Range searching is the problem of preprocessing a set of points P, such that given a query range gamma we can efficiently compute some function f(P cap gamma). For example, in a 1 dimensional range counting query, P is a set of numbers, gamma is a segment and we need to count how many numbers of P are in gamma. In higher dimensions, P is a set of d dimensional points and the query range is some volume in R^d. In general, we want to compute more than just counting, for example, the average of P cap gamma. Range searching has applications in databases where some SELECT queries can be translated to range queries. It had received a lot of attention in computational geometry where a data structure called partition tree was shown to solve range queries in time sub-linear in |P| using space only linear in |P|. In this paper we consider partition trees under FHE where we answer range queries without learning the value of the points or the parameters of the range. We show how partition trees can be securely traversed with O(t n^{1-1/d+epsilon} + n^{1+epsilon}) operations, where n=|P|, t is the number of operations needed to compare to gamma and epsilon>0 is a parameter. When the ranges are axis-parallel hyper-boxes the running time is O(t n^epsilon + n log^{d-1} n). As far as we know, this is the first non-trivial bound on range searching under FHE and it improves over the naive solution that needs O(t n) operations. Our algorithms are independent of the encryption scheme but as an example we implemented them using the CKKS FHE scheme. Our experiments show that for databases of sizes 2^{23} and 2^{25}, our algorithms run x2.8 and x4.7 (respectively) faster than the naive algorithm. The improvement of our algorithm comes from a method we call copy-and-recurse. With it we efficiently traverse a r-ary tree (where each inner node has r children) that also has the property that at most xi of them need to be recursed into when traversing the tree. We believe this method is interesting in its own and can be used to improve traversals in other tree-like structures.

Privacy-preserving solutions enable companies to offload confidential data to third-party services while fulfilling their government regulations. To accomplish this, they leverage various cryptographic techniques such as Homomorphic Encryption (HE), which allows performing computation on encrypted data. Most HE schemes work in a SIMD fashion, and the data packing method can dramatically affect the running time and memory costs. Finding a packing method that leads to an optimal performant implementation is a hard task. We present a simple and intuitive framework that abstracts the packing decision for the user. We explain its underlying data structures and optimizer, and propose a novel algorithm for performing 2D convolution operations. We used this framework to implement an inference operation over an encrypted HE-friendly AlexNet neural network with large inputs, which runs in around five minutes, several orders of magnitude faster than other state-of-the-art non-interactive HE solutions.

Yonatan Bilu, Ariel Gera, Daniel Hershcovich, Benjamin Sznajder, Dan Lahav, Guy Moshkowich, Anael Malet, Assaf Gavron, Noam Slonim. Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics. 2019.

Machines capable of responding and interacting with humans in helpful ways have become ubiquitous.We now expect them to discuss with us the more delicate questions in our world, and they should do so armed with effective arguments.But what makes an argument more persuasive?What will convince you?In this paper, we present a new data set, IBM-EviConv, of pairs of evidence labeled for convincingness, designed to be more challenging than existing alternatives.We also propose a Siamese neural network architecture shown to outperform several baselines on both a prior convincingness data set and our own.Finally, we provide insights into our experimental results and the various kinds of argumentative value our method is capable of detecting.

Shachar Mirkin, Guy Moshkowich, Matan Orbach, Lili Kotlerman, Yoav Kantor, Tamar Lavee, Michal Jacovi, Yonatan Bilu, Ranit Aharonov, Noam Slonim. Proceedings of the 2018 Conference on Empirical Methods in Natural Language Processing. 2018.