Secure Multi-party Computation Problem Research Articles

Confidentially Compare Rational Numbers under the Malicious Model

<p>Secure multi-party computation is a hotspot in the cryptography field, and it is also a significant means to realize privacy computation. The Millionaires’ problem is the most fundamental problem among them, which is the basic module of secure multi-party computation protocols. Although there are many solutions to this problem, there are few anti-malicious adversarial protocols besides protocols based on Yao’s garbled circuit. Only a few solutions have low efficiency, and there is no protocol for rational numbers comparison under the malicious model, which restricts the solution of many secure multi-party computation problems. In this paper, the possible malicious behaviors are analyzed in the existing Millionaires’ problem protocols. These behaviors are discovered and taken precautions against through the triangle area formula, zero-knowledge proof, and cut-and-choose method, so the protocol of comparing confidentially rational numbers is proposed under the malicious model. And this paper adopts the real/ideal model paradigm to prove the security of the malicious model protocol. Efficiency analysis indicates that the proposed protocol is more effective than existing protocols. The protocol of rational numbers comparison under the malicious model is more suitable for the practical applications of secure multi-party computation, which has important theoretical and practical significance.</p> <p> </p>

Securely Computing the Manhattan Distance under the Malicious Model and Its Applications

Manhattan distance is mainly used to calculate the total absolute wheelbase of two points in the standard coordinate system. The secure computation of Manhattan distance is a new geometric problem of secure multi-party computation. At present, the existing research secure computing protocols for Manhattan distance cannot resist the attack of malicious participants. In the real scene, the existence of malicious participants makes it necessary to study a solution that can resist malicious attacks. This paper first analyzes malicious attacks of the semi-honest model protocol of computing Manhattan distance and then designs an advanced protocol under the malicious model by using the Goldwasser–Micali encryption system and Paillier encryption algorithm, and utilizing some cryptographic tools such as the cut-choose method and zero-knowledge proof. Finally, the real/ideal model paradigm method is used to prove the security of the malicious model protocol. Compared with existing protocols, the experimental simulation shows that the proposed protocol can resist malicious participant attacks while maintaining high efficiency. It has practical value.

Secured distributed algorithms without hardness assumptions

We study algorithms in the LOCAL model that produce secured output. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the output of other vertices, with a certain probability. As the extensive research in the distributed algorithms field yielded efficient decentralized algorithms, the discussion about the security of distributed algorithms was somewhat neglected. Nevertheless, many protocols and algorithms were devised in the research area of secure multi-party computation problem. However, the focus in those protocols was to work for every function f at the expense of increasing the round complexity, or the necessity of several computational assumptions. We present a novel approach, which identifies and develops those algorithms that are inherently secure (which means they do not require any further constructions). This approach yields efficient secure algorithms for various labeling and decomposition problems without requiring any hardness assumption, but only a private randomness generator in each vertex.

Secure multi-party computations for privacy-preserving machine learning

The paper is devoted to the analysis of privacy-preserving machine learning (PPML) systems based on secure multi-party computations. It reviews PPML systems, analyses the goals and objectives of its application. A generalized model of PPML architecture is proposed, reflecting the main functional blocks of such systems. The formulation of the problem of secure multi-party computation is considered. The descriptions of cryptographic primitives and protocols used to implement multi-party secure computation protocols, including garbled circuits, secret sharing schemes, and homomorphic encryption are given. The current PPML systems based on two-, three-, and four-party secure computations are analyzed. The main attention is paid to algorithmic aspects of systems, methods and protocols of securing information. Systems secure against semi-honest and active adversaries are considered, both based on universal modules for secure multi-party computations, and specialized ones designed to ensure the privacy of specific machine learning technologies, such as convolutional neural networks. We consider examples of implemented prototypes of several PPML systems. Based on the results of the analysis, conclusions are formulated about the features of the future PPML systems.

