Secure multiparty computation (MPC) allows a set of mutually distrustful parties to compute a public function on their private inputs without revealing anything beyond the output of the computation. This paper focuses on the specific case of actively secure three-party computation with an honest majority. In particular, we are interested in solutions which allow to evaluate arithmetic circuits over real-world CPU word sizes, like 32- and 64-bit words. Our starting point is the novel compiler of Damgård et al. from CRYPTO 2018. First, we present an improved version of it which reduces the online communication complexity by a factor of 2. Next, we replace their preprocessing protocol (with arithmetic modulo a large prime) with a more efficient preprocessing which only performs arithmetic modulo powers of two. Finally, we present a novel "postprocessing" check which replaces the preprocessing phase. These protocols offer different efficiency tradeoffs and can therefore outperform each other in different deployment settings. We demonstrate this with benchmarks in a LAN and different WAN settings. Concretely, we achieve a throughput of 1 million 64-bit multiplications per second with parties located in different continents and 3 million in one location.
Secure multiparty computation (MPC) allows a set of mutually distrustful parties to compute a public function on their private inputs without revealing anything beyond the output of the computation. This paper focuses on the specific case of actively secure three-party computation with an honest majority. In particular, we are interested in solutions which allow to evaluate arithmetic circuits over real-world CPU word sizes, like 32- and 64-bit words. Our starting point is the novel compiler of Damgård et al. from CRYPTO 2018. First, we present an improved version of it which reduces the online communication complexity by a factor of 2. Next, we replace their preprocessing protocol (with arithmetic modulo a large prime) with a more efficient preprocessing which only performs arithmetic modulo powers of two. Finally, we present a novel "postprocessing" check which replaces the preprocessing phase. These protocols offer different efficiency tradeoffs and can therefore outperform each other in different deployment settings. We demonstrate this with benchmarks in a LAN and different WAN settings. Concretely, we achieve a throughput of 1 million 64-bit multiplications per second with parties located in different continents and 3 million in one location.
Secure multiparty computation enables a set of parties to securely carry out a joint computation on their private inputs without revealing anything but the output. A particularly motivated setting is that of three parties with a single corruption (hereafter denoted 3PC). This 3PC setting is particularly appealing for two main reasons: (1) it admits more efficient MPC protocols than in other standard settings; (2) it allows in principle to achieve full security (and fairness). Highly efficient protocols exist within this setting with security against a semi-honest</> adversary; however, a significant gap remains between these and protocols with stronger security against a malicious</> adversary. In this paper, we narrow this gap within concretely efficient protocols. More explicitly, we have the following contributions: Concretely Efficient Malicious 3PC. We present an optimized 3PC protocol for arithmetic circuits over rings with (amortized) communication of 1 ring element per multiplication gate per party, matching the best semi-honest protocols. The protocol applies also to Boolean circuits, significantly improving over previous protocols even for small circuits. Our protocol builds on recent techniques of Boneh et al. (Crypto 2019) for sublinear zero-knowledge proofs on distributed data, together with an efficient semi-honest protocol based on replicated secret sharing (Araki et al., CCS 2016). We present a concrete analysis of communication and computation costs, including several optimizations. For example, for 40-bit statistical security, and Boolean circuit with a million (nonlinear) gates, the overhead on top of the semi-honest protocol can involve less than 0.5KB of communication for the entire circuit,</> while the computational overhead is dominated by roughly 30 multiplications per gate in the field F247. In addition, we implemented and benchmarked the protocol for varied circuit sizes. Full Security. We augment the 3PC protocol to further provide full security</> (with guaranteed output delivery) while maintaining amortized 1 ring element communication per party per multiplication gate, and with hardly any impact on concrete efficiency. This is contrasted with the best previous 3PC protocols from the literature, which allow a corrupt party to mount a denial-of-service attack without being detected.
Abstract We construct the first actively-secure Multi-Party Computation (MPC) protocols with an arbitrary number of parties in the dishonest majority setting, for an arbitrary field F F with constant communication overhead over the “passive-GMW” protocol (Goldreich, Micali and Wigderson, STOC ‘87). Our protocols rely on passive implementations of Oblivious Transfer (OT) in the Boolean setting and Oblivious Linear function Evaluation (OLE) in the arithmetic setting. Previously, such protocols were only known over sufficiently large fields (Genkin et al. STOC ‘14) or a constant number of parties (Ishai et al. CRYPTO ‘08). Conceptually, our protocols are obtained via a new compiler from a passively-secure protocol for a distributed multiplication functionality FMULT F MULT , to an actively-secure protocol for general functionalities. Roughly, FMULT F MULT is parameterized by a linear-secret sharing scheme S S , where it takes S S -shares of two secrets and returns S S -shares of their product. We show that our compilation is concretely efficient for sufficiently large fields, resulting in an overhead of 2 when securely computing natural circuits. Our compiler has two additional benefits: (1) It can rely on any passive implementation of FMULT F MULT , which, besides the standard implementation based on OT (for Boolean) and OLE (for arithmetic), allows us to rely on implementations based on threshold cryptosystems (Cramer et al. Eurocrypt ‘01), and (2) it can rely on weaker-than-passive (i.e., imperfect/leaky) implementations, which in some parameter regimes yield actively-secure protocols with overhead less than 2. Instantiating this compiler with an “honest-majority” implementation of FMULT F MULT , we obtain the first honest-majority protocol (with up to one-third corruptions) for Boolean circuits with constant communication overhead over the best passive protocol (Damgård and Nielsen, CRYPTO ‘07).
