# Private Outsourced Kriging Interpolation

## 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”.

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