Multi-key Homomorphic Encryption Research Articles

Secure Distributed Sparse Gaussian Process Models Using Multi-Key Homomorphic Encryption

Distributed sparse Gaussian process (dGP) models provide an ability to achieve accurate predictive performance using data from multiple devices in a time efficient and scalable manner. The distributed computation of model, however, risks exposure of privately owned data to public manipulation. In this paper we propose a secure solution for dGP regression models using multi-key homomorphic encryption. Experimental results show that with a little sacrifice in terms of time complexity, we achieve a secure dGP model without deteriorating the predictive performance compared to traditional non-secure dGP models. We also present a practical implementation of the proposed model using several Nvidia Jetson Nano Developer Kit modules to simulate a real-world scenario. Thus, secure dGP model plugs the data security issues of dGP and provide a secure and trustworthy solution for multiple devices to use privately owned data for model computation in a distributed environment availing speed, scalability and robustness of dGP.

Random forest evaluation using multi-key homomorphic encryption and lookup tables

In recent years, machine learning (ML) has become increasingly popular in various fields of activity. Cloud platforms have also grown in popularity, as they offer services that are more secure and accessible worldwide. In this context, cloud-based technologies emerged to support ML, giving rise to the machine learning as a service (MLaaS) concept. However, the clients accessing ML services in order to obtain classification results on private data may be reluctant to upload sensitive information to cloud. The model owners may also prefer not to outsource their models in order to prevent model inversion attacks and to protect intellectual property. The privacy-preserving evaluation of ML models is possible through multi-key homomorphic encryption (MKHE), that allows both the client data and the model to be encrypted under different keys. In this paper, we propose an MKHE evaluation method for decision trees and we extend the proposed method for random forests. Each decision tree is evaluated as a single lookup table, and voting is performed at the level of groups of decision trees in the random forest. We provide both theoretical and experimental evaluations for the proposed method. The aim is to minimize the performance degradation introduced by the encrypted model compared to a plaintext model while also obtaining practical classification times. In our experiments with the proposed MKHE random forest evaluation method, we obtained minimal (less than 0.6%) impact on the main ML performance metrics considered for each scenario, while also achieving reasonable classification times (of the order of seconds).

SecFed: A Secure and Efficient Federated Learning Based on Multi-Key Homomorphic Encryption

SecFed: A Secure and Efficient Federated Learning Based on Multi-Key Homomorphic Encryption

MODELING OF OPTIMAL MULTI KEY HOMOMORPHIC ENCRYPTION WITH DEEP LEARNING BIOMETRIC BASED AUTHENTICATION SYSTEM FOR CLOUD COMPUTING

More recently, cloud computing (CC) has gained considerable attention among research communities and business people. Inspite of the advantages of CC, security, and privacy remains a challenging problem. Therefore, biometric authentication systems have been employed and fingerprint is considered as widely employed to attain security. In addition, image encryption techniques can be used to encrypt the fingerprint biometric image to add an extra level of security. Based on these motivation, this study designs an optimal multikey homomorphic encryption (OMHE) with stacked autoencoder (SAE) based biometric authentication system for CC environment. The proposed OMHE-SAE model aims to encrypt the biometrics using OMHE technique and then verification takes place using SAE model. In addition, the OMHE technique involves the optimal key generation process using sandpiper optimization (SPO) algorithm to effectively choose the keys for encryption and decryption. Furthermore, the verification of decrypted biometrics takes place by the use of SAE model. A wide range of simulation analyses take place on benchmark datasets and the experimental outcomes portrayed the betterment of the OMHE-SAE More than cutting edge technology.

