A Survey on Homomorphic Encryption Schemes: Theory and Implementation

Legacy encryption systems depend on sharing a key (public or private) among the peers involved in exchanging an encrypted message. However, this approach poses privacy concerns. Especially with popular cloud services, the control over the privacy of the sensitive data is lost. Even when the keys are not shared, the encrypted material is shared with a third party that does not necessarily need to access the content. Moreover, untrusted servers, providers, and cloud operators can keep identifying elements of users long after users end the relationship with the services. Indeed, Homomorphic Encryption (HE), a special kind of encryption scheme, can address these concerns as it allows any third party to operate on the encrypted data without decrypting it in advance. Although this extremely useful feature of the HE scheme has been known for over 30 years, the first plausible and achievable Fully Homomorphic Encryption (FHE) scheme, which allows any computable function to perform on the encrypted data, was introduced by Craig Gentry in 2009. Even though this was a major achievement, different implementations so far demonstrated that FHE still needs to be improved significantly to be practical on every platform. First, we present the basics of HE and the details of the well-known Partially Homomorphic Encryption (PHE) and Somewhat Homomorphic Encryption (SWHE), which are important pillars of achieving FHE. Then, the main FHE families, which have become the base for the other follow-up FHE schemes are presented. Furthermore, the implementations and recent improvements in Gentry-type FHE schemes are also surveyed. Finally, further research directions are discussed. This survey is intended to give a clear knowledge and foundation to researchers and practitioners interested in knowing, applying, as well as extending the state of the art HE, PHE, SWHE, and FHE systems.Comment: - Updated. (October 6, 2017) - This paper is an early draft of the survey that is being submitted to ACM CSUR and has been uploaded to arXiv for feedback from stakeholder

Private Outsourcing of Polynomial Evaluation and Matrix Multiplication using Multilinear Maps

{\em Verifiable computation} (VC) allows a computationally weak client to outsource the evaluation of a function on many inputs to a powerful but untrusted server. The client invests a large amount of off-line computation and gives an encoding of its function to the server. The server returns both an evaluation of the function on the client's input and a proof such that the client can verify the evaluation using substantially less effort than doing the evaluation on its own. We consider how to privately outsource computations using {\em privacy preserving} VC schemes whose executions reveal no information on the client's input or function to the server. We construct VC schemes with {\em input privacy} for univariate polynomial evaluation and matrix multiplication and then extend them such that the {\em function privacy} is also achieved. Our tool is the recently developed {mutilinear maps}. The proposed VC schemes can be used in outsourcing {private information retrieval (PIR)}.Comment: 23 pages, A preliminary version appears in the 12th International Conference on Cryptology and Network Security (CANS 2013

Survey on securing data storage in the cloud

Cloud Computing has become a well-known primitive nowadays; many researchers and companies are embracing this fascinating technology with feverish haste. In the meantime, security and privacy challenges are brought forward while the number of cloud storage user increases expeditiously. In this work, we conduct an in-depth survey on recent research activities of cloud storage security in association with cloud computing. After an overview of the cloud storage system and its security problem, we focus on the key security requirement triad, i.e., data integrity, data confidentiality, and availability. For each of the three security objectives, we discuss the new unique challenges faced by the cloud storage services, summarize key issues discussed in the current literature, examine, and compare the existing and emerging approaches proposed to meet those new challenges, and point out possible extensions and futuristic research opportunities. The goal of our paper is to provide a state-of-the-art knowledge to new researchers who would like to join this exciting new field

A survey of state-of-the-art methods for securing medical databases

This review article presents a survey of recent work devoted to advanced state-of-the-art methods for securing of medical databases. We concentrate on three main directions, which have received attention recently: attribute-based encryption for enabling secure access to confidential medical databases distributed among several data centers; homomorphic encryption for providing answers to confidential queries in a secure manner; and privacy-preserving data mining used to analyze data stored in medical databases for verifying hypotheses and discovering trends. Only the most recent and significant work has been included

Efficient Computation and FPGA implementation of Fully Homomorphic Encryption with Cloud Computing Significance

