Secure and efficient approximate nearest neighbors search

International audienceThis paper presents a moderately secure but very efficient approximate nearest neighbors search. After detailing the threats pertaining to the "honest but curious" model, our approach starts from a state-of-the-art algorithm in the domain of approximate nearest neighbors search. We gradually develop mechanisms partially blocking the attacks threatening the original algorithm. The loss of performances compared to the original algorithm is mainly an overhead of a constant computation time and communication payload which are independent of the size of the database

SANNS: Scaling Up Secure Approximate k-Nearest Neighbors Search

The $k$-Nearest Neighbor Search ($k$-NNS) is the backbone of several cloud-based services such as recommender systems, face recognition, and database search on text and images. In these services, the client sends the query to the cloud server and receives the response in which case the query and response are revealed to the service provider. Such data disclosures are unacceptable in several scenarios due to the sensitivity of data and/or privacy laws. In this paper, we introduce SANNS, a system for secure $k$-NNS that keeps client's query and the search result confidential. SANNS comprises two protocols: an optimized linear scan and a protocol based on a novel sublinear time clustering-based algorithm. We prove the security of both protocols in the standard semi-honest model. The protocols are built upon several state-of-the-art cryptographic primitives such as lattice-based additively homomorphic encryption, distributed oblivious RAM, and garbled circuits. We provide several contributions to each of these primitives which are applicable to other secure computation tasks. Both of our protocols rely on a new circuit for the approximate top-$k$ selection from $n$ numbers that is built from $O(n + k^2)$ comparators. We have implemented our proposed system and performed extensive experimental results on four datasets in two different computation environments, demonstrating more than $18-31\times$ faster response time compared to optimally implemented protocols from the prior work. Moreover, SANNS is the first work that scales to the database of 10 million entries, pushing the limit by more than two orders of magnitude.Comment: 18 pages, to appear at USENIX Security Symposium 202

Secure kk-ish Nearest Neighbors Classifier

In machine learning, classifiers are used to predict a class of a given query based on an existing (classified) database. Given a database S of n d-dimensional points and a d-dimensional query q, the k-nearest neighbors (kNN) classifier assigns q with the majority class of its k nearest neighbors in S. In the secure version of kNN, S and q are owned by two different parties that do not want to share their data. Unfortunately, all known solutions for secure kNN either require a large communication complexity between the parties, or are very inefficient to run. In this work we present a classifier based on kNN, that can be implemented efficiently with homomorphic encryption (HE). The efficiency of our classifier comes from a relaxation we make on kNN, where we allow it to consider kappa nearest neighbors for kappa ~ k with some probability. We therefore call our classifier k-ish Nearest Neighbors (k-ish NN). The success probability of our solution depends on the distribution of the distances from q to S and increase as its statistical distance to Gaussian decrease. To implement our classifier we introduce the concept of double-blinded coin-toss. In a doubly-blinded coin-toss the success probability as well as the output of the toss are encrypted. We use this coin-toss to efficiently approximate the average and variance of the distances from q to S. We believe these two techniques may be of independent interest. When implemented with HE, the k-ish NN has a circuit depth that is independent of n, therefore making it scalable. We also implemented our classifier in an open source library based on HELib and tested it on a breast tumor database. The accuracy of our classifier (F_1 score) were 98\% and classification took less than 3 hours compared to (estimated) weeks in current HE implementations

Exploring Privacy Preservation in Outsourced K-Nearest Neighbors with Multiple Data Owners

The k-nearest neighbors (k-NN) algorithm is a popular and effective classification algorithm. Due to its large storage and computational requirements, it is suitable for cloud outsourcing. However, k-NN is often run on sensitive data such as medical records, user images, or personal information. It is important to protect the privacy of data in an outsourced k-NN system. Prior works have all assumed the data owners (who submit data to the outsourced k-NN system) are a single trusted party. However, we observe that in many practical scenarios, there may be multiple mutually distrusting data owners. In this work, we present the first framing and exploration of privacy preservation in an outsourced k-NN system with multiple data owners. We consider the various threat models introduced by this modification. We discover that under a particularly practical threat model that covers numerous scenarios, there exists a set of adaptive attacks that breach the data privacy of any exact k-NN system. The vulnerability is a result of the mathematical properties of k-NN and its output. Thus, we propose a privacy-preserving alternative system supporting kernel density estimation using a Gaussian kernel, a classification algorithm from the same family as k-NN. In many applications, this similar algorithm serves as a good substitute for k-NN. We additionally investigate solutions for other threat models, often through extensions on prior single data owner systems

Lower Bounds for Oblivious Near-Neighbor Search

We prove an $\Omega(d \lg n/ (\lg\lg n)^2)$ lower bound on the dynamic cell-probe complexity of statistically $\mathit{oblivious}$ approximate-near-neighbor search ($\mathsf{ANN}$) over the $d$-dimensional Hamming cube. For the natural setting of $d = \Theta(\log n)$, our result implies an $\tilde{\Omega}(\lg^2 n)$ lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for $\mathsf{ANN}$. This is the first super-logarithmic $\mathit{unconditional}$ lower bound for $\mathsf{ANN}$ against general (non black-box) data structures. We also show that any oblivious $\mathit{static}$ data structure for decomposable search problems (like $\mathsf{ANN}$) can be obliviously dynamized with $O(\log n)$ overhead in update and query time, strengthening a classic result of Bentley and Saxe (Algorithmica, 1980).Comment: 28 page