Homomorphic Rank Sort Using Surrogate Polynomials

In this paper we propose a rank based algorithm for sorting encrypted data using monomials. Greedy Sort is a sorting technique that achieves to minimize the depth of the homomorphic evaluations. It is a costly algorithm due to excessive ciphertext multiplications and its implementation is cumbersome. Another method Direct Sort has a slightly deeper circuit than Greedy Sort, nevertheless it is simpler to implement and scales better with the size of the input array. Our proposed method minimizes both the circuit depth and the number of ciphertext multiplications. In addition to its performance, its simple design makes it more favorable compared to the alternative methods which are hard to parallelize, e.g. not suitable for fast GPU implementations. Furthermore, we improve the performance of homomorphic sorting algorithm by adapting the SIMD operations alongside message slot rotation techniques. This method allow us to pack $N$ integers into a single ciphertext and compute $N$ comparisons at once, thus reducing $\mathcal{O}(N^2)$ comparisons to $\mathcal{O}(N)$

On-the-fly Homomorphic Batching/Unbatching

We introduce a homomorphic batching technique that can be used to pack multiple ciphertext messages into one ciphertext for parallel processing. One is able to use the method to batch or unbatch messages homomorphically to further improve the flexibility of encrypted domain evaluations. In particular, we show various approaches to implement Number Theoretic Transform (NTT) homomorphically in FFT speed. Also, we present the limitations that we encounter in application of these methods. We implement homomorphic batching in various settings and present concrete performance figures. Finally, we present an implementation of a homomorphic NTT method which we process each element in an independent ciphertext. The advantage of this method is we are able to batch independent homomorphic NTT evaluations and achieve better amortized time

HOMOMORPHIC AUTOCOMPLETE

With the rapid progress in fully homomorpic encryption (FHE) and somewhat homomorphic encryption (SHE) schemes, we are wit- nessing renewed efforts to revisit privacy preserving protocols. Several works have already appeared in the literature that provide solutions to these problems by employing FHE or SHE techniques. These applications range from cloud computing to computation over confidential patient data to several machine learning problems such as classifying privatized data. One application where privacy is a major concern is web search – a task carried out on a daily basis by billions of users around the world. In this work, we focus on a more surmountable yet essential version of the search problem, i.e. autocomplete. By utilizing a SHE scheme we propose concrete solutions to a homomorphic autocomplete problem. To investigate the real-life viability, we tackle a number of problems in the way towards a practical implementation such as communication and computational efficiency

Blind Web Search: How far are we from a privacy preserving search engine?

Recent rapid progress in fully homomorphic encryption (FHE) and somewhat homomorphic encryption (SHE) has catalyzed renewed efforts to develop efficient privacy preserving protocols. Several works have already appeared in the literature that provide solutions to these problems by employing FHE or SHE techniques. In this work, we focus on a natural application where privacy is a major concern: web search. An estimated 5 billion web queries are processed by the world\u27s leading search engines each day. It is no surprise, then, that privacy-preserving web search was proposed as the paragon FHE application in Gentry\u27s seminal FHE paper. Indeed, numerous proposals have emerged in the intervening years that attack various privatized search problems over encrypted user data, e.g. private information retrieval (PIR). Yet, there is no known work that focuses on implementing a completely blind web search engine using an FHE/SHE construction. In this work, we focus first on single keyword queries with exact matches, aiming toward real-world viability. We then discuss multiple-keyword searches and tackle a number of issues currently hindering practical implementation, such as communication and computational efficiency

Homomorphic sorting with better scalability

Homomorphic sorting is an operation that blindly sorts a given set of encrypted numbers without decrypting them (thus, there is no need for the secret key). In this article, we propose a new, efficient, and scalable method for homomorphic sorting of numbers: polynomial rank sort algorithm. To put the new algorithm in a comparative perspective, we provide an extensive survey of classical sorting algorithms and networks that are not directly suitable for homomorphic computation. We also include, in our discussions, two of our previous algorithms specifically designed for homomorphic sorting operation: direct and greedy sort, and explain how they evolve from classical sorting networks. We theoretically show that the new algorithm is superior in terms of multiplicative depth when compared with all other algorithms. When batched implementation is used, the number of comparisons is reduced from $\mathcal {O}(N^2)$O(N2) to $\mathcal {O}(N)$O(N) provided that the number of slots is larger than or equal to the number of elements in the set. Our software implementation results confirm that the new algorithm is several orders of magnitude faster than many methods in the literature. Also, the polynomial sort algorithm scales better than the fastest algorithm in the literature to the best our knowledge although for small sets the execution times are comparable. The proposed algorithm is amenable to parallel implementation as most time consuming operations in the algorithm can naturally be performed concurrently

Private queries on encrypted genomic data

Abstract Background One of the tasks in the iDASH Secure Genome Analysis Competition in 2016 was to demonstrate the feasibility of privacy-preserving queries on homomorphically encrypted genomic data. More precisely, given a list of up to 100,000 mutations, the task was to encrypt the data using homomorphic encryption in a way that allows it to be stored securely in the cloud, and enables the data owner to query the dataset for the presence of specific mutations, without revealing any information about the dataset or the queries to the cloud. Methods We devise a novel string matching protocol to enable privacy-preserving queries on homomorphically encrypted data. Our protocol combines state-of-the-art techniques from homomorphic encryption and private set intersection protocols to minimize the computational and communication cost. Results We implemented our protocol using the homomorphic encryption library SEAL v2.1, and applied it to obtain an efficient solution to the iDASH competition task. For example, using 8 threads, our protocol achieves a running time of only 4 s, and a communication cost of 2 MB, when querying for the presence of 5 mutations from an encrypted dataset of 100,000 mutations. Conclusions We demonstrate that homomorphic encryption can be used to enable an efficient privacy-preserving mechanism for querying the presence of particular mutations in realistic size datasets. Beyond its applications to genomics, our protocol can just as well be applied to any kind of data, and is therefore of independent interest to the homomorphic encryption community

Next-generation liquefaction database

The Next-Generation Liquefaction database is a resource for the geotechnical hazard community. It is publicly available online under the following digital object identifier (DOI): 10.21222/C2J040. The database organizes objective liquefaction data into tables and fields (columns of information), with the relationships among the tables and fields described by a schema. The data are organized into tables pertaining to (1) sites, including geotechnical and geophysical site investigation data, surface geology information, and laboratory test data; (2) earthquake events, including source and ground motion information; and (3) observations of sites following events. The schema was vetted through community outreach efforts involving multiple workshops and meetings. Users can view the data, download existing data, and upload new data through a geographic information system (GIS)-based graphical user interface. Information uploaded to the database is reviewed by a database working group to verify consistency between uploaded data and source documents. The database is replicated in DesignSafe where users can interact with the data using Python scripts in Jupyter notebooks, view point cloud data using Potree, and interact with geospatial data using QGIS