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

Survey of Homomorphic schemes

Homomorphic encryption is increasingly becoming popular among researchers due to its future promises.Homomorphic encryption is a solution that allows a third party to process data in encrypted form. The decryption keys need not be shared.This paper summarizes the concept of homomorphic encryption and the work has been done in this field

Masteroppgave i kryptografi

In this paper we look at the use of bootstrapping and squashing in order to make an encryption scheme fully homomorphic. The focus will be on what this is and how it can be used. The main focus will be on how this is applied in the paper [11] by van Dijk, Gentry, Halevi and Vaikuntanathan

Efficient Fully Homomorphic Encryption from (Standard) LWE

A fully homomorphic encryption (FHE) scheme allows anyone to transform an encryption of a message, m, into an encryption of any (efficient) function of that message, f(m), without knowing the secret key. We present a leveled FHE scheme that is based solely on the (standard) learning with errors (LWE) assumption. (Leveled FHE schemes are initialized with a bound on the maximal evaluation depth. However, this restriction can be removed by assuming “weak circular security.”) Applying known results on LWE, the security of our scheme is based on the worst-case hardness of “short vector problems” on arbitrary lattices. Our construction improves on previous works in two aspects: 1. We show that “somewhat homomorphic” encryption can be based on LWE, using a new relinearization technique. In contrast, all previous schemes relied on complexity assumptions related to ideals in various rings. 2. We deviate from the “squashing paradigm” used in all previous works. We introduce a new dimension-modulus reduction technique, which shortens the ciphertexts and reduces the decryption complexity of our scheme, without introducing additional assumptions. Our scheme has very short ciphertexts, and we therefore use it to construct an asymptotically efficient LWE-based single-server private information retrieval (PIR) protocol. The communication complexity of our protocol (in the public-key model) is k·polylog(k)+log |DB| bits per single-bit query, in order to achieve security against 2k-time adversaries (based on the best known attacks against our underlying assumptions). Key words. cryptology, public-key encryption, fully homomorphic encryption, learning with errors, private information retrieva

An Improved Fully Homomorphic Encryption Scheme for Cloud Computing

Business in cloud computing is very popular among Small and Medium Enterprises (SMEs). By leveraging services from the cloud, such companies can migrate all of their in-house operations to cloud at low costs with minimum IT facility requirements such as desktop machines and the Internet. Even though the cloud promises tremendous advantages in terms of computing resources and storage spaces, some of the companies are still reluctant to adopt such a technology because of security concerns. To overcome such problems, a fully homomorphic encryption (FHE) scheme with improved efficiency can be implemented as the scheme allows computation on encrypted data without decryption. In this paper, we propose an improved FHE scheme that uses a symmetric key for encryption together with a protocol to implement the scheme. Furthermore, we also provide an analysis regarding to the noise growth in the processed ciphertext and squashing technique that is required to reduce the noise. This analysis is essential to improve the efficiency of the scheme as the squashing technique is time-consuming

Study of Fully Homomorphic Encryption over Integers

Fully homomorphic encryption has long been regarded as an open problem of cryptography. The method of constructing first fully homomorphic encryption scheme by Gentry is complicate so that it has been considered difficult to understand. This paper explains the idea of constructing fully homomorphic encryption and presents a general framework from various scheme of fully homomorphic encryption. Specially, this general framework can show some possible ways to construct fully homomorphic encryption. We then analyze the procedure how to obtaining fully homomorphic encryption over the integers. The analysis of recrypt procedure show the growth of noise, and the bound of noise in recrypt procedure is given. Finally, we describe the steps of implementation.

Exploring the Application of Homomorphic Encryption for a Cross Domain Solution

A cross domain solution is a means of information assurance that provides the ability to access or transfer digital data between varying security domains. Most acceptable cross domain solutions focus mainly on risk management policies that rely on using protected or trusted parties to handle the information in order to solve this problem; thus, a cross domain solution that is able to function in the presence of untrusted parties is an open problem. Homomorphic encryption is a type of encryption that allows its party members to operate and evaluate encrypted data without the need to decrypt it. Practical homomorphic encryption is an emerging technology that may propose a solution to the unsolved problem of cross domain routing without leaking information as well as many other unique scenarios. However, despite much advancement in research, current homomorphic schemes still challenge to achieve high performance. Thus, the plausibility of its implementation relies on the requirements of the tailored application. We apply the concepts of homomorphic encryption to explore a new solution in the context of a cross domain problem. We built a practical software case study application using the YASHE fully homomorphic scheme around the specific challenge of evaluating the gateway bypass condition on encrypted data. Next, we assess the plausibility of such an application through memory and performance profiling in order to find an optimal parameter selection that ensures proper homomorphic evaluation. The correctness of the application was assured for a 64-bit security parameter selection of YASHE resulting in high latency performance. However, literature has shown that the high latency performance can be heavily mitigated through use of hardware accelerators. Other configurations that include reducing number of SIMON rounds or avoiding the homomorphic SIMON evaluation completely were explored that show more promising performance results but either at the cost of security or network bandwidth