Extension of physical activity recognition with 3D CNN using encrypted multiple sensory data to federated learning based on multi-key homomorphic encryption

Background and Objective: The Internet of medical things is enhancing smart healthcare services using physical wearable sensor-based devices connected to the Internet. Machine learning techniques play an important role in the core of these services for remotely consulting patients thanks to the pattern recognition from on-device data, which is transferred to the central servers from local devices. However, transferring personally identifiable information data to servers could become a source for hackers to steal from, manipulate and perform illegal activities. Federated learning is a new branch of machine learning that creates directly training models from on-device data and aggregates these learned models on the servers without centralized data. Another way to protect data confidentiality on computer systems is data encryption. Data encryption transforms data into another form that only users with authority to a decryption key can read. In this work, we propose a novel method enabling preservation of client privacy and protection of client biomedical data from illegal hackers while transmitting through the Internet.Methods: We propose a method applying 3-dimensional convolutional neural networks for human activity recognition using multiple sensory data. In order to protect the data, we apply the bitwise XOR operator encryption technique. Then, we extend our 3-dimensional convolutional neural network methods to both traditional federated learning and the federated learning based on multi-key homomorphic encryption using the proposed encrypting data.Results: Based on leave-one-out-cross-validation, the 3-dimensional method obtains an accuracy of 94.6% and of 94.9% (without data encrypting and without federated learning) tested on two different benchmarked datasets, Sport and DaLiAC respectively. Accuracy is decreased slightly to 89.5% (from 94.6% of the baseline) when we use the proposed encrypting data method. However, the encryption-data-based method still has a potential result compared to the state-of-the-art which only uses raw data. In addition, the proposed full federated learning scheme of this work shows that illegal persons who somehow can get the trained model transmitted via networks cannot infer the private result.Conclusions: This novel method for sensory data representation which translates temporal and frequency bio-signal values to voxel intensities that can encode 3-dimensional activity images. Secondly, the proposed 3-dimensional convolutional neural network methods outperform other deep-learning-based human activity recognition approaches. Finally, extensive experiments show the proposed data-encrypted federated learning approach can achieve feasibility in terms of efficiency in privacy preservation.

Multi-key homomorphic encryption with tightened RGSW ciphertexts without relinearization for ciphertexts product

Most previous RLWE-based multi-key homomorphic encryptions (MKHEs) need to perform complex relinearization operations on ciphertext products to complete the evaluation of circuits of bounded polynomial depth. In this process, many intermediate ciphertexts or keys are needed for computing, resulting in inefficient computing and redundant storage. We propose a more efficient RLWE-based MKHE without relinearization operations to squeeze the storage space provided for homomorphic computation. Firstly, a controllable factor is introduced into the party’s ciphertexts, delineating the ciphertext as a component-like factor in preparation for concatenate operations. Secondly, we construct a tightened RGSW ciphertext extension algorithm that can directly work on the party’s original ciphertext. The extended ciphertext no longer needs to be converted, so no conversion keys are required. Again, by combining the concatenate and bit decomposition techniques, we construct new matching homomorphic computation algorithms, which ensure that the ciphertext product or sum is consistent in morphology with the extended ciphertext. The homomorphic multiplication algorithm allows the resultant ciphertext to directly participate in the next round of homomorphic operations without relinearization. Finally, we propose a specific RLWE-based MKHE scheme and provide the decryption process. Our analysis shows that our scheme guarantees IND-CPA security and performs efficient homomorphic computations correctly without relinearization operations.

A Practical Implementation of Medical Privacy-Preserving Federated Learning Using Multi-Key Homomorphic Encryption and Flower Framework

The digitization of healthcare data has presented a pressing need to address privacy concerns within the realm of machine learning for healthcare institutions. One promising solution is federated learning, which enables collaborative training of deep machine learning models among medical institutions by sharing model parameters instead of raw data. This study focuses on enhancing an existing privacy-preserving federated learning algorithm for medical data through the utilization of homomorphic encryption, building upon prior research. In contrast to the previous paper, this work is based upon Wibawa, using a single key for HE, our proposed solution is a practical implementation of a preprint with a proposed encryption scheme (xMK-CKKS) for implementing multi-key homomorphic encryption. For this, our work first involves modifying a simple “ring learning with error” RLWE scheme. We then fork a popular federated learning framework for Python where we integrate our own communication process with protocol buffers before we locate and modify the library’s existing training loop in order to further enhance the security of model updates with the multi-key homomorphic encryption scheme. Our experimental evaluations validate that, despite these modifications, our proposed framework maintains a robust model performance, as demonstrated by consistent metrics including validation accuracy, precision, f1-score, and recall.

