Toward Efficient Homomorphic Encryption for Outsourced Databases through Parallel Caching

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.

Healthcare data has risen as a top target for cyberattacks due to the rich amount of sensitive patient information. This negatively affects the potential of advanced analytics and collaborative research in healthcare. Homomorphic encryption (HE) has emerged as a promising technology for securing sensitive healthcare data while enabling computations on encrypted information. This paper conducts a background survey of HE and its various types. It discusses Partially Homomorphic Encryption (PHE), Somewhat Homomorphic Encryption (SHE), Fully Homomorphic Encryption (FHE) and Fully Leveled Homomorphic Encryption (FLHE). A critical analysis of these encryption paradigms’ theoretical foundations, implementation schemes, and practical applications in healthcare contexts is presented. The survey encompasses diverse healthcare domains. It demonstrates HE’s versatility in securing electronic health records (EHRs), enabling privacy-preserving genomic data analysis, protecting medical imaging, facilitating privacy-preserving machine learning (ML), supporting secure federated learning, ensuring confidentiality in clinical trials, and enhancing remote monitoring and telehealth services. A comprehensive examination of potential vulnerabilities in HE systems is conducted. The research systematically investigates various attack vectors, including side-channel attacks, key recovery attacks, chosen plaintext attacks (CPA), chosen ciphertext attacks (CCA), known plaintext attacks (KPA), fault injection attacks (FIA), and lattice attacks. A detailed analysis of potential defense mechanisms and mitigation strategies is provided for each identified threat. The analysis underscores the importance of HE for long-term security and sustainability in healthcare systems.

We present passive attacks against CKKS, the homomorphic encryption scheme for arithmetic on approximate numbers presented at Asiacrypt 2017. The attack is both theoretically efficient (running in expected polynomial time) and very practical, leading to complete key recovery with high probability and very modest running times. We implemented and tested the attack against major open source homomorphic encryption libraries, including HEAAN, SEAL, HElib and PALISADE, and when computing several functions that often arise in applications of the CKKS scheme to machine learning on encrypted data, like mean and variance computations, and approximation of logistic and exponential functions using their Maclaurin series. The attack shows that the traditional formulation of $$\textsf {IND}\hbox {-}\textsf {CPA}$$ security (or indistinguishability against chosen plaintext attacks) achieved by CKKS does not adequately capture security against passive adversaries when applied to approximate encryption schemes, and that a different, stronger definition is required to evaluate the security of such schemes. We provide a solid theoretical basis for the security evaluation of homomorphic encryption on approximate numbers (against passive attacks) by proposing new definitions, that naturally extend the traditional notion of $$\textsf {IND}\hbox {-}\textsf {CPA}$$ security to the approximate computation setting. We propose both indistinguishability-based and simulation-based variants, as well as restricted versions of the definitions that limit the order and number of adversarial queries (as may be enforced by some applications). We prove implications and separations among different definitional variants, and discuss possible modifications to CKKS that may serve as a countermeasure to our attacks.

With recent development in internet speed and reliability, cloud computing has become a more reliable solution for the user. In many cases where data privacy is critical, fully homomorphic encryption (FHE) can be a security solution for securing cloud computing. FHE enables computation on encrypted data, hence it ensures data privacy in case of cloud computing. One popular scheme of FHE is the BFV homomorphic encryption scheme, which is based on ring learning with error (RLWE) computation. The BFV scheme uses ring polynomials as the main object, hence its encryption, decryption, and evaluation require high-degree polynomial multiplication. In this paper, we present comprehensive design and implementation of a hardware architecture to accelerate encryption and decryption in BFV scheme. Our accelerator uses convolution approach for calculating a polynomial multiplication. To implement the convolution, we use a systolic array to calculate polynomial convolution followed by a simple delayed subtraction to calculate polynomial modulo reduction inside our accelerator’s core. Moreover, we use a built-in Gaussian pseudo-random number generator (PRNG) to generate Gaussian noise in the encryption operations. Finally, we implement the 1024 degrees BFV accelerator on the Xilinx PYNQ Z1 board and compare the encryption and decryption performances to other methods as well as a software implementation on Intel Core i7 with 8GB memory. Experimental results show that our accelerator outperforms the clock cycles of other methods with the same polynomial degrees 1024 up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$22\times $ </tex-math></inline-formula> . Moreover, our proposed Gaussian PRNG has better <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2\times $ </tex-math></inline-formula> correlation compared to the rotation-only-based PRNG. Finally, our accelerator accelerates up to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$9\times $ </tex-math></inline-formula> for encryption and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3.5\times $ </tex-math></inline-formula> for decryption as well as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.8\times $ </tex-math></inline-formula> for overall compared to Microsoft SEAL on Intel Core i7 processor with 8GB memory. The proposed design is scalable for higher degrees polynomial multiplication and useful for security technology such as high-speed secure cloud computing, blind computing, and secure communication.

