Multiparty Computation Protocols Research Articles

Finding the maximal adversary structure from any given access structure

Secure multi-party computation is an important research area in cryptography, and the secret sharing scheme (SSS) is one of the main tools for constructing multi-party computation protocols. The access structure and the adversary structure are two important subsets of participants in an SSS. In general, the collection of all qualified subsets that can reconstruct the secret s, is known as an access structure, while no information regarding this secret is available to any unqualified subsets, and the collection of unqualified subsets is described as an adversary structure. The maximal adversary, which will become a qualified subset if any one participant not in this unqualified subset is added. At present, there is no effective algorithm to determine the maximal adversary structure for any given access structure. In this paper, we propose two algorithms to determine the maximal adversary structure from any given access structure, in which a binary tree is introduced to construct such algorithms. Moreover, a special type of access structure is established, from which the maximal adversary structure can be directly characterized, and the maximal adversary structure in this case is shown to be the largest when the number of participants of each qualified polynomial in the access structure is three.

An efficient approach for secure multi-party computation without authenticated channel

Secure multi-party sum is one of the most important secure multi-party computation protocols. It has been widely applied to solve many privacy-preservation problems such as privacy-preserving data mining, secure auction, secure electronic voting, and privacy-preserving statistical data analysis. To guarantee the correctness of the final output and to enhance the security level, the existing secure multi-party sum protocols have to use authenticated channels, even secure channels for participants to communicate, however such a usage requirement significantly reduces their performance. Furthermore, these secure multi-party sum protocols are impossible to run on public networks. In this paper, we propose a new secure multi-party sum protocol that can ensure the correctness of the output result as well as securely protecting the parties’ privacy against attacks without requiring any authenticated/secure channel. The proposed protocol is based on a multi-party sum function employing a variant of ElGamal encryption and a Schnorr signature-derived authentication method, in which both these cryptographic tools use the same private and public keys. Additionally, our comparative evaluation shows that the proposed protocol is efficient and practical.

Multi-Party Protocols, Information Complexity and Privacy

We introduce a new information-theoretic measure, which we call Public Information Complexity (PIC), as a tool for the study of multi-party computation protocols, and of quantities such as their communication complexity, or the amount of randomness they require in the context of information-theoretic private computations. We are able to use this measure directly in the natural asynchronous message-passing peer-to-peer model and show a number of interesting properties and applications of our new notion: The Public Information Complexity is a lower bound on the Communication Complexity and an upper bound on the Information Complexity; the difference between the Public Information Complexity and the Information Complexity provides a lower bound on the amount of randomness used in a protocol; any communication protocol can be compressed to its Public Information Cost; and an explicit calculation of the zero-error Public Information Complexity of the k -party, n -bit Parity function, where a player outputs the bitwise parity of the inputs. The latter result also establishes that the amount of randomness needed by a private protocol that computes this function is Ω ( n ).

Outsourcing computation for private function evaluation

Outsourced secure multiparty computation (SMC) protocols allow resource-constrained devices to execute input-private computation with great efficiency. Unfortunately, existing outsourced SMC protocols require that all parties know the function being evaluated, precluding applications where the function itself must remain private. We develop the first linear-complexity protocols for outsourcing private function evaluation (PFE), SMC protocols that provide input and function privacy. Assuming a semi-honest function holder, we build on existing two-party PFE constructions to develop outsourced protocols that are secure against a semi-honest, covert, or malicious outsourcing server and malicious mobile participants. To do this, we develop a garbling technique for combining public and private sub-circuits in a single computation. This allows us to apply auxiliary checks for malicious behaviour using only free-XOR gates. These protocols demonstrate the feasibility of outsourced PFE and provide a first step towards privacy-preserving applications for use in cloud computing.

BFR-MPC: A Blockchain-Based Fair and Robust Multi-Party Computation Scheme

In a general secure multi-party computation (MPC) protocol, two or more participants who do not trust each other, use their respective secret inputs to calculate a joint function in a distributed environment without a centralized organization. They can get correct outputs on the premise of ensuring privacy and independence of input. In this paper, to solve the problem of fairness and robustness in MPC, a blockchain-based multi-party computation scheme (BFR-MPC) was proposed. The blockchain maintains an open reputation system for parties as a public ledger where a more reputable party has a greater chance to be selected. The block height is used as a trusted timestamp. In each round, parties must send the correct information before the deadline. In our scheme, all parties are considered to be foresighted, and an incentive mechanism encourages parties to cooperate rather than deviate from the protocol. Because of non-cooperative parties will be immediately expelled from the protocol and will be penalized financially, the proposed scheme is robust. The penalty will be used to reward honest parties. We also proved the fairness of our scheme through Game Theory. The comparison results of the proposed scheme with other schemes show that it is a more practical scheme for MPC with high fairness and robustness.

