Somewhat Homomorphic Encryption Research Articles

The Next Frontier of Security: Homomorphic Encryption in Action

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.

Fully homomorphic encryption: A case study

Fully Homomorphic Encryption (FHE) is the holy grail of encrypted communications. It opens the door to several advanced functionalities to overcome the security and trust issues of the IT world. After 2009, once Craig Gentry had shown that FHE could be achieved, a study in this field boomed, and significant improvement was made in identifying more efficient and realistic programs. FHE is primitive cryptography that enables arbitrary functions to be calculated via encrypted data. These systems are applicable in different ways since they permit users to encrypt their private information securely while still outsourcing the processing of protected data without fearing disclosing the real data. In 2012, LTV12 presented the first multi-key FHE system and demonstrated the possibility of using multi-key systems in somewhat homomorphic encryption (SHE). Like in the one key context, there have been many advances in the field, but no effort has been made to develop the multi-key methods. This paper presents a discussion of FHE and MKFHE with a specific focus on the current techniques and three implementations, comprising the first in the multi-key setups, to the extent of our understanding.

2D Federated Learning for Personalized Human Activity Recognition in Cyber-Physical-Social Systems

The proliferation of the Internet of Things (IoT), wearable computing, and social media technologies bring forward the realization of the so-called Cyber-Physical-Social Systems (CPSS), which is capable of offering intelligent services in many different aspects of our day-to-day life. While CPSS offer a wide variety of data from wearable devices, challenges such as data silos and secure data sharing still remain. In this study, a 2-Dimensional Federated Learning (2DFL) framework, including the vertical and horizontal federated learning phases, is designed to cope with the insufficient training data and insecure data sharing issues in CPSS during a secure distributed learning process. Considering a specific application of Human Activity Recognition (HAR) across a variety of different devices from multiple individual users, the vertical federated learning scheme is developed to integrate shareable features from heterogeneous data across different devices into a full feature space, while the horizontal federated learning scheme is developed to effectively aggregate the encrypted local models among multiple individual users to achieve a high-quality global HAR model. A computationally efficient somewhat homomorphic encryption (SWHE) scheme is then improved and applied to support the parameter aggregation without giving access to it, which enables heterogeneous data sharing with privacy protection across different personal devices and multiple users in building a more precise personalized HAR model. Experiments are conducted based on two public datasets. Comparing with three conventional machine learning methods, evaluation results demonstrate the usefulness and effectiveness of our proposed model in achieving faster and smoother convergence, with better precision, recall, and F1 scores for HAR applications in CPSS.

A Hybrid Privacy-Preserving Deep Learning Approach for Object Classification in Very High-Resolution Satellite Images

Deep learning (DL) has shown outstanding performances in many fields, including remote sensing (RS). DL is turning into an essential tool for the RS research community. Recently, many cloud platforms have been developed to provide access to large-scale computing capacity, consequently permitting the usage of DL architectures as a service. However, this opened the door to new challenges associated with the privacy and security of data. The RS data used to train the DL algorithms have several privacy requirements. Some of them need a high level of confidentiality, such as satellite images related to public security with high spatial resolutions. Moreover, satellite images are usually protected by copyright, and the owner may strictly refuse to share them. Therefore, privacy-preserving deep learning (PPDL) techniques are a possible solution to this problem. PPDL enables training DL on encrypted data without revealing the original plaintext. This study proposes a hybrid PPDL approach for object classification for very-high-resolution satellite images. The proposed encryption scheme combines Paillier homomorphic encryption (PHE) and somewhat homomorphic encryption (SHE). This combination aims to enhance the encryption of satellite images while ensuring a good runtime and high object classification accuracy. The method proposed to encrypt images is maintained through the public keys of PHE and SHE. Experiments were conducted on real-world high-resolution satellite images acquired using the SPOT6 and SPOT7 satellites. Four different CNN architectures were considered, namely ResNet50, InceptionV3, DenseNet169, and MobileNetV2. The results showed that the loss in classification accuracy after applying the proposed encryption algorithm ranges from 2% to 3.5%, with the best validation accuracy on the encrypted dataset reaching 92%.

