to share a single element from F. Thus our AVSS protocol shows a significant improvement in communication complexity over the AVSS of [CR93]. The AVSS protocol of [PCR09] requires a private communication and A-cast of O((\ell n^3 + n^4) \log{\frac{1}{\epsilon}}) bits to share \ell \geq 1 elements. However, the shared element(s) may be NULL \not \in {\mathbb F}. Thus our AVSS is better than the AVSS of [PCR09] due to the following reasons: 1. The A-cast communication of our AVSS is independent of the number of secrets i.e. \ell; 2. Our AVSS makes sure that the shared value(s) always belong to F. Using our AVSS, we design a new primitive called Asynchronous Complete Secret Sharing (ACSS) which acts as an important building block of asynchronous multiparty computation (AMPC). Using our ACSS scheme, we design a statistical AMPC protocol with optimal resilience; i.e., with n = 3t+1, that privately communicates O(n^5 \log{\frac{1}{\epsilon}}) bits per multiplication gate. This significantly improves the communication complexity of only known optimally resilient statistical AMPC of [BKR93] that privately communicates \Omega(n^{11} (\log{\frac{1}{\epsilon}})^4) bits and A-cast \Omega(n^{11} (\log{\frac{1}{\epsilon}})^2 \log(n)) bits per multiplication gate. Both our ACSS and AVSS employ several new techniques, which are of independent interest

Asynchronous Multi-Party Quantum Computation

Multi-party quantum computation (MPQC) allows a set of parties to securely compute a quantum circuit over private quantum data. Current MPQC protocols rely on the fact that the network is synchronous, i.e., messages sent are guaranteed to be delivered within a known fixed delay upper bound, and unfortunately completely break down even when only a single message arrives late. Motivated by real-world networks, the seminal work of Ben-Or, Canetti and Goldreich (STOC\u2793) initiated the study of multi-party computation for classical circuits over asynchronous networks, where the network delay can be arbitrary. In this work, we begin the study of asynchronous multi-party quantum computation (AMPQC) protocols, where the circuit to compute is quantum. Our results completely characterize the optimal achievable corruption threshold: we present an $n$-party AMPQC protocol secure up to $t<n/4$ corruptions, and an impossibility result when $t\geq n/4$ parties are corrupted. Remarkably, this characterization differs from the analogous classical setting, where the optimal corruption threshold is $t<n/3$

A Framework for Constructing Fast MPC over Arithmetic Circuits with Malicious Adversaries and an Honest-Majority

Protocols for secure multiparty computation enable a set of parties to compute a function of their inputs without revealing anything but the output. The security properties of the protocol must be preserved in the presence of adversarial behavior. The two classic adversary models considered are \emph{semi-honest} (where the adversary follows the protocol specification but tries to learn more than allowed by examining the protocol transcript) and \emph{malicious} (where the adversary may follow any arbitrary attack strategy). Protocols for semi-honest adversaries are often far more efficient, but in many cases the security guarantees are not strong enough. In this paper, we present a new efficient method for ``compiling\u27\u27 a large class of protocols that are secure in the presence of semi-honest adversaries into protocols that are secure in the presence of malicious adversaries. Our method assumes an honest majority (i.e., that $t<n/2$ where $t$ is the number of corrupted parties and $n$ is the number of parties overall), and is applicable to many semi-honest protocols based on secret-sharing. In order to achieve high efficiency, our protocol is \emph{secure with abort} and does not achieve fairness, meaning that the adversary may receive output while the honest parties~do~not. We present a number of instantiations of our compiler, and obtain protocol variants that are very efficient for both a small and large number of parties. We implemented our protocol variants and ran extensive experiments to compare them with each other. Our results show that secure computation with an honest majority can be practical, even with security in the presence of malicious adversaries. For example, we securely compute a large arithmetic circuit of depth 20 with 1,000,000 multiplication gates, in approximately 0.5 seconds with three parties, and approximately 29 seconds with 50 parties, and just under 1 minute with 90 parties

Network-Agnostic Security Comes (Almost) for Free in DKG and MPC

Distributed key generation (DKG) protocols are an essential building block for threshold cryptosystems. Many DKG protocols tolerate up to $t_s<n/2$ corruptions assuming a well-behaved synchronous network, but become insecure as soon as the network delay becomes unstable. On the other hand, solutions in the asynchronous model operate under arbitrary network conditions, but only tolerate $t_a<n/3$ corruptions, even when the network is well-behaved. In this work, we ask whether one can design a protocol that achieves security guarantees in either scenario. We show a complete characterization of network-agnostic DKG protocols, showing that the tight bound is $t_a+2t_s <n$. As a second contribution, we provide an optimized version of the network-agnostic MPC protocol by Blum, Liu-Zhang and Loss [CRYPTO\u2720] which improves over the communication complexity of their protocol by a linear factor. Moreover, using our DKG protocol, we can instantiate our MPC protocol in the plain PKI model, i.e., without the need to assume an expensive trusted setup. Our protocols incur the same communication complexity as state-of-the-art DKG and MPC protocols with optimal resilience in their respective purely synchronous and asynchronous settings, thereby showing that network-agnostic security comes (almost) for free