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Improved Building Blocks for Secure Multi-party Computation Based on Secret Sharing with Honest Majority

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Applied Cryptography and Network Security (ACNS 2020)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12146))

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Abstract

Secure multi-party computation permits evaluation of any desired functionality on private data without disclosing the data to the participants. It is gaining its popularity due to increasing collection of user, customer, or patient data and the need to analyze data sets distributed across different organizations without disclosing them. Because adoption of secure computation techniques depends on their performance in practice, it is important to continue improving their performance. In this work, we focus on common non-trivial operations used by many types of programs, where any advances in their performance would impact the runtime of programs that rely on them. In particular, we treat the operation of reading or writing an element of an array at a private location and integer multiplication. The focus of this work is on secret sharing setting with honest majority in the semi-honest security model. We demonstrate improvement of the proposed techniques over prior constructions via analytical and empirical evaluation.

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Notes

  1. 1.

    Because the original \(\mathsf{EQZ}\) in [7] was designed for signed k-bit integers, it also specified to add \(2^{k-1}\) to the value being opened, to move the input into the positive range. In our application, we use only non-negative values and let the entire k-bit space be occupied by them. For that reason, one should omit adding \(2^{k-1}\).

  2. 2.

    This information is not explicitly provided in [24], but rather is deduced by us.

  3. 3.

    Note that it is very easy to generate a fixed representation of [1] by choosing any degree-t polynomial that evaluates to 1 at 0, e.g., by setting all of its coefficients to 1. Each party computes \([1]_p\) using that polynomial and uses it in all calls to \(\mathsf{DRand()}\).

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Acknowledgments

This work was supported in part by grant CNS-1705262 from the National Science Foundation, Google Faculty Research Award, and grant 2018R1A6A3A01011337 from the National Research Foundation of Korea. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the funding agencies. We also acknowledge the NSF-sponsored Global Environment for Network Innovations (GENI) test bed, which allowed us to run WAN experiments.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, University at Buffalo (SUNY), Buffalo, USA

    Marina Blanton & Chen Yuan

  2. SCH Media Labs, Soonchunhyang University, Asan-si, South Korea

    Ahreum Kang

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  1. Marina Blanton
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  2. Ahreum Kang
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  3. Chen Yuan
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Correspondence to Chen Yuan .

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Editors and Affiliations

  1. Department of Mathematics, University of Padua, Padua, Italy

    Mauro Conti

  2. Singapore University of Technology and Design, Singapore, Singapore

    Jianying Zhou

  3. Dipt di Informatica Sistemi e Produ, Università di Roma “Tor Vergata”, Rome, Roma, Italy

    Emiliano Casalicchio

  4. Sapienza University of Rome, Rome, Italy

    Angelo Spognardi

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Blanton, M., Kang, A., Yuan, C. (2020). Improved Building Blocks for Secure Multi-party Computation Based on Secret Sharing with Honest Majority. In: Conti, M., Zhou, J., Casalicchio, E., Spognardi, A. (eds) Applied Cryptography and Network Security. ACNS 2020. Lecture Notes in Computer Science(), vol 12146. Springer, Cham. https://doi.org/10.1007/978-3-030-57808-4_19

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  • DOI: https://doi.org/10.1007/978-3-030-57808-4_19

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