Efficient secure multiparty computation of sparse vector dot products

We give a protocol for secure multi-party computation of the scalar product of two sparse vectors of length n with O(log(log n)) rounds and polylogarithmic communication.

A Cloud Based Solution for Collaborative and Secure Sharing of Medical Data

Healthcare sector is under pressure to reduce costs while delivering high quality of care services. This situation requires that clinical staff, equipment and IT tools to be used more equitably, judiciously and efficiently. In this sense, collaborative systems have the ability to provide opportunities for healthcare organizations to share resources and create a collaborative working environment. The lack of interoperability between dissimilar systems and operating costs are the major obstacle to the implementation of this concept. Fortunately, cloud computing has great potential for addressing interoperability issues and significantly reducing operating costs. Since the laws and regulations prohibit the disclosure of health information, it is necessary to carry out a comprehensive study on security and privacy issues in cloud computing. Based on their analysis of these constraints, the authors propose a simple and efficient method that enables secure collaboration between healthcare institutions. For this reason, they propose Secure Multi-party Computation (SMC) protocols to ensure compliance with data protection legislation. Specifically, the authors use Paillier scheme to protect medical data against unauthorized usage when outsourcing computations to a public cloud. Another useful feature of this algorithm is the possibility to perform arithmetic operations over encrypted data without access to the original data. In fact, the Paillier algorithm is an efficient homomorphic encryption that supports addition operations on ciphertexts. Based on the simulation results, the proposed framework helps healthcare organizations to successfully evaluate a public function directly on encrypted data without revealing their private inputs. Consequently, the proposed collaborative application ensures privacy of medical data while completing a task.

Rational protocol of quantum secure multi-party computation

In a rational protocol, players are supposed to be rational, rather than honest, semi-honest or dishonest. This kind of protocols is practical and important, but seldom researched in quantum computation field. In this paper, a multifunctional rational quantum secure multi-party computation protocol is investigated. Firstly, a rational quantum summation protocol is proposed. Secondly, the protocol is generalized to a rational quantum multi-party computation protocol. The computation which is homomorphic can be resolved by our protocol. Thirdly, from the view of utilities, correctness, Nash equilibrium and fairness, analyses show that our protocol is rational. Besides, our protocol is also proved to be secure, efficient and practical. Our research will promote the development of rational quantum multi-party protocol.

On the Power of Hybrid Networks in Multi-Party Computation

Perfectly-secure verifiable secret sharing (VSS) and multi-party computation (MPC) protocols in asynchronous network tolerate only at most one-fourth of corruption, while their counterparts in synchronous network sustain against at most one-third corruption. Moreover property-wise, synchronous protocols provide much stronger guarantees than the asynchronous counterparts. Taking note of the fact that asynchronous network is more realistic on one hand and on the other, synchrony of a network has positive impact on several aspects of distributed protocols including properties and fault-tolerance, we explore the power of hybrid networks that combines best of both the worlds by supporting a few synchronous rounds at the onset of a protocol execution, before turning to asynchronous mode. In hybrid networks, we investigate various feasibility questions pertaining to protocols giving guarantees attainable in synchronous and asynchronous networks. For the asynchronous protocols in hybrid networks, we hope to leverage the initial synchronous rounds to bridge the gap in the fault-tolerance with the synchronous protocols under minimal synchrony assumption. We ask the following fundamental question of both theoretical and practical importance: What is the minimum number of initial synchronous rounds necessary and sufficient in a hybrid network to construct asynchronous perfectly-secure VSS and MPC protocols with the fault-tolerance of synchronous protocols? On the positive note, we show that the answer is one for VSS which is clearly optimal. Notably no broadcast oracle is invoked in the synchronous round of our proposed VSS protocol. On the negative side, we prove that one synchronous round is not enough for MPC, putting MPC on a higher pedestal than VSS in terms of difficulty. For synchronous protocols in hybrid networks, we hope to save on the synchronous rounds leveraging conveniently the available asynchronous phase. We settle the question for VSS in the negative showing that three rounds that are known to be necessary (and sufficient) for VSS in synchronous networks, are also required in hybrid networks. VSS being a special case of MPC, the lower bound holds true for MPC. We match the lower bound with a three-round protocol. Notably, synchronous MPC with cryptographic security is known to be achievable in hybrid networks with one synchronous round.

