A Secure Private Information Retrieval in Cloud Environment

In cryptography, there has been tremendous success in building various two-party protocols with small communication complexity out of homomorphic semantically-secure encryption schemes, using their homomorphic properties in a black-box way. A few notable examples of such primitives include items like single database Private Information Retrieval (PIR) schemes (introduced in [15]) and private database update with small communication (introduced in [5]). In this paper, we illustrate a general methodology for determining what types of protocols can and cannot be implemented with small communication by using homomorphic encryption in a black-box way. We hope that this work will provide a simple litmus test of feasibility for black-box use of known homomorphic encryption schemes by other cryptographic researchers attempting to develop new protocols with low communication. Additionally, a precise mathematical language for reasoning about such problems is developed in this work, which may be of independent interest. We stress that the class of algebraic structures for which we prove communication complexity lower bounds is large, and covers practically all known semantically-secure homomorphic cryptosystems (including those based upon bilinear maps). Finally, we show the following equivalence which relates group homomorphic encryption and a major open question of designing a so-called fully-homomorphic cryptosystem: a fully homomorphic encryption scheme (over a non-zero ring) exists if and only if there exists homomorphic encryption over any finite non-abelian simple group. This result somewhat generalizes results of Barrington [1] (to any group containing a finite non-abelian simple subgroup) and of Maurer and Rhodes [18], and in fact gives a constructiveproof of the 1974 result Werner [28]. (This also answers an open question posed by Rappe in [23], who in 2004 proved a special case of this result.)

Abstract: Encryption is essential in preventing unauthorized access to sensitive data in light of the growing concerns about data security in cloud computing. Homomorphic encryption promises to enable secure calculations on encrypted data without the need for decryption, particularly for cloud-based operations. To evaluate the effectiveness and applicability of several homomorphic encryption algorithms for safe cloud computing, we compare and contrast them in this research paper. Partially homomorphic encryption (PHE), somewhat homomorphic encryption (SHE), and fully homomorphic encryption (FHE) are the three basic homomorphic encryption subtypes that we examine. The implications of this study can aid cloud service providers and organizations in selecting the most appropriate homomorphic encryption scheme based on their specific security requirements and performance considerations. The research contributes to the ongoing efforts to enhance data privacy in cloud computing environments, opening new possibilities for secure data processing in an increasingly connected digital world. The exploration of homomorphic encryption schemes in this study opens new avenues for research and development in the field of cryptographic techniques. As technology continues to evolve, so too must our approaches to safeguarding data. This research serves as a catalyst for further innovations in homomorphic encryption algorithms, enabling even more efficient and robust methods for secure data processing in cloud environments and beyond. The insights derived from this research paper not only empower cloud service providers and organizations to make informed decisions about selecting the most appropriate homomorphic encryption scheme but also contribute to the broader mission of fortifying data privacy and security in cloud computing.

Homomorphic encryption (HE) schemes enable computing functions on encrypted data, by means of a public Eval procedure that can be applied to ciphertexts. But the evaluated ciphertexts so generated may differ from freshly encrypted ones. This brings up the question of whether one can keep computing on evaluated ciphertexts. An i-hop homomorphic encryption scheme is one where Eval can be called on its own output up to i times, while still being able to decrypt the result. A multi-hop homomorphic encryption is a scheme which is i-hop for all i. In this work we study i-hop and multi-hop schemes in conjunction with the properties of function-privacy (i.e., Eval's output hides the function) and compactness (i.e., the output of Eval is short). We provide formal definitions and describe several constructions. First, we observe that bootstrapping techniques can be used to convert any (1-hop) homomorphic encryption scheme into an i-hop scheme for any i, and the result inherits the function-privacy and/or compactness of the underlying scheme. However, if the underlying scheme is not compact (such as schemes derived from Yao circuits) then the complexity of the resulting i-hop scheme can be as high as nO(i). We then describe a specific DDH-based multi-hop homomorphic encryption scheme that does not suffer from this exponential blowup. Although not compact, this scheme has complexity linear in the size of the composed function, independently of the number of hops. The main technical ingredient in this solution is a re-randomizable variant of the Yao circuits. Namely, given a garbled circuit, anyone can re-garble it in such a way that even the party that generated the original garbled circuit cannot recognize it. This construction may be of independent interest.

