After the first plausible fully homomorphic encryption (FHE) scheme designed by Gentry, interests of a building a practical scheme in FHE has kept increasing. This paper presents an engineering study of accelerating the FHE with BGV scheme and proves the feasibility of implement certain parts of HElib on GPU. The BGV scheme is a RLWE-based FHE scheme, which introduces a set of algorithms in polynomial arithmetic. The encryption scheme is implemented in finite field. Therefore, acceleration of the large polynomial arithmetic with efficient modular reduction is the most crucial part of our research efforts. Note that our implementation does not include the noise management yet. Hence all the work is still in the stage of somewhat homomorphic encryption, namely SWHE. Finally, our implementation of the encryption procedure, when comparing with HElib compiled by 9.3.0 version NTL library on Xeon CPU, has achieved 3.4x speedup on the platform with GTX 780ti GPU.

" In the last decade, cloud computing became popular among companies for outsourcing some of their services. Companies use cloud services to store crucial information such as financial and client data. Cloud services are not only cost effective but also easier to manage since the companies avoid maintenance of servers. Although cloud has its advantages, maintaining the security is a big concern. Cloud services might not have any malicious intent, but attacks targeting cloud systems could easily steal vital data belong to the companies. The only protection that assures the security of the information is a strong encryption. However, these schemes only protects the information but prevent you to do any computation on the data. This was an open problem for more than 30 years and it has been solved recently by the introduction of the first fully homomorphic encryption (FHE) scheme by Gentry. The FHE schemes allow you to do arbitrary computation on an encrypted data by still preserving the encryption. Namely, the message is not revealed (decrypted) at any given time while computing the arbitrary circuit. However, the first FHE scheme is not practical for any practical application. Later, numerous research work has been published aiming at making fully homomorphic encryption practical for daily use, but still they were too inefficient to be used in everyday practical applications. In this dissertation we tackle the efficiency problems of fully homomorphic encryption (FHE) schemes. We propose two new FHE schemes that improve the storage requirement and runtime performance. The first scheme (Doröz, Hu and Sunar) reduces the size of the evaluation keys in existing NTRU based FHE schemes. In the second scheme (F-NTRU) we designed an NTRU based FHE scheme which is not only free of costly evaluation keys but also competitive in runtime performance. We further proposed two hardware accelerators to increase the performance of arithmetic operations underlying the schemes. The first accelerator is a custom hardware architecture for realizing the Gentry-Halevi fully homomorphic encryption scheme. This contribution presents the first full realization of FHE in hardware. The architecture features an optimized multi-million bit multiplier based on the Schönhage-Strassen multiplication algorithm. Moreover, a number of optimizations including spectral techniques as well as a precomputation strategy is used to significantly improve the performance of the overall design. The other accelerator is optimized for a class of reconfigurable logic for somewhat homomorphic encryption (SWHE) based schemes. Our design works as a co-processor: the most compute-heavy operations are offloaded to this specialized hardware. The core of our design is an efficient polynomial multiplier as it is the most compute-heavy operation of our target scheme. The presented architecture can compute the product of very-large polynomials more efficiently than software implementations on CPUs. Finally, to assess the performance of proposed schemes and hardware accelerators we homomorphically evaluate the AES and the Prince block ciphers. We introduce various optimizations including a storage-runtime trade-off. Our benchmarking results show significant speedups over other existing instantiations. Also, we present a private information retrieval (PIR) scheme based on a modified version of Doröz, Hu and Sunar’s homomorphic scheme. The scheme is capable of privately retrieving data from a database containing 4 billion entries. We achieve asymptotically lower bandwidth cost compared to other PIR schemes which makes it more practical. "