A critical review on application of secure multi party computation protocols in cloud environment

Security is the essential entity of the digital computations in the internet world. Many internet and mobile applications require private data inputs from different clients for data analysis. Now a days many of the Mobile Apps collect the sensitive user data for analysis may be without knowledge of users. Secure Multi Party computation enables distributed users to share their private inputs to a third party which computes a common function over these inputs and the collaborative outcome shared to the user. It is very essential in many engineering, medical and financial sectors where privacy of the sensitive data provided by the user. Many medical researchers require sensitive patient’s data for typical diagnosis. This paper detailed the origin for SMC which is secret sharing. It discussed the evolution of two party computation to secure multiparty computation. Several protocols and their pros and limitations are described. Cloud computing changed the way SMC was interpreted by earlier works. Cloud provides all the computations as a service basis is used to drastically reducing the communications overhead of the SMC. Our contribution is focused on evolution from conventional SMC with towards Secure Multiple Computation in collaboration with the cloud. The works focuses on the research issues to be addressed because of the untrustworthy nature of the cloud. A comparative analysis of different approach of SMC is presented. The comparative study details the open issues like transparency, public data auditability in SMC with cloud architecture.

Privacy-Preserving Secure Multiparty Computation on Electronic Medical Records for Star Exchange Topology

Nowadays, a huge amount of data are available and shared in collaborative scenarios. These scenarios exist due to the need for joint computations of cooperating data owners for the purpose of making analysis and knowledge extraction. This requirement comes together with some privacy issues. One major issue is how to enable query execution, while no party is allowed to see the entire dataset (computational privacy). Thus, secure multiparty computation protocols allow a group of distrustful data owners to jointly cooperate in executing analytical queries against their data while revealing nothing about the entire dataset. In this paper, we propose a technique that enables a privacy-preserving query processing on horizontally partitioned electronic medical records among a set of hospitals, which have no desire to share their confidential data; however, they all need to cooperate to answer global queries about patients’ medical history. The proposed technique depends on a bucketization technique to reduce computational costs. It relies on a head party, which acts as a mediator between the authorized users and the cooperating parties, which are arranged in a star exchange topology. It ensures that the head party learns nothing about the sensitive data. Our experimental results prove that our technique provides a smaller computational cost and better privacy without the need for a trusted third party.

Round-Efficient Black-Box Construction of Composable Multi-Party Computation

We present a round-efficient black-box construction of a general multi-party computation (MPC) protocol that satisfies composability in the plain model. The security of our protocol is proven in the angel-based UC framework [Prabhakaran and Sahai, STOC’04] under the minimal assumption of the existence of semi-honest oblivious transfer protocols. The round complexity of our protocol is $$\max (\widetilde{O}(\log ^2n), O(R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}))$$ when the round complexity of the underlying oblivious transfer protocol is $$R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}$$ . Since constant-round semi-honest oblivious transfer protocols can be constructed under standard assumptions (such as the existence of enhanced trapdoor permutations), our result gives a $$\widetilde{O}(\log ^2n)$$ -round protocol under these assumptions. Previously, only an $$O(\max (n^{\epsilon }, R_{{{{\mathsf {O}}}{{\mathsf {T}}}}}))$$ -round protocol was shown, where $$\epsilon >0$$ is an arbitrary constant. We obtain our MPC protocol by constructing a $$\widetilde{O}(\log ^2n)$$ -round CCA-secure commitment scheme in a black-box way under the assumption of the existence of one-way functions.

