Abstract
The Wasserstein distance, also known in computer science as the Earth Mover’s Distance (EMD) is a distance metric between two probability distributions. EMD has often been used as a distance metric to compare images and documents, and is central to privacy models such as t-closeness. In this work, we show that, given one-dimensional discrete probability distributions, the computation of EMD can be reduced to the computation of the cardinality of the intersection of two sets. We then use a private matching scheme to create a privacy-preserving computation protocol for EMD: two parties can compute EMD between their privately-owned documents without revealing them to the other party. We demonstrate our proposal by implementing a privacy-preserving reverse image search, where images are kept encrypted at an external server.
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We acknowledge support from: European Commission (projects H2020-871042 “SoBigData++” and H2020-101006879 “MobiDataLab”), Government of Catalonia (ICREA Acadèmia Prize to the second author and grant 2017 SGR 705) and Spanish Government (project RTI2018-095094-B-C21). The authors are with the UNESCO Chair in Data Privacy, but their views here are not necessarily shared by UNESCO.
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Blanco-Justicia, A., Domingo-Ferrer, J. (2020). Privacy-Preserving Computation of the Earth Mover’s Distance. In: Susilo, W., Deng, R.H., Guo, F., Li, Y., Intan, R. (eds) Information Security. ISC 2020. Lecture Notes in Computer Science(), vol 12472. Springer, Cham. https://doi.org/10.1007/978-3-030-62974-8_23
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DOI: https://doi.org/10.1007/978-3-030-62974-8_23
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