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International Conference on Machine Learning and Cybernetics

Information-Theoretically Secure Number-Product Protocol

Chih-Hao Shen, Justin Z. Zhan, Dawei Wang, Tsan‐sheng Hsu, Churn‐Jung Liau

Published Jan 1, 2007• 15 citations
Publisher

Abstract

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.

DOI
10.1109/icmlc.2007.4370663

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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.
Abstract Secure multi-party computation(SMPC) is an important research area in cryptography with many application scenarios, but there are still many problems to be solved. Aiming at security and fairness issues in SMPC, we consider that semi-honest participants are able to execute the protocol according to the specification, but there would be some additional malicious operations such as collusion and refuse to exchange information in the process of information interaction, which leads to deviations in the security and fairness of the protocol. To solve the above problems, we combine information entropy and mutual information to propose an n-round information exchange protocol, in which each participant broadcasts a relevant information value in each round without revealing additional information. The uncertainty of the correct result value is fuzzed by the interactive information in each round, and each participant cannot determine the correct result value until the end of the protocol, which effectively prevents malicious behavior and ensures the correct execution of the protocol. Security analysis and fairness analysis show that under the semi-honest model, our protocol guarantees the security and relative fairness of the output obtained by the participants after completing the protocol.
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.
Secure scalar product protocol is an important fundamental protocol in secure multi-party computation. Serving as a basic building block for many other secure protocols, it is widely used in data mining, statistical analysis and scientific computation. Based on additive homomorphism public key cryptosystem, we develop a new secure scalar product protocol under semi-honest model with low communication complexity which is easy to implement and understanding. Furthermore, we firstly apply it to position relationship decision for privacy preserving space vectors.
Many deployments of secure multi-party computation (MPC) in practice have used information-theoretic three-party protocols that tolerate a single, semi-honest corrupt party, since these protocols enjoy very high efficiency. We propose a new approach for secure three-party computation (3PC) that improves security while maintaining practical efficiency that is competitive with traditional information-theoretic protocols. Our protocol is based on garbled circuits and provides security against a single, malicious corrupt party. Unlike information-theoretic 3PC protocols, ours uses a constant number of rounds. Our protocol only uses inexpensive symmetric-key cryptography: hash functions, block ciphers, pseudorandom generators (in particular, no oblivious transfers) and has performance that is comparable to that of Yao's (semi-honest) 2PC protocol.
As far as we know, the literature on secure computation from cut-and-choose has focused on achieving computational security against malicious adversaries. It is unclear whether the idea of cut-and-choose can be adapted to secure computation with information-theoretic security. In this work we explore the possibility of using cut-and-choose in information theoretic setting for secure three-party computation (3PC). Previous work on 3PC has mainly focus on the semi-honest case, and is motivated by the observation that real-word deployments of multi-party computation (MPC) seem to involve few parties. We propose a new protocol for information-theoretically secure 3PC tolerating one malicious party with cheating probability 2−s2^{-s}2−s using sss runs of circuit computation in the cut-and-choose paradigm. The computational cost of our protocol is essentially only a small constant worse than that of state-of-the-art 3PC protocols against a semi-honest corruption, while its communication round is greatly reduced compared to other maliciously secure 3PC protocols in information-theoretic setting.
In the setting of secure multiparty computation, a set of parties with private inputs wish to compute some function of their inputs without revealing anything but their output. Over the last decade, the efficiency of secure two-party computation has advanced in leaps and bounds, with speedups of some orders of magnitude, making it fast enough to be of use in practice. In contrast, progress on the case of multiparty computation (with more than two parties) has been much slower, with very little work being done. Currently, the only implemented efficient multiparty protocol has many rounds of communication (linear in the depth of the circuit being computed) and thus is not suited for Internet-like settings where latency is not very low. In this paper, we construct highly efficient constant-round protocols for the setting of multiparty computation for semi-honest adversaries. Our protocols work by constructing a multiparty garbled circuit, as proposed in BMR (Beaver et al., STOC 1990). Our first protocol uses oblivious transfer and constitutes the first concretely-efficient constant-round multiparty protocol for the case of no honest majority. Our second protocol uses BGW, and is significantly more efficient than the FairplayMP protocol (Ben-David et al., CCS 2008) that also uses BGW.