Secure Scalar Product Protocols

Secure scalar product computation is a special secure multi-party computation problem. A secure scalar product protocol can be used by two parties to jointly compute the scalar product of their private vectors without revealing any information about the private vector of either party. Secure scalar product protocol is of great significance in privacy-preserving scientific computing, privacy preserving data mining, privacy-preserving cooperative statistical analysis and privacy-preserving geometry computation, etc. Many privacy preserving computing problems can be transformed to secure scalar product computation. At present, existing scalar product protocols cannot be used to privately compute scalar product of private vectors with both positive and negative components. Based on homomorphic encryption scheme, we design three protocols to compute scalar product of three different kinds of private vectors. The components of the first kind vector are arbitrary integers; those of the second kind are positive rational numbers and those of the third kind are arbitrary rational numbers. We use simulation paradigm proving that the protocols are secure in the semi-honest model. Theoretical analysis and experimental results show that the protocols designed in this paper are efficient.

Secure Coded Multi-Party Computation for Massive Matrix Operations

In this article, we consider a secure multi-party computation problem (MPC), where the goal is to offload the computation of an arbitrary polynomial function of some massive private matrices (inputs) to a cluster of workers. The workers are not reliable. Some of them may collude to gain information about the input data (semi-honest workers). The system is initialized by sharing a (randomized) function of each input matrix to each server. Since the input matrices are massive, each share's size is assumed to be at most 1/k fraction of the input matrix, for some k ∈ \mathbb N. The objective is to minimize the number of workers needed to perform the computation task correctly, such that even if an arbitrary subset of t-1 workers, for some t ∈ \mathbb N, collude, they cannot gain any information about the input matrices. We propose a sharing scheme, called polynomial sharing, and show that it admits basic operations such as adding and multiplication of matrices and transposing a matrix. By concatenating the procedures for basic operations, we show that any polynomial function of the input matrices can be calculated, subject to the problem constraints. We show that the proposed scheme can offer order-wise gain in terms of the number of workers needed, compared to the approaches formed by the concatenation of job splitting and conventional MPC approaches.

Protocol for millionaires' problem in malicious models

Secure multiparty computation is a focus of the international cryptographic community. The millionaires problem is the most important problem in secure multiparty computation and is a building block for constructing other secure multiparty computation protocols. Several solutions are available to solve this problem, but except for protocols based on garbled circuits, the existing solutions based on public key cryptosystems are only secure in semihonest models. No solution based on a public key cryptosystem is secure against malicious adversaries. This state restricts the resolution of many secure multiparty computation problems in malicious scenarios. A solution that is secure in malicious models is highly applicable in practical application scenarios and is generally appealing. Therefore, the study of the solution to the millionaires problem in a malicious model is of great theoretical and practical significance. In this work, we propose a multiparty computation protocol for the millionaires problem that is secure in a semihonest model. The proposed protocol is simple and easily understandable. We analyze the possible malicious behaviors in this protocol and use zero-knowledge proof and cut-and-choose techniques to resist possible malicious behaviors and thereby convert the protocol into one that is secure in the malicious model. We prove that the proposed protocol is secure in the malicious model by using the well-accepted ideal-real paradigm. Theoretical efficiency analysis shows that the efficiency of our protocol is at least six times that of existing protocols.

An attempt at universal quantum secure multi-party computation with graph state

Quantum secure multi-party computation (SMC) is a vital field in quantum cryptography. In this paper, we try to resolve SMC problems universally via graph states. Firstly, three kinds of quantum SMC protocols are investigated, which are quantum private comparison protocol, quantum millionaire protocol and quantum multi-party summation protocol. Secondly, three proposed protocols are reviewed, and then the core of them is summarized. We further find that the computation, deduced as modulo subtraction, can be resolved by using graph state. This implies that our protocols are universal in part and will be widely applicable. Thirdly, analyses show that the proposed protocols are correct and secure. Our research will promote the development of quantum secure multi-party computation.

Secure two-party computation of solid triangle area and tetrahedral volume based on cloud platform.

