Efficient Constant-Round Multi-party Computation Combining BMR and SPDZ

© 2019, International Association for Cryptologic Research. Recently, there has been huge progress in the field of concretely efficient secure computation, even while providing security in the presence of malicious adversaries. This is especially the case in the two-party setting, where constant-round protocols exist that remain fast even over slow networks. However, in the multi-party setting, all concretely efficient fully secure protocols, such as SPDZ, require many rounds of communication. In this paper, we present a constant-round multi-party secure computation protocol that is fully secure in the presence of malicious adversaries and for any number of corrupted parties. Our construction is based on the constant-round protocol of Beaver et al. (the BMR protocol) and is the first version of that protocol that is concretely efficient for the dishonest majority case. Our protocol includes an online phase that is extremely fast and mainly consists of each party locally evaluating a garbled circuit. For the offline phase, we present both a generic construction (using any underlying MPC protocol) and a highly efficient instantiation based on the SPDZ protocol. Our estimates show the protocol to be considerably more efficient than previous fully secure multi-party protocols.status: publishe

Generalizing the SPDZ Compiler For Other Protocols

Protocols for secure multiparty computation (MPC) enable a set of mutually distrusting parties to compute an arbitrary function of their inputs while preserving basic security properties like \emph{privacy} and \emph{correctness}. The study of MPC was initiated in the 1980s where it was shown that any function can be securely computed, thus demonstrating the power of this notion. However, these proofs of feasibility were theoretical in nature and it is only recently that MPC protocols started to become efficient enough for use in practice. Today, we have protocols that can carry out large and complex computations in very reasonable time (and can even be very fast, depending on the computation and the setting). Despite this amazing progress, there is still a major obstacle to the adoption and use of MPC due to the huge expertise needed to design a specific MPC execution. In particular, the function to be computed needs to be represented as an appropriate Boolean or arithmetic circuit, and this requires very specific expertise. In order to overcome this, there has been considerable work on compilation of code to (typically) Boolean circuits. One work in this direction takes a different approach, and this is the SPDZ compiler (not to be confused with the SPDZ protocol) that takes high-level Python code and provides an MPC run-time environment for securely executing that code. The SPDZ compiler can deal with arithmetic and non-arithmetic operations and is extremely powerful. However, until now, the SPDZ compiler could only be used for the specific SPDZ family of protocols, making its general applicability and usefulness very limited. In this paper, we extend the SPDZ compiler so that it can work with general underlying protocols. Our SPDZ extensions were made in mind to enable the use of SPDZ for arbitrary protocols and to make it easy for others to integrate existing and new protocols. We integrated three different types of protocols, an honest-majority protocol for computing arithmetic circuits over a field (for any number of parties), a three-party honest majority protocol for computing arithmetic circuits over the ring of integers $\Z_{2^n}$, and the multiparty BMR protocol for computing Boolean circuits. We show that a single high-level SPDZ-Python program can be executed using all of these underlying protocols (as well as the original SPDZ protocol), thereby making SPDZ a true general run-time MPC environment. In order to be able to handle both arithmetic and non-arithmetic operations, the SPDZ compiler relies on conversions from field elements to bits and back. However, these conversions do not apply to ring elements (in particular, they require element division), and we therefore introduce new bit decomposition and recomposition protocols for the ring over integers with replicated secret sharing. These conversions are of independent interest and utilize the structure of $\Z_{2^n}$ (which is much more amenable to bit decomposition than prime-order fields), and are thus much more efficient than all previous methods. We demonstrate our compiler extensions by running a complex SQL query and a decision tree evaluation over all protocols

Efficient, Actively Secure MPC with a Dishonest Majority: a Survey

The last ten years have seen a tremendous growth in the interest and practicality of secure multiparty computation (MPC) and its possible applications. Secure MPC is indeed a very hot research topic and recent advances in the eld have already been translated into commercial products world-wide. A major pillar in this advance has been in the case of active security with a dishonest majority, mainly due to the SPDZ-line of work protocols. This survey gives an overview of these protocols, with a focus of the original SPDZ paper (CRYPTO 2012) and its subsequent optimizations. It also covers some alternative approaches based on oblivious transfer, oblivious linear-function evaluation, and constant-round protocols