Password-Based Authentication Protocol for Secret-Sharing-Based Multiparty Computation

The performance of secret-sharing (SS)-based multiparty computation (MPC) has recently increased greatly, and several efforts to implement and use it have been put into practice. Authentication of clients is one critical mechanism for implementing SS-based MPC successfully in practice. We propose a password-based authentication protocol for SS-based MPC. Our protocol is secure in the presence of secure channels, and it is optimized for practical use with SS-based MPC in the following ways. Threshold security: Our protocol is secure in the honest majority, which is necessary and sufficient since most practical results on SS-based MPC are secure in the same environment. Establishing distinct channels: After our protocol, a client has distinct secure and two-way authenticated channels to each server. Ease of implementation: Our protocol consists of SS, operations involving SS, and secure channels, which can be reused from an implementation of SS-based MPC. Furthermore, we implemented our protocol with an optimization for the realistic network. A client received the result within 2 sec even when the network delay was 200 ms, which is almost the delay that occurs between Japan and Europe.

Secure “Ratio” Computation and Efficient Protocol for General Secure Two-Party Comparison

Many privacy protections in distributed setting are based on secure comparison, according to which two distrusted users try to jointly determine whether $a>b$ , $a=b$ , or $a . Performing “secure comparison” is fundamental to achieve widespread acceptance of privacy protection for distributed setting users. Surprisingly, however, no attention has been paid to secure comparison on fractions, to the best of our knowledge. In this paper, we first present an efficient system for computing $(({ka+k_{1}})/({kb+k_{1}}))$ , which implies the potential relationship ( $a>b, a=b$ , and $a ) between $a$ and $b$ , where $k$ , $k_{1}$ , and $b$ belong to the party who doesn’t have the secret of the system. Based on this system, two distrusted users in distributed setting can learn whether $a>b, a=b$ , or $a in one execution, without disclosing $a$ and $b$ to each other. Then, we develop two efficient protocols for secure comparison on integers and secure comparison on fractions, respectively. Our schemes, based on homomorphic encryption, are cryptographically secure. We prove that these protocols are secure using simulation paradigm. Our approaches can be used in many secure multi-party computation protocols that involve fractions, rational numbers, and integers. They can also be more convenient to solve some secure multiparty computational geometry problems that often involve ratio evaluation.

A multi-key SMC protocol and multi-key FHE based on some-are-errorless LWE

We study the hardness of learning with errors (LWE) problem with some equation constraints ( $$\hbox {LWE}_{n,l,q,\chi }$$ , some-are-errorless LWE). Previously, it was proved that LWE with one equation (first-is-errorless LWE) can be made as hard as the standard $$\hbox {LWE}_{n,q,\chi }$$ , given a large lattice dimension n. We show that the some-are-errorless LWE problem can also be made equivalently hard as long as n is big enough and $$n \gg l$$ (A similar conclusion was given using fuzzy extrators by Fuller). A second work in this paper is to construct a multi-key secure multi-party computation (SMC) protocol, whose security relies on LWE and the some-are-errorless LWE problem in semi-honest and semi-malicious environments assuming the common random string model. We study the Gentry–Sahai–Waters (GSW13) fully homomorphic encryption (FHE) scheme and its key homomorphism, which is essential for the construction of our multi-key SMC protocol. The proposed protocol naturally constitutes a multi-key FHE scheme in the same settings. Finally, we show the excellence of the proposed SMC protocol in time and space complexity by comparisons with existing relative schemes.

Privacy-Preserving Distributed Linear Regression on High-Dimensional Data

Abstract We propose privacy-preserving protocols for computing linear regression models, in the setting where the training dataset is vertically distributed among several parties. Our main contribution is a hybrid multi-party computation protocol that combines Yao’s garbled circuits with tailored protocols for computing inner products. Like many machine learning tasks, building a linear regression model involves solving a system of linear equations. We conduct a comprehensive evaluation and comparison of different techniques for securely performing this task, including a new Conjugate Gradient Descent (CGD) algorithm. This algorithm is suitable for secure computation because it uses an efficient fixed-point representation of real numbers while maintaining accuracy and convergence rates comparable to what can be obtained with a classical solution using floating point numbers. Our technique improves on Nikolaenko et al.’s method for privacy-preserving ridge regression (S&P 2013), and can be used as a building block in other analyses. We implement a complete system and demonstrate that our approach is highly scalable, solving data analysis problems with one million records and one hundred features in less than one hour of total running time.