With the emergence and widespread application of cloud computing, the use of cloud platforms to solve the problem of secure multi-party computation has emerged as a new research direction. The traditional computation of a solid geometry is performed through mutual interactions between two parties, which is not suitable in an untrusted cloud computing environment. In this paper, we first design a basic protocol for a secure Euclidean distance calculation that is suitable for cloud platforms and can serve as a building block for other protocols on cloud platforms. Using the solution of the Euclidean distance problem as such a building block, we provide a new method that converts the problems of calculating solid triangular areas and solid tetrahedral volumes into the calculation of distances and determinants in three-dimensional space. Then, we discuss solid point-line distance calculations, which extent the idea of the spatial geometry security problem. We present protocols for the above problems and prove that the proposed protocols can resist conspiracy among users and the untrusted cloud platform so that they can effectively ensure the privacy of the users. We also analyze the performances of these solutions. The analysis results show that our scheme is more versatile.

Efficient solution to the millionaires' problem based on asymmetric commutative encryption scheme

AbstractSecure multiparty computation is an important scheme in cryptography and can be applied in various real‐life problems. The first secure multiparty computation problem is the millionaires' problem, and its protocol is an important building block. Because of the less efficiency of public key encryption scheme, most existing solutions based on public key cryptography to this problem are inefficient. Thus, a solution based on the symmetric encryption scheme has been proposed. In this paper, we formally analyse the vulnerability of this solution, and propose a new scheme based on the decisional Diffie‐Hellman assumption. Our solution also uses 0‐encoding and 1‐encoding generated by our modified encoding method to reduce the computation cost. We implement the solution based on symmetric encryption scheme and our protocol. Extensive experiments are conducted to evaluate the efficiency of our solution, and the experimental results show that our solution can be much more efficient and be approximately 8000 times faster than the solution based on symmetric encryption scheme for a 32‐bit input and short‐term security. Moreover, our solution is also more efficient than the state‐of‐the‐art solution without precomputation and can also compare well with the state‐of‐the‐art protocol while the bit length of private inputs is large enough.

Secure multi-party computation in large networks

We describe scalable protocols for solving the secure multi-party computation (MPC) problem among a significant number of parties. We consider both the synchronous and the asynchronous communication models. In the synchronous setting, our protocol is secure against a static malicious adversary corrupting less than a 1/3 fraction of the parties. In the asynchronous environment, we allow the adversary to corrupt less than a 1/8 fraction of parties. For any deterministic function that can be computed by an arithmetic circuit with m gates, both of our protocols require each party to send a number of messages and perform an amount of computation that is $$\tilde{O}(m/n + \sqrt{n})$$O~(m/n+n). We also show that our protocols provide statistical and universally-composable security. To achieve our asynchronous MPC result, we define the threshold counting problem and present a distributed protocol to solve it in the asynchronous setting. This protocol is load balanced, with computation, communication and latency complexity of $$O(\log {n})$$O(logn), and can also be used for designing other load-balanced applications in the asynchronous communication model.

Two Quantum Protocols for Oblivious Set-member Decision Problem.

In this paper, we defined a new secure multi-party computation problem, called Oblivious Set-member Decision problem, which allows one party to decide whether a secret of another party belongs to his private set in an oblivious manner. There are lots of important applications of Oblivious Set-member Decision problem in fields of the multi-party collaborative computation of protecting the privacy of the users, such as private set intersection and union, anonymous authentication, electronic voting and electronic auction. Furthermore, we presented two quantum protocols to solve the Oblivious Set-member Decision problem. Protocol I takes advantage of powerful quantum oracle operations so that it needs lower costs in both communication and computation complexity; while Protocol II takes photons as quantum resources and only performs simple single-particle projective measurements, thus it is more feasible with the present technology.

Study on Commitment Schemes of Secure Multi-party Computation

The problem of secure multi-party computation(SMPC) is one of the most fundamental problems in information security. First, we introduce the basic concept of SMPC and four SMPC basic agreement: key distribution,oblivious transfer, bit commitment and zero knowledge proof. Secondly, we separately illustrate commitment schemes commitment transfer protocol, commitment sharing protocol and commitment multiplication protocol. Finally, we present unconditionally secure multi-party computation with a passive adversary, an active adversary, general adversary structures.