Non-Interactive MPC with Trusted Hardware Secure Against Residual Function Attacks

Secure multiparty computation (MPC) has been repeatedly optimized, and protocols with two communication rounds and strong security guarantees have been achieved. While progress has been made constructing non-interactive protocols with just one-round of online communication (i.e., non-interactive MPC or NI-MPC), since correct evaluation must be guaranteed with only one round, these protocols are by their nature vulnerable to the residual function attack in the standard model. This is because a party that receives a garbled circuit may repeatedly evaluate the circuit locally, while varying their own inputs and fixing the input of others to learn the values entered by other participants. We present the first MPC protocol with a one-round online phase that is secure against the residual function attack. We also present rigorous proofs of correctness and security in the covert adversary model, a reduction of the malicious model that is stronger than the semi-honest model and better suited for modeling the behaviour of parties in the real world, for our protocol. Furthermore, we rigorously analyze the communication and computational complexity of current state of the art protocols which require two rounds of communication or one-round during the online-phase with a reduced security requirement, and demonstrate that our protocol is comparable to or outperforms their complexity

Scalable Mixed-Mode MPC

Protocols for secure multi-party computation (MPC) supporting mixed-mode computation have found a lot of applications in recent years due to their flexibility in representing the function to be evaluated. However, existing mixed-mode MPC protocols are only practical for a small number of parties: they are either tailored to the case of two/three parties, or scale poorly for a large number of parties. In this paper, we design and implement a new system for highly efficient and scalable mixed-mode MPC tolerating an arbitrary number of semi-honest corruptions. Our protocols allow secret data to be represented in Encrypted, Boolean, Arithmetic, or Yao form, and support efficient conversions between these representations. 1. We design a multi-party table-lookup protocol, where both the index and the table can be kept private. The protocol is scalable even with hundreds of parties. 2. Using the above protocol, we design efficient conversions between additive arithmetic secret sharings and Boolean secret sharings for a large number of parties. For 32 parties, our conversion protocols require 1184× to 8141× less communication compared to the state- of-the-art protocols MOTION and MP-SPDZ; this leads to up to 1275× improvement in running time under 1 Gbps network. The improvements are even larger with more parties. 3. We also use new protocols to design an efficient multi-party distributed garbling protocol. The protocol could achieve asymptotically constant communication per party. Our implementation will be made public

Trifecta: Faster High-throughput Three-party Computation over WAN using Multi-fan-in Logic Gates

Multi-party computation (MPC) has been a very active area of research and recent industrial deployments exist. Practical MPC is currently limited to low-latency, high- throughput network setups, i.e., local-area networks (LAN). However, many use cases require the participation of different entities located in different data centers, i.e., communication over wide-area networks (WAN). Although, constant-round MPC exists, it has very high communication cost. In contrast, protocols based on secret-sharing are suitable for efficient parallelization but their running time is limited by the network latency. In this work, we investigate the reduction of the round complexity of secret-shared based multi-party computation. We propose a new three-party computation protocol that allows to compute multi-fan-in AND gates in one round of communication without any preprocessing. Using this primitive, we describe depth-optimized constructions for major building blocks in multi-party computation including addition, multiplication and comparison. We demonstrate the increased performance of our approach by evaluating several such functionalities in a real WAN environment. For the common benchmark of AES, our protocol achieves subsecond running time for all key lengths of AES over WAN, outperforming even constant-round protocols. We also improve upon state-of-the-art secret-shared based protocols in terms of throughput. For example, we observe that our protocol has a higher throughput by a factor of 2.2× compared to the best previous work. Our work shows that it is possible to have fast high-throughput multi-party computation with practical applications between parties in distant global regions