Secure multi-party computation (MPC) allows a set of parties to compute a function jointly while keeping their inputs private. Compared with the MPC based on garbled circuits, some recent research results show that MPC based on secret sharing (SS) works at a very high speed. Moreover, SS-based MPC can be easily vectorized and achieve higher throughput. In SS-based MPC, however, we need many communication rounds for computing concrete protocols like equality check, less-than comparison, etc. This property is not suited for large-latency environments like the Internet (or WAN). In this paper, we construct semi-honest secure communication-efficient two-party protocols. The core technique is Beaver triple extension, which is a new tool for treating multi-fan-in gates, and we also show how to use it efficiently. We mainly focus on reducing the number of communication rounds, and our protocols also succeed in reducing the number of communication bits (in most cases). As an example, we propose a less-than comparison protocol (under practical parameters) with three communication rounds. This is less than a half compared with the previous work. Moreover, the number of communication bits is also 38.4% fewer. As a result, total online execution time is 56.1% shorter than the previous work adopting the same settings. Although the computation costs of our protocols are more expensive than those of previous work, we confirm via experiments that such a disadvantage has small effects on the whole online performance in the typical WAN environments.
Secure Multi-party Computation (MPC) allows a set of mutually distrusting parties to jointly evaluate a function on their private inputs while maintaining input privacy. In this work, we improve semi-honest secure two-party computation (2PC) over rings, with a focus on the efficiency of the online phase. We propose an efficient mixed-protocol framework, outperforming the state-of-the-art 2PC framework of ABY. Moreover, we extend our techniques to multi-input multiplication gates without inflating the online communication, i.e., it remains independent of the fan-in. Along the way, we construct efficient protocols for several primitives such as scalar product, matrix multiplication, comparison, maxpool, and equality testing. The online communication of our scalar product is two ring elements irrespective of the vector dimension, which is a feature achieved for the first time in the 2PC literature. The practicality of our new set of protocols is showcased with four applications: i) AES S-box, ii) Circuit-based Private Set Intersection, iii) Biometric Matching, and iv) Privacy-preserving Machine Learning (PPML). Most notably, for PPML, we implement and benchmark training and inference of Logistic Regression and Neural Networks over LAN and WAN networks. For training, we improve online runtime (both for LAN and WAN) over SecureML (Mohassel et al., IEEE S&P '17) in the range 1.5x–6.1x, while for inference, the improvements are in the range of 2.5x–754.3x.
Multiparty computation (MPC) over rings such as Z232 or Z264 has received a great deal of attention recently due to its ease of implementation and attractive performance. Several actively secure protocols over these rings have been implemented, for both the dishonest majority setting and the setting of three parties with one corruption. However, in the honest majority setting, no concretely efficient protocol for arithmetic computation over rings has yet been proposed that allows for an arbitrary number of parties.
Secure multiparty computation enables a set of parties to securely carry out a joint computation of their private inputs without revealing anything but the output. In the past few years, the efficiency of secure computation protocols has increased in leaps and bounds. However, when considering the case of security in the presence of malicious adversaries (who may arbitrarily deviate from the protocol specification), we are still very far from achieving high efficiency. In this paper, we consider the specific case of three parties and an honest majority. We provide general techniques for improving efficiency of cut-and-choose protocols on multiplication triples and utilize them to significantly improve the recently published protocol of Furukawa et al. (ePrint 2016/944). We reduce the bandwidth of their protocol down from 10 bits per AND gate to 7 bits per AND gate, and show how to improve some computationally expensive parts of their protocol. Most notably, we design cache-efficient shuffling techniques for implementing cut-and-choose without randomly permuting large arrays (which is very slow due to continual cache misses). We provide a combinatorial analysis of our techniques, bounding the cheating probability of the adversary. Our implementation achieves a rate of approximately 1.15 billion AND gates per second on a cluster of three 20-core machines with a 10Gbps network. Thus, we can securely compute 212,000 AES encryptions per second (which is hundreds of times faster than previous work for this setting). Our results demonstrate that high-throughput secure computation for malicious adversaries is possible.