Privacy-Preserving Location-Based Data Queries in Fog-Enhanced Sensor Networks

Fog computing has emerged as a promising framework with the rapid growth of the Internet of Things (IoT). In fog computing, the new entity, named fog device, can help the cloud process the large amount of data generated by IoT devices. Along with this trend, a location-based query scheme that collects IoT devices’ data from specific areas is an important application, especially in fog-enhanced sensor networks. However, in this application, the cloud and fog devices require the user’s query, sensors’ locations, and sensor data so that it raises critical privacy and security concerns. In this article, we devise a privacy-preserving-location-based data query scheme in fog-enhanced sensor networks, which allows the cloud and fog devices to collect sensor data from a query area without learning the three kinds of information. Specifically, we resort to a cryptographic primitive, named somewhat homomorphic encryption (SHE), with ciphertext packing to encrypt query, locations, and sensor data and efficiently calculate the distances between the user’s query and sensors. Then, we show how to build a hardware-assisted data query scheme to extract the matched data based on the distances. We formally analyze the security strengths and implement the system prototype. In order to implement secure processing within software guard extension (SGX), we make an effort to adapt the existing mathematical libraries to the advanced SGX trusted environment. Evaluation results demonstrate that our proposed design is secure and efficient.

On the IND-CCA1 Security of FHE Schemes

Fully homomorphic encryption (FHE) is a powerful tool in cryptography that allows one to perform arbitrary computations on encrypted material without having to decrypt it first. There are numerous FHE schemes, all of which are expanded from somewhat homomorphic encryption (SHE) schemes, and some of which are considered viable in practice. However, while these FHE schemes are semantically (IND-CPA) secure, the question of their IND-CCA1 security is much less studied, and we therefore provide an overview of the IND-CCA1 security of all acknowledged FHE schemes in this paper. To give this overview, we grouped the SHE schemes into broad categories based on their similarities and underlying hardness problems. For each category, we show that the SHE schemes are susceptible to either known adaptive key recovery attacks, a natural extension of known attacks, or our proposed attacks. Finally, we discuss the known techniques to achieve IND-CCA1-secure FHE and SHE schemes. We concluded that none of the proposed schemes were IND-CCA1-secure and that the known general constructions all had their shortcomings.

Shortest Distance Queries on Encrypted Graph Data Based on GENOA

Abstract: In the execution time of the nearest distance queries, which means shortest distance queries on the encrypted graph data that stored in external storage like cloud storage, in previous scheme there are some challenges as how to figure the accurate shortest distance in efficient and secure way. In previous work a novel scheme of Somewhat Homomorphic Encryption (SWHE) is implemented to overcome the issues mentioned above and this SWHE is used for encryption. The SWHE will encrypt the output values (shortest distance) by 2-hop cover labeling (2HCL). The storage space of this SWHE is not sufficient for the data owner and it mostly gives the negative results and very low efficient. So, to provide the best efficient, accurate result and better storage for data owner a new novel scheme is implemented in this paper. A new proposed scheme called Graph Encryption scheme for shortest distance queries (GENOA) and the 2HCL index is also implemented. This GENOA is for execution of the shortest distance queries of graph data, this proposed scheme is highly efficient, and give the accurate result as per the queries. This new scheme help in storage and security also. Index Terms: Graph encryption; 2-hop cover labelling; Graph Encryption scheme for shortest distance queries (GENOA); Shortest distance queries.

FSDS: A practical and fully secure document similarity search over encrypted data with lightweight client

In this paper, we propose a highly accurate, fully secure document similarity search (FSDS) scheme that makes use of both a novel variant of the secure K-NN algorithm and somewhat homomorphic encryption (SWHE). The scheme provides data, query and search pattern privacy and is amenable to access pattern privacy. We provide formal security analyzes of both the original and the new secure K-NN algorithms and show the latter is IND-CPA secure. We also rely on IND-CPA security of the SWHE scheme to meet the strong privacy claims. The scheme provides a speedup of about two orders of magnitude over the schemes using only SWHE while its overall performance is comparable (and faster for certain cases) to other schemes in the literature with weaker forms of privacy claims. We present implementation results including those from the literature pertaining to response times, storage and bandwidth requirements and show that the proposed scheme facilitates a lightweight client implementation.

