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Secure and Efficient Matrix Multiplication with MapReduce

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E-Business and Telecommunications (ICETE 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1247))

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Abstract

MapReduce is one of the most popular distributed programming paradigms that allows processing big data sets in parallel on a cluster. MapReduce users often outsource data and computations to a public cloud, which yields inherent security concerns. In this paper, we consider the problem of matrix multiplication and one of the most efficient matrix multiplication algorithms: the Strassen-Winograd (\(\text {SW} \)) algorithm. Our first contribution is a distributed MapReduce algorithm based on \(\text {SW} \). Then, we tackle the security concerns that occur when outsourcing matrix multiplication computation to a honest-but-curious cloud i.e., that executes tasks dutifully, but tries to learn as much information as possible. Our main contribution is a secure distributed MapReduce algorithm called \(\mathrm {S2M3} \) (Secure Strassen-Winograd Matrix Multiplication with MapReduce) that enjoys security guarantees such as: none of the cloud nodes can learn the input or the output data. We formally prove the security properties of \(\mathrm {S2M3} \) and we present an empirical evaluation devoted to show its efficiency.

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Notes

  1. 1.

    https://github.com/actuallyachraf/gomorph.

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Authors and Affiliations

  1. INSA Centre Val de Loire, Univ. Orléans, LIFO, EA 4022, Bourges, France

    Radu Ciucanu

  2. Université Clermont Auvergne, LIMOS CNRS UMR 6158, Aubière, France

    Matthieu Giraud & Pascal Lafourcade

  3. Harbin Institute of Technology, Harbin, China

    Lihua Ye

Authors
  1. Radu Ciucanu
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  2. Matthieu Giraud
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  3. Pascal Lafourcade
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  4. Lihua Ye
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Corresponding author

Correspondence to Radu Ciucanu .

Editor information

Editors and Affiliations

  1. Fellow of IEEE, Dean of College of Computing & Informatics, University of Sharjah, Sharjah, United Arab Emirates

    Mohammad S. Obaidat

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Ciucanu, R., Giraud, M., Lafourcade, P., Ye, L. (2020). Secure and Efficient Matrix Multiplication with MapReduce. In: Obaidat, M. (eds) E-Business and Telecommunications. ICETE 2019. Communications in Computer and Information Science, vol 1247. Springer, Cham. https://doi.org/10.1007/978-3-030-52686-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-52686-3_6

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  • Online ISBN: 978-3-030-52686-3

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