Comparative Evaluation of Elliptic Curve Cryptography Based Homomorphic Encryption Schemes for a Novel Secure Multiparty Computation

In this paper, we focus on Elliptic Curve Cryptography based approach for Secure Multiparty Computation (SMC) problem. Widespread proliferation of data and the growth of communication technologies have enabled collaborative computations among parties in distributed scenario. Preserving privacy of data owned by parties is crucial in such scenarios. Classical approach to SMC is to perform computation using Trusted Third Party (TTP). However, in practical scenario, TTPs are hard to achieve and it is imperative to eliminate TTP in SMC. In addition, existing solutions proposed for SMC use classical homomorphic encryption schemes such as RSA and Paillier. Due to the higher cost incurred by such cryptosystems, the resultant SMC protocols are not scalable. We propose Elliptic Curve Cryptography (ECC) based approach for SMC that is scalable in terms of computational and communication cost and avoids TTP. In literature, there do exist various ECC based homomorphic schemes and it is imperative to investigate and analyze these schemes in order to select the suitable for a given application. In this paper, we empirically analyze various ECC based homomorphic encryption schemes based on performance metrics such as computational cost and communication cost. We recommend an efficient algorithm amongst several selected ones, that offers security with lesser overheads and can be applied in any application demanding privacy.

SMC Protocol for Naïve Bayes Classification over Grid Partitioned Data using Multiple UTPs

The case where data is distributed horizontally as well as vertically, it refers as grid partitioned data. SMC protocol for Naive Bayes classification over grid partitioned data is offered in this paper. Also present a solution of the Secure Multi-party Computation (SMC) problem in the form of a protocol that preserves privacy. In this system, a protocol with several Untrusted Third Parties (UTPs) is used, where there is almost impossible of privacy leakage. Multiple UTPs will calculate the model parameters for integrating the horizontally partitioned data. After that secure multiplication protocol will apply on vertical partitioned data (multiple UTPs) to classify the new tuple. The main contribution of this paper is that it shows a simple and easy calculation for developing Naive Bayes classifier for grid partitioned data. The evaluation method is simple and more efficient. General Terms SMC, Naive Bayes Classification.

Distributed RK- Secure Sum Protocol for Privacy Preserving

Secure multi party computation allows several parties to compute some function of their inputs without disclosing the actual input to one another. Secure sum computation is an easily understood example and the component of the various secure multi party computation solutions. Secure sum computation allows parties to compute the sum of their individual inputs without disclosing the inputs to one another. In this paper, we propose a protocol with more security, when a group of the computing parties want to know the data of some other party. I. INTRODUCTION The huge growth of the Internet and its easy access by common man created opportunities for joint computations by multiple parties. All the participating parties for the sake of their mutual benefit want to compute the common function of their inputs but at the same time they are worried about the privacy of their data. This subject of the information security is called secure multi party computation. This subject has two goals; one is the privacy of the individual data inputs and another is the correctness of the result. Mainly two models exist in the literature for the analysis of the secure multi party computation problems. Ideal model of the secure multi party computation uses a Trusted Third Party apart from the participating parties. Parties supply their inputs to the Trusted Third Party. Computation of the function is done by the Trusted Third Party and then the result is sent to all the parties. In this paradigm the trustworthiness of the Trusted Third Party is critically important because if the Trusted Third Party turns corrupt, it can supply the private inputs of one party to others. But it is extensively used model of the secure multi party computation due to its easy implementation and the protocols available which prevent the Trusted Third Party to act maliciously. Real model of the secure multi party computation does not use any Trusted Third Party but the parties themselves agree on some protocol for the computation. The parties behavior in the secure multi party computation is important to consider. An honest party follows the protocol and respects the privacy of other parties. A semi honest party follows the protocol but also tries to learn other information than the result. The corrupt party neither follows the protocol nor respects the privacy of other parties. Different protocols are needed for different secure multi party computation models and the behavior of the party. Solutions are available for secure multi party computation problems using cryptographic techniques, randomization techniques and anonymization methods. The subject of secure multi party computation has been evolved from two party comparison problems (1) to multiparty image template matching problems. Many specific secure multi party computation problems have been defined and analyzed by researchers like Private Information Retrieval, Selective Function Evaluation, Privacy-Preserving Database Query, Privacy-Preserving Geometric Computation, Privacy- Preserving Statistical Analysis, Privacy-Preserving Intrusion Detection and Privacy-Preserving Cooperative Scientific Computation. Based on these general secure multi party computation problems many real life applications have been emerged like Privacy- Preserving Electronic Voting, Privacy-Preserving Bidding and Auctions, Privacy-Preserving Social Network Analysis, Privacy-Preserving Signature and Face Detection, Etc. Secure sum computation problem of secure multi party computation can be defined as: How multiple parties can compute the sum of their input values without disclosing actual values to one another. Secure sum can work as the tool for the secure multi party computation solutions in the privacy preserving distributed data mining problems (2). We proposed a secure sum protocol using random numbers (2). In this paper, we proposed a novel changing neighbors approach Distributed RK secure sum protocol for achieving more security in case a group of the parties collude to know the private data of some other party. 1.1 Distributed Database Partition: - Database is divided into three main portioning horizontal partition, vertical partition and hybrid partition. 1.1.1 Horizontal Partitioning: - Horizontal partitioning divides the whole database into the number of small database according to the row splitting. So that the execution of query will be very fast as well as we will be able to provide more privacy to the portioned database.