Efficient Private Conjunctive Query Protocol Over Encrypted Data

Conjunctive queries play a key role in retrieving data from a database. In a database, a query containing many conditions in its predicate, connected by an “and/&/∧” operator, is called a conjunctive query. Retrieving the outcome of a conjunctive query from thousands of records is a heavy computational task. Private data access to an outsourced database is required to keep the database secure from adversaries; thus, private conjunctive queries (PCQs) are indispensable. Cheon, Kim, and Kim (CKK) proposed a PCQ protocol using search-and-compute circuits in which they used somewhat homomorphic encryption (SwHE) for their protocol security. As their protocol is far from being able to be used practically, we propose a practical batch private conjunctive query (BPCQ) protocol by applying a batch technique for processing conjunctive queries over an outsourced database, in which both database and queries are encoded in binary format. As a main technique in our protocol, we develop a new data-packing method to pack many data into a single polynomial with the batch technique. We further enhance the performances of the binary-encoded BPCQ protocol by replacing the binary encoding with N-ary encoding. Finally, we compare the performance to assess the results obtained by the binary-encoded BPCQ protocol and the N-ary-encoded BPCQ protocol.

Enabling Privacy-Preserving Shortest Distance Queries on Encrypted Graph Data

When coming to perform shortest distance queries on encrypted graph data outsourced in external storage infrastructure such as cloud, a significant challenge is how to compute the shortest distance in an accurate, efficient and secure way. This issue is addressed by a recent work, which makes use of somewhat homomorphic encryption (SWHE) to encrypt distance values output by a 2-hop cover labeling (2HCL) scheme. However, it may import large errors and even yield negative results. Besides, SWHE would be too inefficient for normal clients. In this paper, we propose GENOA, a novel Graph ENcryption scheme for shOrtest distAnce queries. GENOA employs only efficient symmetric-key primitives while significantly enhances the accuracy compared to the prior work. As a reasonable trade-off, it additionally reveals the order information among queried distance values in the 2HCL index. We theoretically prove the accuracy and security of GENOA under rigorous cryptographic model. Detailed experiments on eight real-world graphs demonstrate that GENOA is efficient and can produce almost exact results.

Privacy-Preserving Matrix Factorization for Cross-Domain Recommendation

Cross-domain recommender systems are known to provide solutions to the cold start and data sparsity problems in recommender systems. This can be achieved by leveraging sufficient ratings and users' profiles in one domain to enhance accurate recommendations in another domain. However, domains with sufficient ratings are not willing to share their users' ratings with other recommender systems or domains due to users' privacy and legal concern. Hence this shows a need for a privacy-preserving mechanism that encourages secure knowledge transfer between different domains. This study proposes a privacy-preserving cross-domain recommender system based on matrix factorization. Specifically, the study formally described the privacy requirements of a cross-domain recommender system, which are different from a single domain recommender system. It designs a new framework for a privacy-preserving cross-domain recommender system and then utilized the somewhat homomorphic encryption (SWHE) scheme to ensure users' privacy. The SWHE scheme was used to encrypt users' ratings in different domains, shared latent factor approach was implemented between the domains and extracted knowledge was securely transferred from the source domain to the target domain. We prove that users' privacy is secured throughout the stages involved in the proposed protocol. Experiments on both synthetic and real datasets demonstrate the efficiency of our protocol.

Smart and Practical Privacy-Preserving Data Aggregation for Fog-Based Smart Grids

With the increasingly powerful and extensive deployment of edge devices, edge/fog computing enables customers to manage and analyze data locally, and extends computing power and data analysis applications to network edges. Meanwhile, as the next generation of the power grid, the smart grid can achieve the goal of efficiency, economy, security, reliability, use safety and environmental friendliness for the power grid. However, privacy and secure issues in fog-based smart grid communications are challenging. Without proper protection, customers’ privacy will be readily violated. This article presents a smart and practical Privacy-preserving Data Aggregation (PDA) scheme with smart pricing and packing method for fog-based smart grids, which achieves diversified tariffs, multifunctional statistics and efficiency. Especially, we first propose a smart PDA scheme with Smart Pricing (PDA-SP). With PDA-SP, the Control Center (CC) can compute more complex and higher-order aggregation statistics to provide various services, provide diversiform pricing strategies and choose a double-winning strategy. Subsequently, we put forward a practical PDA scheme with Packing Method (PDA-PM), which is able to reduce the size of encrypted data and improve performance in performing various secure computations. Moreover, we extend our original packing method and present a more useful packing method, which can handle general vectors with large entries. The security analysis shows that our proposed scheme is secure against many threats. The performance evaluation reveals that the computation and communication overheads of our proposed scheme are effectively reduced by employing the Somewhat Homomorphic Encryption (SHE), and our packing method can further significantly reduce these overheads.

