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Private Outsourced Kriging Interpolation

  • James Alderman
  • Benjamin R. CurtisEmail author
  • Oriol Farràs
  • Keith M. Martin
  • Jordi Ribes-González
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10323)

Abstract

Kriging is a spatial interpolation algorithm which provides the best unbiased linear prediction of an observed phenomena by taking a weighted average of samples within a neighbourhood. It is widely used in areas such as geo-statistics where, for example, it may be used to predict the quality of mineral deposits in a location based on previous sample measurements. Kriging has been identified as a good candidate process to be outsourced to a cloud service provider, though outsourcing presents an issue since measurements and predictions may be highly sensitive. We present a method for the private outsourcing of Kriging interpolation using a tailored modification of the Kriging algorithm in combination with homomorphic encryption, allowing crucial information relating to measurement values to be hidden from the cloud service provider.

Notes

Acknowledgements

Oriol Farràs and Jordi Ribes-González were supported by the European Comission through H2020-ICT-2014-1-644024 “CLARUS” and H2020-DS-2015-1-700540 “CANVAS”, by the Government of Spain through TIN2014-57364-C2-1-R “SmartGlacis” and TIN2016-80250-R “Sec-MCloud”, by the Government of Catalonia through Grant 2014 SGR 537, and by COST Action IC1306. James Alderman was supported by the European Comission through H2020-ICT-2014-1-644024 “CLARUS”. Benjamin R. Curtis was supported by the UK EPSRC through EP/K035584/1 “Centre for Doctoral Training in Cyber Security at Royal Holloway”.

References

  1. 1.
    CLARUS: User centered privacy and security in the cloud. http://clarussecure.eu. Accessed 11 Dec 2016
  2. 2.
    InGeoCloudS: inspired geo-data cloud services. https://www.ingeoclouds.eu/. Accessed 11 Dec 2016
  3. 3.
    python-paillier: a library for partially homomorphic encryption in python, Data61\(|\)CSIRO. https://github.com/NICTA/python-paillier. Accessed 11 Dec 2016
  4. 4.
    SEAL: Simple encrypted arithmetic library, cryptography research group, microsoft research. http://sealcrypto.codeplex.com/. Accessed 11 Dec 2016
  5. 5.
    Burrough, P.A., McDonnell, R., McDonnell, R.A., Lloyd, C.D.: Principles of Geographical Information Systems. Oxford University Press, Oxford (2015)Google Scholar
  6. 6.
    Chilès, J.-P., Delfiner, P.: Multivariate methods. In: Geostatistics: Modeling Spatial Uncertainty, Second Edn., pp. 299–385 (1999)Google Scholar
  7. 7.
    Cressie, N.: Statistics for spatial data. Terra Nova 4(5), 613–617 (1992)CrossRefGoogle Scholar
  8. 8.
    EU Parliament: Directive 2007/2/EC of the European Parliament and of the Council of 14 establishing an infrastructure for spatial information in the European Community (INSPIRE). Off. J. Eur. Union 50(L108) (2007)Google Scholar
  9. 9.
    Krige, D.: A statistical approach to some basic mine valuation problems on the Witwatersrand. J. South Afr. Inst. Min. Metall. 52(6), 119–139 (1951)Google Scholar
  10. 10.
    Matheron, G.: Traité de géostatistique appliquée. Mémoires du Bureau de Recherches Géologiques et Minières. Éditions Technip (1962–1963)Google Scholar
  11. 11.
    Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999).  https://doi.org/10.1007/3-540-48910-X_16 Google Scholar
  12. 12.
    Tugrul, B., Polat, H.: Estimating kriging-based predictions with privacy. Int. J. Innov. Comput. Inf. Control (2013, accepted for publication)Google Scholar
  13. 13.
    Tugrul, B., Polat, H.: Privacy-preserving kriging interpolation on partitioned data. Knowl.-Based Syst. 62, 38–46 (2014)CrossRefGoogle Scholar
  14. 14.
    Wackernagel, H.: Multivariate Geostatistics: An Introduction with Applications. Springer Science & Business Media, Berlin (2013)zbMATHGoogle Scholar

Copyright information

© International Financial Cryptography Association 2017

Authors and Affiliations

  • James Alderman
    • 1
  • Benjamin R. Curtis
    • 1
    Email author
  • Oriol Farràs
    • 2
  • Keith M. Martin
    • 1
  • Jordi Ribes-González
    • 2
  1. 1.Information Security Group, Royal HollowayUniversity of LondonLondonUK
  2. 2.Universitat Rovira i VirgiliTarragonaSpain

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