An encryption scheme is homomorphic if it supports operations on encrypted data. Homomorphic encryption allows a device to perform arbitrary computations on encrypted data without user secret key. Recently it is introduced new homomorphic encryption schemes with improved performance that can be implemented in IoT device in production environments. The IoT concept encompasses devices, sensors, and services existing within an interconnected infrastructure with an efficient access to sample computational facilities. In this paper we evaluated features of exact arithmetic homomorphic encryption mechanisms: BFV and BGV and approximate homomorphic encryption scheme: CKKS. In the paper we measured performances of operations of homomorphic encryption schemes: BGV, BFV and CKKS that are implemented in Raspberry Pi 4 IoT device.

Parallel private information retrieval protocol with index anonymity for untrusted databases

The objective of this research is to develop a novel image encryption method that can be used to considerably increase the security of encrypted images. To solve this image security problem, we propose a distributed homomorphic image encryption scheme where the images of interest are those in the visible electromagnetic spectrum. In our encryption phase, a red green blue (RGB) image is first separated into its constituent channel images, and then the numerical intensity value of a pixel from each channel is written as a sum of smaller pixel intensity sub-values, leading to having several component images for each of the R, G, and B-channel images. A homomorphic encryption function is used to separately encrypted each of the pixel intensity sub-values in each component image using an encryption key, leading to a distributed image encryption approach. Each of the encrypted component images can be compressed before transmission and/or storage. In our decryption phase, each encrypted component image is decompressed if necessary, and then the homomorphic property of the encryption function is used to transform the product of individually encrypted pixel intensity sub-values in each encrypted component images, to the encryption of their sum, before applying the corresponding decryption function with a decryption key to recover the original pixel's intensity values for each channel image, and then recovering the original RGB image. Furthermore, a special case of an RGB image encryption and decryption where a pixel's intensity value from each channel is written as a sum of only two sub-values is implemented and simulated with a software. The resulting cipher-images are subject to a range of security tests and analyses. Results from these tests shown that our proposed homomorphic image encryption scheme is robust and can resist security attacks, as well as increases the security of the associated encrypted images. Our proposed homomorphic image encryption scheme has produced highly secure encrypted images.

The ability to perform computations on ciphertexts without knowing any information about the plaintexts makes homomorphic encryption technique useful in a wide variety of confidentiality preserving protocols (e.g., e-voting, e-health, etc.). Unfortunately, the traditional encyption schemes support a limited number of homomorphic operations (usually addition or multiplication). Indeed, in 2009, Gentry proposed a fully homomorphic encryption scheme which supports both multiplicative and additive homomorphic operations. Since then, several fully homomorphic encryption schemes have been proposed. However, the fully homomorphic encryption schemes are still undergoing experimentation and improvement. The hybridization of homomorphic encryption schemes seems to be an effective way to overcome their limitations and to benefit from their resistance against the confidentiality attacks. In this paper, we will study the possibility to hybridize the homomorphic encryption schemes so as to support all homomorphic properties.

Homomorphic encryption is a novel encryption method for it enables computing over encrypted data. This has a wide range of real world ramifications such as being able to blindly compute a search result sent to a remote server without revealing it's content. In this paper we summarize how SQL queries can be made secure using a homomorphic encryption scheme based on the ideas of Gahi, et al [1]. Gahi's model is based on the DGHV scheme which is a homomorphic encryption scheme which acts on plaintext bits and produce corresponding ciphertext. We use Gahi's blueprint to propose an improved model which is based on the more recent Ring based homomorphic encryption scheme by Braserski, et al [2]. Our method is more general in the sense that it can be extended to use with any fully homomorphic encryption scheme rather than being restricted to the DGHV scheme as in Gahi's method.

