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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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Author information

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 .

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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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