Notre approche dans cette thèse était d'identifier où le chiffrement complètement homomorphe (FHE) pouvait être utilisé pour le domaine des sciences informatiques et de construire une plate-forme expérimentale qui nous permette de tester des algorithmes de traitement de l'information manipulant des données chiffrées. La première partie de cette thèse est consacrée à l'état de l'art. Nous présentons d'abord les systèmes de chiffrement homomorphes conçus avant 2008, puis nous présentons ceux adressant la problématique du chiffrement complètement homomorphe. Nous décrivons plusieurs méthodes de chiffrement d'intérêt pour cette thèse et discutons de leurs implémentations FHE. Enfin, nous présentons des circuits de Yao car ils peuvent résoudre des problèmes similaires que le FHE et nous parlons brièvement du chiffrement fonctionnel (FE). La deuxième partie de cette thèse présente nos contributions. Nous commençons par expliquer comment le FHE peut être utile dans divers scénarios et décrivons plusieurs cas d'utilisation pratique identifiés au cours de la thèse. Ensuite, nous décrivons notre approche pour effectuer des calculs sur des données chiffrées à l'aide du FHE et expliquons comment nous avons pu développer une plate-forme pour l'exécution dans le domaine chiffré d'une large gamme d'algorithmes en s'appuyant seulement sur l'addition et la multiplication homomorphes. Nous détaillons ensuite notre solution pour effectuer des requêtes privées sur une base de données chiffrées en utilisant le chiffrement homomorphe. Dans un dernier chapitre, nous présentons nos résultats expérimentaux. / Our approach in this thesis was to identify where FHE could be used in computer science and to build an experimental platform that allow us to test real-life algorithm running on homomorphically-encrypted data. The first part of this thesis is dedicated to the state of the art. We first present homomorphic encryption schemes designed before 2008 and then move to the Fully Homomorphic Encryption period. We describe several schemes of interest for this thesis and discuss FHE implementations. Finally, we present Yao’s garbled circuits as they can solve similar problems as FHE and briefly talk about Functional Encryption (FE). The second part of this thesis is for our contributions to the subject. We begin by explaining how FHE can be useful in various scenarios and try to provide practical use cases that we identified during the thesis. Then, we describe our approach to perform computations on encrypted data using FHE and explain how we were able to build on just the homomorphic addition and multiplication a platform for the execution in the encrypted domain of a wide range of algorithms. We then detail our solution for performing private queries on an encrypted database using homomorphic encryption. In a final chapter, we present our experimental results.

abstract: Lattice-based Cryptography is an up and coming field of cryptography that utilizes the difficulty of lattice problems to design lattice-based cryptosystems that are resistant to quantum attacks and applicable to Fully Homomorphic Encryption schemes (FHE). In this thesis, the parallelization of the Residue Number System (RNS) and algorithmic efficiency of the Number Theoretic Transform (NTT) are combined to tackle the most significant bottleneck of polynomial ring multiplication with the hardware design of an optimized RNS-based NTT polynomial multiplier. The design utilizes Negative Wrapped Convolution, the NTT, RNS Montgomery reduction with Bajard and Shenoy extensions, and optimized modular 32-bit channel arithmetic for nine RNS channels to accomplish an RNS polynomial multiplication. In addition to a full software implementation of the whole system, a pipelined and optimized RNS-based NTT unit with 4 RNS butterflies is implemented on the Xilinx Artix-7 FPGA(xc7a200tlffg1156-2L) for size and delay estimates. The hardware implementation achieves an operating frequency of 47.043 MHz and utilizes 13239 LUT's, 4010 FF's, and 330 DSP blocks, allowing for multiple simultaneously operating NTT units depending on FGPA size constraints. / Dissertation/Thesis / Masters Thesis Electrical Engineering 2020

The main aim of this thesis is to develop a library for integrating fully homomorphic encryption-based computations on a standard database. The fully homomorphic encryption is an encryption scheme that allows functions to be performed directly on encrypted data without the requirement of decrypting the data and yields the same results as if the functions were run on the plaintext. This implementation is a promising solution for preserving the privacy of the health care system, where millions of patients’ data are stored. The personal health care tools gather medical data and store it in a database. Upon importing this library into the database, the data that is being entered into the database is encrypted and the computations can be performed on the encrypted data without decrypting.

Everyone is in need for their own privacy and data protection, since encryption transmission was becoming common. Fully Homomorphic Encryption (FHE) has received increased attention because of its capability to execute calculations over the encoded domain. Through using FHE approach, model training can be properly outsourced. The goal of FHE is to enable computations on encrypted files without decoding aside from the end outcome. The CKKS scheme is used in FHE.Network threats are serious danger to credential information, which enable an unauthorised user to extract important and sensitive data by evaluating the information of computations done on raw data. Thus the study provided an efficient solution to the problem of privacy protection in data-driven applications using Machine Learning. The study used an encrypted NSL KDD dataset. Machine learning-based techniques have emerged as a significant trend for detecting malicious attack. Thus, Random Forest (RF) is proposed for the detection of malicious attacks on Homomorphic encrypted data in the cloud server. Logistic Regression (LR) machine learning model is used to predict encrypted data on cloud server. Regardless of the distributed setting, the technique may retain the accuracy and integrity of the previous methods to obtain the final results.

The purpose of this study was to describe and explore three phenomenon of the L.D.S. Family Home Evening Program: (1) the nature of religious commitment in an L.D.S. sample, (2) the degree of participation, (3) the relation of certain religious and secular variables.The data for the study were made available to the researcher by A. L. Mauss, as part of a larger study designed to measure the impact of Urbanism upon Mormonism. The instrument, modeled after the Glock and Stark studies, was adapted to a random sample of 958 members of the L.D.S. Church in Utah.The nature of religious commitment was found to be multi-dimensional. Normative participation in the program was low when compared with similar Church programs. None of the variables showed a high correlation with participation.It was concluded that the Church has not yet succeeded in designing the Program to meet the needs of most Church members, and that some weightier factors must account for participation and/or non-participation in the Program than those tested.