Toward Practical Privacy-Preserving Processing Over Encrypted Data in IoT: An Assistive Healthcare Use Case

With the advancement of Internet of Things (IoT), a large number of electronic devices are connected to the Internet. These connected electronic devices acquire and transmit information, and respond to any received actions. In the medical ecosystem, hospitals can implement medical diagnosis (MD) with medical sensors, especially for remote auxiliary MD. But, in this context, patients’ privacy (PP) is of paramount importance, and confidentiality of medical data is crucial. Therefore, the main challenge ahead is how to realize remote auxiliary MD while protecting confidentiality of the medical data and ensuring PP. In this article, based on somewhat homomorphic encryption (SHE) scheme addressed by Junfeng Fan and Frederik Vercauteren (FV), we provide the first instance of a new efficient SHE scheme for homomorphic evaluation over single instruction multiple data (SIMD). We also implement a new set of efficient SIMD homomorphic comparison and division schemes. Based on these findings, we implement efficient privacy preserving and SIMD homomorphic surf and multiretina-image matching schemes. Offered functionalities include SIMD homomorphic feature point detection, multiretina-image matching, and lesion detection for the encrypted retinal image of diabetic retinopathy. Finally, we provide a proof-of-concept application implementation toward remote auxiliary diagnosis systems for diabetes in order to showcase the core security and privacy pillars of our solution. In the meantime, our IoT system designed with lattice-based cryptography preserves data confidentiality under quantum computation and quantum computers.

PrivateGraph: Privacy-Preserving Spectral Analysis of Encrypted Graphs in the Cloud

Big graphs, such as user interactions in social networks and customer rating matrices in collaborative filters, possess great values for both businesses and research. They are not only big but often keep evolving, which requires a large amount of computing resources to maintain. With the wide deployment of public cloud resources, owners of big graphs may want to use cloud resources to obtain storage and computation scalability. However, privacy and ownership of the graphs in the cloud has become a major concern. In this paper, we study privacy-preserving algorithms for one of the important graph analysis techniques—graph spectral analysis for outsourced graph in the cloud. The core operation: eigendecomposition of large matrix is also important to many data mining algorithms. We consider a cloud-centric framework with three collaborative parties: data contributors, data owner, and cloud provider. Graphs are represented as matrices such as adjacency matrix and Laplacian matrix, the elements of which are encrypted and submitted by distributed contributors. The data owner then interacts with the cloud-side programs to conduct spectral analysis, while protecting data privacy from the honest-but-curious cloud provider. For a $N\times N$N×N graph matrix, we aim to design algorithms with the cloud handling expensive storage and computation in $O(N^2)$O(N2) complexity, while data owner and data contributors’ algorithms take only $O(N)$O(N). To achieve this goal, we develop the privacy-preserving versions of the two approximate eigendecomposition algorithms: the Lanczos algorithm and the Nystrom algorithm, considering two encryption methods: additive homomorphic encryption (AHE) methods and somewhat homomorphic encryption (SHE) methods. Both dense and sparse matrices are studied, while sparse matrices also involve a differentially private data submission protocol to allow the trade-off between data sparsity and privacy. Experimental results show that the Nystro algorithm with sparse encoding can dramatically reduce data owners’ costs. SHE-based methods have lower computational time while AHE-based methods have lower communication/storage costs.

Reversible data hiding in encrypted images with somewhat homomorphic encryption based on sorting block-level prediction-error expansion

This paper proposes a reversible data hiding scheme for encrypted images with SHE (Somewhat Homomorphic Encryption) based on sorting block-level prediction-error expansion (SBPEE). The image provider divides the image into 2 × 2 image blocks and uses SHE to protect the content of the image. In encrypted images, the data hider embeds the secret data with the method of SBPEE, which is based on the pixel redundancy within each block. And the sorting technique shows a good performance at low embedding rate. With the watermarked encrypted image, if the receiver has only the data hiding key, he can extract the additional data. If the receiver has both the data hiding key and the encryption key, he can extract the additional data correctly and recover the original image without loss. The experimental results show that the performance of the method is better than that of the existing similar methods when the embedding rate is low and is consistent with the existing methods when the embedding rate is high.