At present study, homomorphic encryption scheme is most focusing on algorithm efficiency and security and the rare for homomorphic encryption simulation research. This paper for the Gentry's Somewhat Homomorphic Encryption scheme for the simulation research, in clear text size within a certain range simulation was Somewhat Homomorphic Encryption scheme, and presents the relationship between the length of plaintext and ciphertext size.

We present SlicedPIR, a distributed Private Information Retrieval (PIR) protocol. SlicedPIR efficiently alleviates the server's compute bottleneck by offloading its load across multiple untrusted client machines. In contrast to prior work, SlicedPIR induces only a modest network overhead when the server offloads its work. It achieves those communication savings by exploiting the polynomial encoding of homomorphic encryption schemes typically used in PIR protocols. This encoding lets the server make novel use of the Number Theoretic Transform (NTT) to distribute points on the polynomials as ''slices'' of its data rather than the polynomials themselves. Using NTT allows the clients to process recursive PIR queries on their slices and return a succinct result to the server. The server efficiently verifies the clients' results by leveraging the Schwartz-Zippel lemma, which we adapt to the PIR use case. We show how to integrate SlicedPIR into a private messaging system, where clients write messages to the server's database and then use PIR to secretly query for messages from their friends. We implement a prototype of SlicedPIR and run experiments to show that it scales well with the number of clients and database size. Concretely, SlicedPIR achieves better performance and cuts network usage by over 95% compared to the state-of-the-art.

Private information retrieval (PIR) is an essential cryptographic protocol for privacy-preserving applications, enabling a client to retrieve a record from a server's database without revealing which record was requested. Single-server PIR based on homomorphic encryption has particularly gained immense attention for its ease of deployment and reduced trust assumptions. However, single-server PIR remains impractical due to its high computational and memory bandwidth demands. Specifically, reading the entirety of large databases from storage, such as SSDs, severely limits its performance. To address this, we propose IVE, an accelerator for single-server PIR with a systematic extension that enables practical retrieval from large databases using DRAM. Recent advances in DRAM capacity allow PIR for large databases to be served entirely from DRAM, removing its dependence on storage bandwidth. Although the memory bandwidth bottleneck still remains, multi-client batching effectively amortizes database access costs across concurrent requests to improve throughput. However, client-specific data remains a bottleneck, whose bandwidth requirements ultimately limits performance. IVE overcomes this by employing a large on-chip scratchpad with an operation scheduling algorithm that maximizes data reuse, further boosting throughput. Additionally, we introduce sysNTTU, a versatile functional unit that enhances area efficiency without sacrificing performance. We also propose a heterogeneous memory system architecture, which enables a linear scaling of database sizes without a throughput degradation. Consequently, IVE achieves up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1,275 \times$</tex> higher throughput compared to prior PIR hardware solutions.

Outsourcing database as service instead of using in-house database management is a new trend emerging in a computing industry; there has been growing interest in outsourcing database services in both the commercial world and the research community. In this paper, we present analysis of non-concurrent model of fast single-database Private Information Retrieval (PIR) scheme for maintaining data privacy with data confidentiality using encryption algorithm like AES for Outsourced Database Service (ODBS) Model. In this model encryption method maintains data confidentiality and a utility that help to create PIR reply which maintains data privacy. In PIR Scheme data privacy is achieved by adding noise data into the result of a typical query which is called as PIR reply. Single-database PIR schemes are generally not practical because of its expensiveness from computational point of view. Here we propose a model that suggests the use of General-Purpose computation using Graphic Processing Units (GPGPU) commodity to process such type of computationally intensive operations. This model will help to achieve practical implementation of single-database PIR scheme which uses encryption algorithm to maintain data confidentiality as secondary goal and it serves to create database reply to maintain data privacy as primary goal. This paper shows some real time results that proves need of concurrency in PIR algorithms. It also describes the use of lattice based single-database PIR protocol with GPGPU as a processing unit to achieve high speed-up and hence, the performance of the system.

