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

Unconditionally Secure Multiparty Computation for Symmetric Functions with Low Bottleneck Complexity

Bottleneck complexity is an efficiency measure of secure multiparty computation (MPC) introduced by Boyle et al. (ICALP 2018) to achieve load-balancing. Roughly speaking, it is defined as the maximum communication complexity required by any player within the protocol execution. Since it is impossible to achieve sublinear bottleneck complexity in the number of players $n$ for all functions, a prior work constructed MPC protocols with low bottleneck complexity for specific functions including the AND function and general symmetric functions. However, the previous protocol for a symmetric function needs to assume a computational primitive of garbled circuits. Its unconditionally secure variant has exponentially large bottleneck complexity in the depth of an arithmetic formula computing the function, which limits the class of symmetric functions the protocol can compute with sublinear bottleneck complexity in $n$. In this paper, we propose for the first time unconditionally secure MPC protocols computing any symmetric function with sublinear bottleneck complexity in $n$. Our first protocol is an application of the one-time truth-table protocol by Ishai et al. (TCC 2013). We devise a novel technique to express the truth-table as an array of two or higher dimensions and obtain two other protocols with better trade-offs. We also propose an unconditionally secure protocol with lower bottleneck complexity tailored to the AND function. It avoids pseudorandom functions used by the previous protocol, preserving bottleneck complexity up to a logarithmic factor in $n$. As an application, we construct an unconditionally secure protocol for private set intersection (PSI), which computes the intersection of players\u27 private sets. This is the first PSI protocol with sublinear bottleneck complexity in $n$ and to the best of our knowledge, there has been no such protocol even under cryptographic assumptions

MPC with Low Bottleneck-Complexity: Information-Theoretic Security and More

The bottleneck-complexity (BC) of secure multiparty computation (MPC) protocols is a measure of the maximum number of bits which are sent and received by any party in protocol. As the name suggests, the goal of studying BC-efficient protocols is to increase overall efficiency by making sure that the workload in the protocol is somehow "amortized" by the protocol participants. Orlandi et al. [Orlandi et al., 2022] initiated the study of BC-efficient protocols from simple assumptions in the correlated randomness model and for semi-honest adversaries. In this work, we extend the study of [Orlandi et al., 2022] in two primary directions: (a) to a larger and more general class of functions and (b) to the information-theoretic setting. In particular, we offer semi-honest secure protocols for the useful function classes of abelian programs, "read-k" non-abelian programs, and "read-k" generalized formulas. Our constructions use a novel abstraction, called incremental function secret-sharing (IFSS), that can be instantiated with unconditional security or from one-way functions (with different efficiency trade-offs)

A Performance and Resource Consumption Assessment of Secure Multiparty Computation

In recent years, secure multiparty computation (SMC) advanced from a theoretical technique to a practically applicable technology. Several frameworks were proposed of which some are still actively developed. We perform a first comprehensive study of performance characteristics of SMC protocols using a promising implementation based on secret sharing, a common and state-of-the-art foundation. Therefor, we analyze its scalability with respect to environmental parameters as the number of peers, network properties -- namely transmission rate, packet loss, network latency -- and parallelization of computations as parameters and execution time, CPU cycles, memory consumption and amount of transmitted data as variables. Our insights on the resource consumption show that such a solution is practically applicable in intranet environments and -- with limitations -- in Internet settings

Multiparty computations in varying contexts

Recent developments in the automatic transformation of protocols into Secure Multiparty Computation (SMC) interactions, and the selection of appropriate schemes for their implementation have improved usabililty of SMC. Poor performance along with data leakage or errors caused by coding mistakes and complexity had hindered SMC usability. Previous practice involved integrating the SMC code into the application being designed, and this tight integration meant the code was not reusable without modification. The progress that has been made to date towards the selection of different schemes focuses solely on the two-party paradigm in a static set-up, and does not consider changing contexts. Contexts, for secure multiparty computation, include the number of participants, link latency, trust and security requirements such as broadcast, dishonest majority etc. Variable Interpretation is a concept we propose whereby specific domain constructs, such as multiparty computation descriptions, are explicitly removed from the application code and expressed in SMC domain representation. This mirrors current practice in presenting a language or API to hide SMC complexity, but extends it by allowing the interpretation of the SMC to be adapted to the context. It also decouples SMC from human co-ordination by introducing a rule-based dynamic negotiation of protocols. Experiments were carried out to validate the method, running a multiparty computation on a variable interpreter for SMC using different protocols in different contexts

ARPA Whitepaper

We propose a secure computation solution for blockchain networks. The correctness of computation is verifiable even under malicious majority condition using information-theoretic Message Authentication Code (MAC), and the privacy is preserved using Secret-Sharing. With state-of-the-art multiparty computation protocol and a layer2 solution, our privacy-preserving computation guarantees data security on blockchain, cryptographically, while reducing the heavy-lifting computation job to a few nodes. This breakthrough has several implications on the future of decentralized networks. First, secure computation can be used to support Private Smart Contracts, where consensus is reached without exposing the information in the public contract. Second, it enables data to be shared and used in trustless network, without disclosing the raw data during data-at-use, where data ownership and data usage is safely separated. Last but not least, computation and verification processes are separated, which can be perceived as computational sharding, this effectively makes the transaction processing speed linear to the number of participating nodes. Our objective is to deploy our secure computation network as an layer2 solution to any blockchain system. Smart Contracts\cite{smartcontract} will be used as bridge to link the blockchain and computation networks. Additionally, they will be used as verifier to ensure that outsourced computation is completed correctly. In order to achieve this, we first develop a general MPC network with advanced features, such as: 1) Secure Computation, 2) Off-chain Computation, 3) Verifiable Computation, and 4)Support dApps' needs like privacy-preserving data exchange