Fully homomorphic encryption over the integers for non-binary plaintexts without the sparse subset sum problem

In this work, we solve the open problem of designing a fully homomorphic encryption scheme over the integers for non-binary plaintexts in ZQ for prime Q (Q-FHE-OI) without the hardness of the sparse subset sum problem (SSSP). Furthermore, we show that our Q-FHE-OI scheme is a useful optimization for evaluating arithmetic circuits on encrypted data for some primes. To that end, we provide a natural extension of the somewhat homomorphic encryption (SHE) scheme over the integers proposed by Cheon and Stehlé (Eurocrypt 2015) to support non-binary plaintexts. Then, a novel bootstrapping algorithm is proposed for this extended SHE scheme by introducing generalizations of several functions in binary arithmetic. As a result, we obtain a Q-FHE-OI scheme for any constant-sized prime Q≥3 without the hardness of the SSSP, whose bootstrapping algorithm is asymptotically as efficient as previous best results. Beyond that, we compare the efficiency of our scheme against a Q-FHE-OI scheme obtained by emulating mod-Q gates with boolean circuits as proposed by Kim and Tibouchi (CANS 2016). Our analysis indicates our proposed scheme performs better for prime Q up to 11287, which improves on the result of Kim and Tibouchi, who showed there is at most one prime, Q=3 where the Q-FHE-OI scheme by Nuida and Kurosawa (Eurocrypt 2015) is a better approach. This overturns our previous understanding that Q-FHE-OI schemes do not provide significant benefits.

A Survey on Homomorphic Encryption Schemes

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. The users or service providers with the key have exclusive rights on the data. Especially with popular cloud services, 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. Therefore, this survey focuses on HE and FHE schemes. 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 for 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, and extending the state-of-the-art HE, PHE, SWHE, and FHE systems.

High-Performance FV Somewhat Homomorphic Encryption on GPUs: An Implementation using CUDA

Homomorphic encryption (HE) offers great capabilities that can solve a wide range of privacy-preserving computing problems. This tool allows anyone to process encrypted data producing encrypted results that only the decryption key’s owner can decrypt. Although HE has been realized in several public implementations, its performance is quite demanding. The reason for this is attributed to the huge amount of computation required by secure HE schemes. In this work, we present a CUDAbased implementation of the Fan and Vercauteren (FV) Somewhat HomomorphicEncryption (SHE) scheme. We demonstrate several algebraic tools such as the Chinese Remainder Theorem (CRT), Residual Number System (RNS) and Discrete Galois Transform (DGT) to accelerate and facilitate FV computation on GPUs. We also show how the entire FV computation can be done on GPU without multi-precision arithmetic. We compare our GPU implementation with two mature state-of-the-art implementations: 1) Microsoft SEAL v2.3.0-4 and 2) NFLlib-FV. Our implementation outperforms them and achieves on average 5.37x, 7.37x, 22.22x, 5.11x and 13.18x (resp. 2.03x, 2.94x, 27.86x, 8.53x and 18.69x) for key generation, encryption, decryption, homomorphic addition and homomorphic multiplication against SEAL-FVRNS (resp. NFLlib-FV).

Practical somewhat-secure quantum somewhat-homomorphic encryption with coherent states

We present a scheme for implementing homomorphic encryption on coherent states encoded using phase-shift keys. The encryption operations require only rotations in phase space, which commute with computations in the codespace performed via passive linear optics, and with generalized non-linear phase operations that are polynomials of the photon-number operator in the codespace. This encoding scheme can thus be applied to any computation with coherent state inputs, and the computation proceeds via a combination of passive linear optics and generalized non-linear phase operations. An example of such a computation is matrix multiplication, whereby a vector representing coherent state amplitudes is multiplied by a matrix representing a linear optics network, yielding a new vector of coherent state amplitudes. By finding an orthogonal partitioning of the support of our encoded states, we quantify the security of our scheme via the indistinguishability of the encrypted codewords. Whilst we focus on coherent state encodings, we expect that this phase-key encoding technique could apply to any continuous-variable computation scheme where the phase-shift operator commutes with the computation.

Practical Parameters for Somewhat Homomorphic Encryption (SHE) Schemes on Binary Circuits

Post-quantum cryptography gets increasing attention lately, as we have to prepare alternative cryptographic solutions that will resist attacks from quantum computers. A very large effort is being done to replace the usual primitives such as encryption, signature or authentication. This effort also pulls new cryptographic features such as Somewhat or Fully Homomorphic Encryption schemes, based on lattices. Since their introduction in 2009, lots of the burden has been overcome and real applications now become possible. However many papers suffer from the fast constant pace of evolution on the attack side, so their parameter analysis is usually incomplete or obsolete. In this work we present a thorough study of two schemes that have proven their worth: FV and SHIELD, providing a deep analysis of how to setup and size their parameters, to ensure both correctness and security. Our overall aim is to provide easy-to-use guidelines for implementation purposes.