Outsourcing Machine Learning (ML) tasks to cloud servers is a cost-effective solution when dealing with distributed data. However, outsourcing these tasks to cloud servers could lead to data breaches. Secure computing methods, such as Homomorphic Encryption (HE) and Trusted Execution Environments (TEE), have been used to protect outsourced data. Nevertheless, HE remains inefficient in processing complicated functions (e.g., non-linear functions) and TEE (e.g., Intel SGX) is not ideal for directly processing ML tasks due to side-channel attacks and parallel-unfriendly computation.In this paper, we propose a hybrid framework integrating SGX and HE, called HT2ML, to protect user's data and models. In HT2ML, HE-friendly functions are protected with HE and performed outside the enclave, while the remaining operations are performed inside the enclave obliviously. HT2ML leverages optimised HE matrix multiplications to accelerate HE computations outside the enclave while using oblivious blocks inside the enclave to prevent access-pattern-based attacks. We evaluate HT2ML using Linear Regression (LR) training and Convolutional Neural Network (CNN) inference as two instantiations. The performance results show that HT2ML is up to ∼11× faster than HE only baseline with 6-dimensional data in LR training. For CNN inference, HT2ML is ∼196× faster than the most recent approach (Xiao et al., ICDCS'21).

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.

Homomorphic encryption facilitates secure computations on encrypted data without necessitating decryption, thereby ensuring robust protection of sensitive information. Nevertheless, these computations impose substantial performance overheads due to their inherent complexity. This research proposes an innovative approach that amalgamates GPU and FPGA acceleration, dynamic code generation, and parallelization to enhance the performance and scalability of homomorphic encryption algorithms.Our methodology employs GPU acceleration to harness the parallel processing capabilities of GPUs, FPGA acceleration to exploit custom, application-specific hardware configurations, dynamic code generation to produce optimized machine code, and automatic parallelization to distribute computations across multiple processing units. WE demonstrate the efficacy of our approach through extensive benchmarking against existing optimization strategies. Our findings reveal that this comprehensive optimization significantly reduces computational overhead and bolsters the performance of homomorphic encryption algorithms, particularly when processing large datasets. In summary, the proposed approach offers a practical solution for augmenting the performance of homomorphic encryption, rendering it suitable for real-world applications involving confidential data. Our contributions hold significant ramifications for the domains of cybersecurity and data privacy and provide fertile ground for future research endeavours.

Reinforcement learning (RL) is a learning technique that enables state-dependent learning through feedback from an environment and makes an action decision for maximizing a reward without prior knowledge of the environment. If these RL techniques are used for data-centric services running on cloud computing, serious data privacy issues may occur because it is required to exchange privacy-related user data for RL-based services between the users and the cloud computing platform. We consider using homomorphic encryption (HE) scheme, which enables cloud computing platforms to perform arithmetic operations without decrypting ciphertexts. Using the HE scheme, users are allowed to deliver only ciphertexts to the cloud computing platform for using RL-based services. We propose a privacy-preserving reinforcement learning (PPRL) framework for the cloud computing platform. The proposed framework exploits a cryptosystem based on learning with errors (LWE) for fully homomorphic encryption (FHE). Performance analysis and evaluation for the proposed PPRL framework are conducted in a variety of cloud computing-based intelligent service scenarios.

We can say that we are surrounded by the computing world from every nook and corner. Cloud Computing is deemed as the most fundamentally changing phenomenon happening in Information Technology. But with great perks, comes great challenges as well, especially in the field of data security and privacy protection. The Cloud Service Providers take over chunks of private data from users for providing better functionalities. But for the sake of privacy and protection, this sensitive data should be encrypted and then outsourced to the cloud consoles. Since traditional cloud computing is performed on plaintext, many encryption algorithms were applied in the cloud for security purposes and ‘encrypted’ data was stored in the cloud from then on. This change gives fruition to a new type of encryption technique called Homomorphic Encryption. Primarily, the paper will focus on a subtype of Homomorphic Encryption called Fully Homomorphic Encryption. The objective of the paper is to propose a method to convert the sequentially processing Fully Homomorphic Encryption into parallel processing Fully Homomorphic Encryption using a Parallel Computing concept called Partitioning and thereby producing a better performing Fully Homomorphic Encryption.

