[Resource Topic] 2020/319: Secure k-ish nearest neighbors classifier

Welcome to the resource topic for 2020/319

Secure k-ish nearest neighbors classifier

Authors: Hayim Shaul, Dan Feldman, Daniela Rus


The k-nearest neighbors ($k$NN) classifier predicts a class of a query, q, by taking the majority class of its k neighbors in an existing (already classified) database, S. In secure $k$NN, q and S are owned by two different parties and q is classified without sharing data. In this work we present a classifier based on $k$NN, that is more efficient to implement with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make to consider \kappa nearest neighbors for \kappa\approx k with probability that increases as the statistical distance between Gaussian and the distribution of the distances from q to S decreases. We call our classifier k-ish Nearest Neighbors (k-ish NN). For the implementation we introduce {\em double-blinded coin-toss} where the bias and output of the toss are encrypted. We use it to approximate the average and variance of the distances from q to S in a scalable circuit whose depth is independent of |S|. We believe these to be of independent interest. We implemented our classifier in an open source library based on HElib and tested it on a breast tumor database. Our classifier has accuracy and running time comparable to current state of the art (non-HE) MPC solution that have better running time but worse communication complexity. It also has communication complexity similar to naive HE implementation that have worse running time.

ePrint: https://eprint.iacr.org/2020/319

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