Non-interactive secure multi-party arithmetic computations with confidentiality for P2P networks
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Non-interactive secure multi-party arithmetic computations with confidentiality for P2P networks Lein Harn 1 & Zhe Xia 2 & Chingfang Hsu 3 Received: 27 March 2020 / Accepted: 9 November 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract A fundamental feature of Peer-to-Peer (P2P) networks is the honest collaboration among a heterogeneous community of participants. Secure Multi-Party Computation (SMPC) finds ways for parties to jointly compute a function using their inputs, while keeping these inputs private. In this paper, we propose a secure three-party computation which takes three inputs and outputs their sum and product without revealing each individual input. Recall that any general function is composed of multiple additions and multiplications, our result serves as a solution for general SMPC. Our proposal is non-interactive and can be easily extended to SMPC with any number of inputs. Furthermore, in our proposed solution, the computational results can be made only available to a designated participant. Keywords Secure multi-party computation . Non-interaction . Confidentiality . Information-theoretical security
1 Introduction A fundamental feature of Peer-to-Peer (P2P) networks is the honest collaboration among a heterogeneous community of participants. Secure Multi-Party Computation (SMPC) finds ways for parties to jointly compute a function using their inputs, while keeping these inputs private. As demonstrated in the literature [1], SMPC protocol can be used in electronic voting, electronic auction, electronic cash, contract signing, etc. Wide-scale use of SMPC protocols has attracted great attentions in the past few years. For example, since 2015, SMPC has been used to evaluate gender pay disparities in
* Chingfang Hsu [email protected] Lein Harn [email protected] Zhe Xia [email protected] 1
Department of Computer Science Electrical Engineering, University of Missouri-Kansas City, Kansas City, MO 64110, USA
2
School of Computer Science, Wuhan University of Technology, Wuhan 430071, China
3
Computer School, Central China Normal University, Wuhan 430079, China
Boston, detect tax fraud in Estonia, and prevent satellite collisions [2]. SMPC protocols can be designed using various cryptographic building blocks, e.g. Shamir’s secret sharing scheme [3], homomorphic encryption [4], oblivious transfer [5] or using a Trusted Third Party [6]. Nowadays, a few SMPC implementations are available [7]. Some of them are designed for two-party environment only, while the others are more generic that transform programs into circuits or use oblivious transfer [8, 9]. Despite this progress, and some emerging real-world deployments, SMPC is not widespread in practice yet [1]. There remain several challenges to overcome before SMPC can be used in a wide range of privacy-preserving applications. One of the challenges is that most SMPC evaluations still incur several orders of magnitude cost penalty over non-SMPC executions. The exact overheads vary greatly and mostly depend on the
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