To address the growing security challenges in cloud computing, homomorphic encryption (HE) offers a promising solution for a third party to evaluate functions and maintain data privacy even during calculation, as it allows for the evaluation on ciphertexts. However, the practical use of HE is constrained by limited arithmetic capabilities and high computational overhead. A promising strategy to mitigate these challenges is to evaluate HE-unfriendly functions through precomputed lookup tables (LUTs). This paper proposes a non-interactive model for evaluating arbitrary one-input functions using homomorphic encrypted LUTs with word-wise HE. Existing methods based on BFV/BGV schemes require precomputing outputs for all possible inputs, which leads to significant computational overhead. Furthermore, they are restricted to integer computations. This paper proposes a new LUT-based method that extends these approaches by employing the CKKS scheme, which supports approximate realnumber computation, thereby enhancing flexibility and efficiency. Our CKKS-based LUT computation method enables a flexible trade-off between accuracy and latency while supporting realnumber operations. Specifically, increasing the LUT size improves the output accuracy for a given function, allowing users to balance computational precision and processing speed according to their needs. Our experimental evaluation confirms that the proposed method achieves up to a $19 \%$ reduction in latency and up to an $\mathbf{8 1. 1 \%}$ reduction in MAPE compared to baselines with larger domains, i.e., plaintext space, while maintaining acceptable memory consumption.

Recent trend towards cloud computing and outsourcing has led to the requirement for face recognition (FR) to be performed remotely by third-party servers. When outsourcing the FR, client's test image and classification result will be revealed to the servers. Within this context, we propose a novel privacy-preserving (PP) FR algorithm based on randomization. Existing PP FR algorithms are based on homomorphic encryption (HE) which requires higher computational power and communication bandwidth. Since we use randomization, the proposed algorithm outperforms the HE based algorithm in terms of computational and communication complexity.We validated our algorithm using popular ORL database. Experimental results demonstrate that accuracy of the proposed algorithm is the same as the accuracy of existing algorithms, while improving the computational efficiency by 120 times and communication complexity by 2.5 times against the existing HE based approach.

Cloud computing has garnered increasing attention from researchers who have presented much work on performing massive computing tasks efficiently. Many security vulnerabilities have simultaneously occurred; therefore dealing with security problems in cloud computing has become an urgent issue. The purpose of this paper is to create a cloud computing framework based on the Map Reduce platform, a Google cloud-computing platform, and solve some security problems in the process of distributed computation. Inspired by SMC (Secure Multi-Party Computation), a protocol naturally suitable for distributed computation, we adopted homomorphic encryption, which could be used for processing a large amount of data securely in cloud computation. We also find that order preserving encryption(OPE), an encryption algorithm put forward in 2004, can be used in our secure framework. Cognizant of the applicability of SMC and OPE in cloud computing, we combine them with Map Reduce to design a security framework of distributed computation. Our major contributions consist of designing an innovative cloud computation framework in security based on Map Reduce, applying the order preserving encryption(OPE) algorithm, homomorphic encryption, and constructing a real distributed computation platform.

The ring variant of learning with errors (Ring-LWE) problem has provided efficient post-quantum cryptographic schemes including homomorphic encryption (HE) schemes. Usually, cyclotomic fields are used as underlying number fields of Ring-LWE from the viewpoints of efficiency and security. However, especially in the case of HE schemes, improving the efficiency and ensuring the security are important tasks even now. Arita and Handa proposed to use decomposition fields as underlying number fields of Ring-LWE and successfully constructed a HE scheme which can encrypt many plaintexts efficiently at a time. However, there is no enough evidence that decomposition fields do not provide weak Ring-LWE instances.In this paper, we give an experimental analysis on lattice attacks against Ring-LWE over decomposition fields. More precisely, we conducted lattice attacks against Ring-LWE over decomposition fields and over the ℓ-th cyclotomic fields with some prime numbers ℓ, respectively, and compared each of the running-time, the success rate and the root hermite factor. We also compared the results of the same attacks on various decomposition fields to find decomposition fields providing weak Ring-LWE instances. As a result of our analysis, we expect that decomposition fields would provide more secure and efficient HE schemes based on Ring-LWE compared to the ℓ-th cyclotomic fields.

Homomorphic encryption is an important means for cloud computing to ensure information security when outsourcing data. Among them, threshold fully homomorphic encryption (ThFHE) is a key enabler for homomorphic encryption and, from a wider perspective, secure distributed computing. However, current ThFHE schemes are unsatisfactory in terms of security and efficiency. In this paper, a novel ThFHE is proposed for the first time based on an NTRU-based GSW-like scheme of symmetric encryption—Th-S-NGS scheme. Additionally, the threshold structure is realized by combining an extended version of the linear integer secret sharing scheme such that the scheme requires a predetermined number of parties to be online, rather than all the parties being online. The Th-S-NGS scheme is not only more attractive in terms of ciphertext size and computation time for homomorphic multiplication, but also does not need re-linearization after homomorphic multiplication, and thus does not require the computing key, which can effectively reduce the communication burden in the scheme and thus simplify the complexity of the scheme.

HEFactory: A symbolic execution compiler for privacy-preserving Deep Learning with Homomorphic Encryption