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IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews)

Toward Empirical Aspects of Secure Scalar Product

I-Cheng Wang, Chih-Hao Shen, Justin Z. Zhan, Tsan‐sheng Hsu, Churn‐Jung Liau, Da-Wei Wang

Published Apr 18, 2009• 35 citations
Publisher

Abstract

There is a fair amount of research about privacy, but few empirical studies about its cost have been conducted. In the area of secure multiparty computation, the scalar product has long been reckoned as one of the most promising alternatives to classic logic gates. The reason for this is that the scalar product is not only complete, which is as good as logic gates, but also much more efficient than logic gates. As a result, we set out to study the computation and communication resources needed for some of the most well-known and frequently referenced secure scalar product protocols, including the composite residuosity, the invertible matrix, the polynomial sharing, and the commodity-based approaches. In addition to the implementation details of these approaches, we analyze and compare their execution time, computation time, and memory and random number consumption. Moreover, Fairplay, the benchmark approach that implements Yao's circuit evaluation protocol, is also included in our experiments in order to demonstrate the potential for the scalar products to replace logic gates.

DOI
10.1109/tsmcc.2009.2016430

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Privacy is ultimately important, and there is a fair amount of research about it. However, few empirical studies about the cost of privacy are conducted. In the area of secure multiparty computation, the scalar product has long been reckoned as one of the most promising building blocks in place of the classic logic gates. The reason is not only the scalar product complete, which is as good as logic gates, but also the scalar product is much more efficient than logic gates. As a result, we set to study the computation and communication resources needed for some of the most well-known and frequently referred secure scalar-product protocols, including the composite-residuosity, the invertible-matrix, the polynomial-sharing, and the commodity-based approaches. Besides the implementation remarks of these approaches, we analyze and compare their execution time, computation time, and random number consumption, which are the most concerned resources when talking about secure protocols. Moreover, Fairplay the benchmark approach implementing Yao's famous circuit evaluation protocol, is included in our experiments in order to demonstrate the potential for the scalar product to replace logic gates.

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In this model we propose protocols for generic secure computation that offload the work of most of the parties to the computation server. We also construct a specialized server-aided two party set intersection protocol that achieves better efficiencies for the two participants than existing solutions. Outsourcing in many cases concerns only data storage and while outsourcing the data of a single party is useful, providing a way for data sharing among different clients of the service is the more interesting and useful setup. However, this scenario brings new challenges for access control since the access control rules and data accesses become private data for the clients with respect to the service provide. We propose an approach that offers trade-offs between the privacy provided for the clients and the communication overhead incurred for each data access. Efficient Private Search in Practice - We consider the question of private search from a different perspective compared to traditional settings for MPC. We start with strict efficiency requirements motivated by speeds of available hardware and what is considered acceptable overhead from practical point of view. Then we adopt relaxed definitions of privacy, which still provide meaningful security guarantees while allowing us to meet the efficiency requirements. In this setting we design a security architecture and implement a system for data sharing based on encrypted search, which achieves only 30% overhead compared to non-secure solutions on realistic workloads.

•Jan 1, 2012•4 citations

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Secure multiparty computation (\(\mathsf {MPC}\)) addresses the challenge of evaluating functions on secret inputs without compromising their privacy. A central question in multiparty computation is to understand the amount of communication needed to securely evaluate a circuit of size s. In this work, we revisit this fundamental question in the setting of information-theoretically secure \(\mathsf {MPC}\) in the correlated randomness model, where a trusted dealer distributes correlated random coins, independent of the inputs, to all parties before the start of the protocol. This setting is of strong theoretical interest, and has led to the most practically efficient \(\mathsf {MPC}\) protocols known to date.

•Jan 1, 2018•0 citations

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Elette Boyle, Niv Gilboa, Yuval Ishai +1 more

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.