Homomorphic Encryption provides unique security solution for cloud computing. It ensures not only that data in cloud have confidentiality but also that data processing by cloud server does not compromise data privacy. The Fully Homomorphic Encryption (FHE) scheme proposed by Lopez-Alt, Tromer, and Vaikuntanathan (LTV), also known as NTRU(Nth degree truncated polynomial ring) based method, is considered one of the most important FHE methods suitable for practical implementation. In this thesis, an efficient algorithm and architecture for LTV Fully Homomorphic Encryption is proposed. Conventional linear feedback shift register (LFSR) structure is expanded and modified for performing the truncated polynomial ring multiplication in LTV scheme in parallel. Novel and efficient modular multiplier, modular adder and modular subtractor are proposed to support high speed processing of LFSR operations. In addition, a family of special moduli are selected for high speed computation of modular operations. Though the area keeps the complexity of O(Nn^2) with no advantage in circuit level. The proposed architecture effectively reduces the time complexity from O(N log N) to linear time, O(N), compared to the best existing works. An FPGA implementation of the proposed architecture for LTV FHE is achieved and demonstrated. An elaborate comparison of the existing methods and the proposed work is presented, which shows the proposed work gains significant speed up over existing works

Enhanced fully homomorphic encryption scheme using modified key generation for cloud environment

Fully homomorphic encryption (FHE) is a special class of encryption that allows performing unlimited mathematical operations on encrypted data without decrypting it. There are symmetric and asymmetric FHE schemes. The symmetric schemes suffer from the semantically security property and need more performance improvements. While asymmetric schemes are semantically secure however, they pose two implicit problems. The first problem is related to the size of key and ciphertext and the second problem is the efficiency of the schemes. This study aims to reduce the execution time of the symmetric FHE scheme by enhancing the key generation algorithm using the Pick-Test method. As such, the Binary Learning with Error lattice is used to solve the key and ciphertext size problems of the asymmetric FHE scheme. The combination of enhanced symmetric and asymmetric algorithms is used to construct a multi-party protocol that allows many users to access and manipulate the data in the cloud environment. The Pick-Test method of the Sym-Key algorithm calculates the matrix inverse and determinant in one instance requires only n-1 extra multiplication for the calculation of determinant which takes 0(N3) as a total cost, while the Random method in the standard scheme takes 0(N3) to find matrix inverse and 0(N!) to calculate the determinant which results in 0(N4) as a total cost. Furthermore, the implementation results show that the proposed key generation algorithm based on the pick-test method could be used as an alternative to improve the performance of the standard FHE scheme. The secret key in the Binary-LWE FHE scheme is selected from {0,1}n to obtain a minimal key and ciphertext size, while the public key is based on learning with error problem. As a result, the secret key, public key and tensored ciphertext is enhanced from logq , 0(n2log2q) and ((n+1)n2log2q)2log q to n, (n+1)2log q and (n+1)2log q respectively. The Binary-LWE FHE scheme is a secured but noise-based scheme. Hence, the modulus switching technique is used as a noise management technique to scale down the noise from e and c to e/B and c/B respectively thus, the total cost for noise management is enhanced from 0(n3log2q) to 0(n2log q) . The Multi-party protocol is constructed to support the cloud computing on Sym-Key FHE scheme. The asymmetric Binary-LWE FHE scheme is used as a small part of the protocol to verify the access of users to any resource. Hence, the protocol combines both symmetric and asymmetric FHE schemes which have the advantages of efficiency and security. FHE is a new approach with a bright future in cloud computing

On the security of NoSQL cloud database services

Processing a vast volume of data generated by web, mobile and Internet-enabled devices, necessitates a scalable and flexible data management system. Database-as-a-Service (DBaaS) is a new cloud computing paradigm, promising a cost-effective and scalable, fully-managed database functionality meeting the requirements of online data processing. Although DBaaS offers many benefits it also introduces new threats and vulnerabilities. While many traditional data processing threats remain, DBaaS introduces new challenges such as confidentiality violation and information leakage in the presence of privileged malicious insiders and adds new dimension to the data security. We address the problem of building a secure DBaaS for a public cloud infrastructure where, the Cloud Service Provider (CSP) is not completely trusted by the data owner. We present a high level description of several architectures combining modern cryptographic primitives for achieving this goal. A novel searchable security scheme is proposed to leverage secure query processing in presence of a malicious cloud insider without disclosing sensitive information. A holistic database security scheme comprised of data confidentiality and information leakage prevention is proposed in this dissertation. The main contributions of our work are: (i) A searchable security scheme for non-relational databases of the cloud DBaaS; (ii) Leakage minimization in the untrusted cloud. The analysis of experiments that employ a set of established cryptographic techniques to protect databases and minimize information leakage, proves that the performance of the proposed solution is bounded by communication cost rather than by the cryptographic computational effort