Privacy-Preserving k-NN for Small and Large Data Sets

It is not surprising that there is strong interest in k- NN queries to enable clustering, classification and outlier- detection tasks. However, previous approaches to privacy-preserving k-NN are costly and can only be realistically applied to small data sets. We provide efficient solutions for k-NN queries queries for vertically partitioned data. We provide the first solution for the L_infin (or Chessboard) metric as well as detailed privacy-preserving computation of all other Minkowski metrics. We enable privacy-preserving L_infin by providing a solution to the Yao's Millionaire Problem with more than two parties. This is based on a new and practical solution to Yao's Millionaire with shares. We also provide privacy-preserving algorithms for combinations of local metrics into a global that handles the large dimensionality and diversity of attributes common in vertically partitioned data.