A Secure Scalar Product Protocol Against Malicious Adversaries

A secure scalar product protocol is a type of specific secure multi-party computation problem. Using this kind of protocol, two involved parties are able to jointly compute the scalar product of their private vectors, but no party will reveal any information about his/her private vector to another one. The secure scalar product protocol is of great importance in many privacy-preserving applications such as privacy-preserving data mining, privacy-preserving cooperative statistical analysis, and privacy-preserving geometry computation. In this paper, we give an efficient and secure scalar product protocol in the presence of malicious adversaries based on two important tools: the proof of knowledge of a discrete logarithm and the verifiable encryption. The security of the new protocol is proved under the standard simulation-based definitions. Compared with the existing schemes, our scheme offers higher efficiency because of avoiding inefficient cut-and-choose proofs.

Two privacy-preserving protocols for point-curve relation

Numerous privacy-preserving issues have emerged along with the fast development of Internet, both in theory and in real-life applications. To settle the privacy-preserving problems, secure multi-party computation is essential and critical. In this paper, we have solved two problems regarding to how to determine the position relation between points and curves without revealing any private information. Two protocols have been proposed in order to solve the problems in different conditions. In addition, some building blocks have been developed, such as scalar product protocol, so that we can take advantage of them to settle the privacy-preserving computational geometry problems which are a kind of special secure multi-party computation problems. Moreover, oblivious transfer and power series expansion serve as significant parts in our protocols. Analyses and proofs have also been given to argue our conclusion.

Secure Distributed Computation in the Exponent

A secure multi-party computation problem deals with computing a function on any input, in a distributed network, ensuring that no more information is revealed to a player in the computation. New protocols are developed for the following interesting variation on a typical problem of secure multi-party computation: Given secrets shared among a group of players, compute the function value of basic computations, such as interpolation, addition, multiplication or inversion, in the exponent. The protocols can be proven robust and secure in standard computation models.

Secure Two-party Protocols for Point Inclusion Problem

It is well known that, in theory, the general secure multiparty computation problem is solvable using circuit evaluation protocols. However, the communication complexity of the resulting protocols depend on the size of the circuit that expresses the functionality to be computed and hence can be impractical. Hence special solutions are needed for specific problems for efficiency reasons. The point inclusion problem in computational geometry is a special multiparty computation and has got many applications. Previous protocols for the secure point inclusion problem are not adequate. In this paper we modify some known solutions to the point inclusion problem in computational geometry to the frame work of secure two-party computation.