Somewhat Homomorphic Encryption (SHE) schemes allow to carry out operations on data in the cipher domain. In a cloud computing scenario, personal information can be processed secretly, inferring a high level of confidentiality. Most practical Somewhat Homomorphic Encryption (SHE) schemes require the implementation of fast polynomial arithmetic, that is why hardware accelerators usually target the FFT/NTT algorithm. This paper proposes a co-design hardware/software approach to accelerate SHE using Karatsuba algorithm. Depending on the needs, Karatsuba algorithm allows to implement additional computations to the hardware in order to reduce software computation time. Our accelerator is designed to speed up arithmetic on degree 2560 polynomials with 125 bits coefficients. We provide 3 different approaches: An area efficient design, a balanced design, and a performance-oriented design. Our accelerator performs a polynomial multiplication in respectively 2.46 ms, 1.70 ms and 1.24 ms, and a relinearization operation in 2.28 ms, 1.53 ms and 1.1 ms, while a functionally equivalent design using the FFT [1] performs the multiplication in 1.96 ms and the relinearization in 4.79 ms for hardware resources consumption equivalent to the balanced design.

Homomorphic encryption was introduced to enable untrusted parties to apply computation over encrypted data, without decrypting the message. It makes a promising future to solve security challenges with Cloud Computing. Still, because of complex problems, HE is not yet usable in real-world applications. However homomorphic encryption suffers from many complex issues like large-time computation, which is difficult to implement, and huge ciphertext size. In this paper, we take into account many vital homomorphic encryption schemes, all of them is depend on computing over integers, by converting the message to a binary format, then the ciphertext is calculated to every single bit of plaintext. So, we suggested another symmetric Fully Homomorphic encryption that depends on an integer number without converting it to binary format, it encrypts the message using a prime secret key. The proposed system is considered a great improvement to the DGHV system. Where it reduced the ciphertext size and the execution time significantly. The present proposed system shows an improvement of DGHV where it is faster about 23.8 times from DGHV, and we gain one ciphertext for the whole message instead of ciphertext for every bit of the message. The scheme's hardness depends on the greatest common divisor (GCD) problem. We present a detailed explanation of these schemes showing their efficient techniques and compare it with the proposed algorithm in terms of ciphertext size of algorithm, and execution time and analyze their security them finally draw several conclusions.

We present lower bounds for the static cryptographic data structure problem of single-server private information retrieval (PIR). PIR considers the setting where a server holds a database of n entries and a client wishes to privately retrieve the i-th entry without revealing the index i to the server. In our work, we focus on PIR with preprocessing where an r-bit hint may be computed in a preprocessing stage and stored by the server to be used to perform private queries in expected time t. As our main result, we prove that for any single-server, computationally secure PIR with preprocessing, it must be that tr = Ω(n log n) when r = Ω(log n). If r = O(log n), then we show that t = Ω(n). Our lower bound holds even when the scheme errs with probability 1/n2 and the adversary's distinguishing advantage is 1/n. Our work improves upon the tr = Ω(n) lower bound of Beimel, Ishai and Malkin [JoC'04]. For information-theoretic security, we present a stronger lower bound of t + r = Ω(n) and show a matching construction. Both our lower bounds apply for public-key doubly-efficient PIRs of Boyle, Ishai, Pass and Wootters [TCC'17]. Additionally, our lower bound for information-theoretic security also applies for offline-online PIRs as defined by Corrigan-Gibbs and Kogan [Eurocrypt'20], where the hint is private and only viewed by the client. We prove our lower bounds in a variant of the cell probe model where only accesses to the database are charged cost and computation and accesses to the hint are free. Our main technical contribution is a novel use of the cell sampling technique (also known as the incompressibility technique) used to obtain lower bounds on data structures. In previous works, this technique only leveraged the correctness guarantees to prove lower bounds even when used for cryptographic primitives. Our work combines the cell sampling technique with the privacy guarantees of PIR to construct a powerful, polynomial-time adversary that is critical to proving our higher lower bounds.