ACM SIGSAC Conference on Computer and Communications Security (CCS)•Nov 6, 2019•58 citations
There is a fair amount of research about privacy, but few empirical studies about its cost have been conducted. In the area of secure multiparty computation, the scalar product has long been reckoned as one of the most promising alternatives to classic logic gates. The reason for this is that the scalar product is not only complete, which is as good as logic gates, but also much more efficient than logic gates. As a result, we set out to study the computation and communication resources needed for some of the most well-known and frequently referenced secure scalar product protocols, including the composite residuosity, the invertible matrix, the polynomial sharing, and the commodity-based approaches. In addition to the implementation details of these approaches, we analyze and compare their execution time, computation time, and memory and random number consumption. Moreover, Fairplay, the benchmark approach that implements Yao's circuit evaluation protocol, is also included in our experiments in order to demonstrate the potential for the scalar products to replace logic gates.
Privacy is ultimately important, and there is a fair amount of research about it. However, few empirical studies about the cost of privacy are conducted. In the area of secure multiparty computation, the scalar product has long been reckoned as one of the most promising building blocks in place of the classic logic gates. The reason is not only the scalar product complete, which is as good as logic gates, but also the scalar product is much more efficient than logic gates. As a result, we set to study the computation and communication resources needed for some of the most well-known and frequently referred secure scalar-product protocols, including the composite-residuosity, the invertible-matrix, the polynomial-sharing, and the commodity-based approaches. Besides the implementation remarks of these approaches, we analyze and compare their execution time, computation time, and random number consumption, which are the most concerned resources when talking about secure protocols. Moreover, Fairplay the benchmark approach implementing Yao's famous circuit evaluation protocol, is included in our experiments in order to demonstrate the potential for the scalar product to replace logic gates.
A secure multiparty number-product protocol is an important building block in the area of secure multiparty computation. With proper composition of the building block, most applications, such as circuit evaluation, data mining, and private information retrieval, can be executed securely and collaboratively by potentially dishonest parties. In this work, we propose a commodity-based secure number-product protocol, the security of which has been validated with the metrics proposed by Chiang et al. based on information theory. We prove that the protocol can be executed securely under the assumption of semi-honest behavior. Furthermore, if an extra semi-trusted party exists, the proposed protocol can resist any number of corrupt parties. In addition to the security issue, we compare the protocol's communication and computation costs with those of the theoretically secure solution proposed by Ben-Or et al.
Secure multiparty computation is a very important research topic in cryptography. The sub-problem of secure multiparty computation that has received special attention by researchers because of its close relation to many cryptographic tasks is secure two-party computation. This area of research is concerned with the question: ldquoCan two party computation be achieved more efficiently and under weaker security assumptions than general multiparty computation?rdquo Yaopsilas protocol provided security against passive adversaries, while Lindell and Pinkas proposed secure two party protocols that are secure against active adversaries. In this paper, we would like to propose a set of information theoretically secure protocols based on scalar product protocol. The detailed complexity analysis is also provided.
Many services that people use daily require computation that depends on the private data of multiple parties. While the utility of the final result of such interactions outweighs the privacy concerns related to output release, the inputs for such computations are much more sensitive and need to be protected. Secure multiparty computation (MPC) considers the question of constructing computation protocols that reveal nothing more about their inputs than what is inherently leaked by the output. There have been strong theoretical results that demonstrate that every functionality can be computed securely. However, these protocols remain unused in practical solutions since they introduce efficiency overhead prohibitive for most applications. Generic multiparty computation techniques address homogeneous setups with respect to the resources available to the participants and the adversarial model. On the other hand, realistic scenarios present a wide diversity of heterogeneous environments where different participants have different available resources and different incentives to misbehave and collude. In this thesis we introduce techniques for multiparty computation that focus on heterogeneous settings. We present solutions tailored to address different types of asymmetric constraints and improve the efficiency of existing approaches in these scenarios. We tackle the question from three main directions: New Computational Models for MPC - We explore different computational models that enable us to overcome inherent inefficiencies of generic MPC solutions using circuit representation for the evaluated functionality. First, we show how we can use random access machines to construct MPC protocols that add only polylogarithmic overhead to the running time of the insecure version of the underlying functionality. This allows to achieve MPC constructions with computational complexity sublinear in the size for their inputs, which is very important for computations that use large databases. We also consider multivariate polynomials which yield more succinct representations for the functionalities they implement than circuits, and at the same time a large collection of problems are naturally and efficiently expressed as multivariate polynomials. We construct an MPC protocol for multivariate polynomials, which improves the communication complexity of corresponding circuit solutions, and provides currently the most efficient solution for multiparty set intersection in the fully malicious case. Outsourcing Computation - The goal in this setting is to utilize the resources of a single powerful service provider for the work that computationally weak clients need to perform on their data. We present a new paradigm for constructing verifiable computation (VC) schemes, which enables a computationally limited client to verify efficiently the result of a large computation. Our construction is based on attribute-based encryption and avoids expensive primitives such as fully homomorphic encryption andprobabilistically checkable proofs underlying existing VC schemes. Additionally our solution enjoys two new useful properties: public delegation and verification. We further introduce the model of server-aided computation where we utilize the computational power of an outsourcing party to assist the execution and improve the efficiency of MPC protocols. For this purpose we define a new adversarial model of non-collusion, which provides room for more efficient constructions that rely almost completely only on symmetric key operations, and at the same time captures realistic settings for adversarial behavior. In this model we propose protocols for generic secure computation that offload the work of most of the parties to the computation server. We also construct a specialized server-aided two party set intersection protocol that achieves better efficiencies for the two participants than existing solutions. Outsourcing in many cases concerns only data storage and while outsourcing the data of a single party is useful, providing a way for data sharing among different clients of the service is the more interesting and useful setup. However, this scenario brings new challenges for access control since the access control rules and data accesses become private data for the clients with respect to the service provide. We propose an approach that offers trade-offs between the privacy provided for the clients and the communication overhead incurred for each data access. Efficient Private Search in Practice - We consider the question of private search from a different perspective compared to traditional settings for MPC. We start with strict efficiency requirements motivated by speeds of available hardware and what is considered acceptable overhead from practical point of view. Then we adopt relaxed definitions of privacy, which still provide meaningful security guarantees while allowing us to meet the efficiency requirements. In this setting we design a security architecture and implement a system for data sharing based on encrypted search, which achieves only 30% overhead compared to non-secure solutions on realistic workloads.
Secure multiparty computation (MPC\mathsf {MPC}MPC) addresses the challenge of evaluating functions on secret inputs without compromising their privacy. A central question in multiparty computation is to understand the amount of communication needed to securely evaluate a circuit of size s. In this work, we revisit this fundamental question in the setting of information-theoretically secure MPC\mathsf {MPC}MPC in the correlated randomness model, where a trusted dealer distributes correlated random coins, independent of the inputs, to all parties before the start of the protocol. This setting is of strong theoretical interest, and has led to the most practically efficient MPC\mathsf {MPC}MPC protocols known to date.
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.