On compiling Boolean circuits optimized for secure multi-party computation

Secure multi-party computation (MPC) allows two or more distrusting parties to jointly evaluate a function over private inputs. For a long time considered to be a purely theoretical concept, MPC transitioned into a practical and powerful tool to build privacy-enhancing technologies. However, the practicality of MPC is hindered by the difficulty to implement applications on top of the underlying cryptographic protocols. This is because the manual construction of efficient applications, which need to be represented as Boolean or arithmetic circuits, is a complex, error-prone, and time-consuming task. To facilitate the development of further privacy-enhancing technology, multiple compilers have been proposed that create circuits for MPC. Yet, almost all presented compilers only support domain specific languages or provide very limited optimization methods. In this work (this is an extended and revised version of the paper ‘Secure Two-party Computations in ANSI C’ (Holzer et al., in: ACM CCS, 2012) that reflects the progress in secure computation and describes the current optimization tool chain of CBMC-GC) we describe our compiler CBMC-GC that implements a complete tool chain from ANSI C to circuit. Moreover, we give a comprehensive overview of circuit minimization techniques, which we have identified and adapted for the creation of efficient circuits for MPC. With the help of these techniques, our compilation approach allows for a high level of abstraction from the cryptographic primitives used in MPC protocols, as well as the complex design of digital circuits. By using the model checker CBMC as a compiler frontend, we illustrate the link between MPC, formal methods, and digital logic design. Our experimental results illustrate the effectiveness of the implemented optimizations techniques for various example applications. In particular, compared with other state-of-the-art compilers, we show that CBMC-GC compiles circuits from the same source code that are up to four times smaller.

Quantum security analysis of a lattice-based oblivious transfer protocol

Because of the concise functionality of oblivious transfer (OT) protocols, they have been widely used as building blocks in secure multiparty computation and high-level protocols. The security of OT protocols built upon classical number theoretic problems, such as the discrete logarithm and factoring, however, is threatened as a result of the huge progress in quantum computing. Therefore, post-quantum cryptography is needed for protocols based on classical problems, and several proposals for post-quantum OT protocols exist. However, most post-quantum cryptosystems present their security proof only in the context of classical adversaries, not in the quantum setting. In this paper, we close this gap and prove the security of the lattice-based OT protocol proposed by Peikert et al. (CRYPTO, 2008), which is universally composably secure under the assumption of learning with errors hardness, in the quantum setting. We apply three general quantum security analysis frameworks. First, we apply the quantum lifting theorem proposed by Unruh (EUROCRYPT, 2010) to prove that the security of the lattice-based OT protocol can be lifted into the quantum world. Then, we apply two more security analysis frameworks specified for post-quantum cryptographic primitives, i.e., simple hybrid arguments (CRYPTO, 2011) and game-preserving reduction (PQCrypto, 2014).

Privacy-Preserving Interdomain Routing at Internet Scale

Abstract The Border Gateway Protocol (BGP) computes routes between the organizational networks that make up today’s Internet. Unfortunately, BGP suffers from deficiencies, including slow convergence, security problems, a lack of innovation, and the leakage of sensitive information about domains’ routing preferences. To overcome some of these problems, we revisit the idea of centralizing and using secure multi-party computation (MPC) for interdomain routing which was proposed by Gupta et al. (ACM HotNets’12). We implement two algorithms for interdomain routing with state-of-the-art MPC protocols. On an empirically derived dataset that approximates the topology of today’s Internet (55 809 nodes), our protocols take as little as 6 s of topology-independent precomputation and only 3 s of online time. We show, moreover, that when our MPC approach is applied at country/region-level scale, runtimes can be as low as 0.17 s online time and 0.20 s pre-computation time. Our results motivate the MPC approach for interdomain routing and furthermore demonstrate that current MPC techniques are capable of efficiently tackling real-world problems at a large scale.

Privacy-preserving evaluation techniques and their application in genetic tests

Abstract We discuss several protocols that apply secure multiparty computation to privacy preserving genetic testing. We categorize methods into those using oblivious finite automata, additive homomorphic encryption, garbled circuits, and private set intersection. Through comparison of performance and security metrics, we aim to make recommendations for efficient and secure multiparty computation protocols for various genetic tests including edit distance, disease susceptibility, identity/paternity/common ancestry testing, medicine and treatment efficacy for personalized medicine, and genetic compatibility.