Multi-Key Homomorphic Encryption Scheme with Multi-Output Programmable Bootstrapping

Multi-key Homomorphic Encryption (MKHE) scheme can homomorphically evaluate ciphertexts encrypted by different keys, which can effectively protect the privacy information of data holders in the joint computing of cloud services. Since the first full Homomorphic encryption scheme was proposed, bootstrapping is the only way to realize the arbitrary depth homomorphic computation of MKHE schemes. But bootstrap operation is quite expensive. In order to implement fast bootstrapping in MKHE schemes, previous works proposed multi-key TFHE schemes to implement low-latency bootstrapping and output a univariate function of messages after bootstrapping, called Programmable Bootstrapping (PBS). However, these schemes can only encrypt single-bit messages. PBS only outputs a function. And after a homomorphic operation, a bootstrap is required, which undoubtedly results in an increase in the cost of the whole multi-key homomorphic encryption operation. In this paper, we propose a MKHE scheme for multi-output PBS. For this purpose, we study the encryption method and homomorphic operation steps of MKHE, and add BFV homomorphic encryption multiplication and multi-key ciphertext relinearization. We separate the homomorphic operation from bootstrapping. We homomorphically evaluate test polynomials for multiple functions. In contrast to previous MKHE schemes, we support the output of multiple message-related functions with a single bootstrapping operation on the ciphertext. It is no longer limited to encrypting single-bit plaintext, and an effective ciphertext packaging technology is added. According to the analysis given in this paper, it is known that in the scenario of multi-party joint computation, the proposed scheme can be implemented with less bootstrapping when the same number of functions are homomorphically operated. This will effectively reduce the computational overhead.

Privacy preserving via multi-key homomorphic encryption in cloud computing

As the world grapples with the COVID-19 and its variants, multi-user collaboration by means of cloud computing is ubiquitous. How to make better use of cloud resources while preventing user privacy leakage has become particularly important. Multi-key homomorphic encryption(MKHE) can effectively deal with the privacy disclosure issue during the multi-user collaboration in the cloud computing setting. Firstly, we improve the DGHV homomorphic scheme by modifying the selection of key and the coefficients in encryption, so as to eliminate the restriction on the parity of the ciphertext modulus in the public key. On this basis, we further propose a DGHV-type MKHE scheme based on the number theory. In our scheme, an extended key is introduced for ciphertext extension, and we prove that it is efficient in performance analysis. The semantic security of our schemes is proved under the assumption of error-free approximate greatest common divisor and the difficulty of large integer factorization. Furthermore, the simulation experiments show the availability and computational efficiency of our MKHE scheme. Therefore, our scheme is suitable for the multi-user scenario in cloud environment.

A efficient and robust privacy-preserving framework for cross-device federated learning

To ensure no private information is leaked in the aggregation phase in federated learning (FL), many frameworks use homomorphic encryption (HE) to mask local model updates. However, the heavy overheads of these frameworks make them unsuitable for cross-device FL, where the clients are a huge number of mobile and edge devices with limited computing resources. Even worse, some of them also fail to manage the dynamic changes of clients. To overcome these shortcomings, we propose a threshold multi-key HE scheme tMK-CKKS and design an efficient and robust privacy-preserving FL framework. Robustness means that our framework allows clients to join in or drop out during the training process. Besides, because our tMK-CKKS scheme can pack multiple messages in a single ciphertext, our framework significantly reduces the computation and communication overhead. Moreover, the threshold mechanism in tMK-CKKS ensures that our framework can resist collusion attacks between the server and no more than t (threshold value) curious internal clients. Finally, we implement our framework in FedML and conduct extensive experiments to evaluate our framework. Utility evaluations on 6 benchmark datasets show that our framework can protect privacy without sacrificing the model accuracy. Efficiency evaluations on 4 typical deep learning models demonstrate that: our framework can speed up the computation by at least 1.21times over xMK-CKKS-based framework, 15.84times over Batchcrypt-based framework, and 20.30times over CRT-Paillier-based framework. Our framework can reduce the communication burden by at least 8.61 MB over Batchcrypt-based framework, 35.36 MB over xMK-CKKS-based framework and 42.58 MB over CRT-Paillier-based framework. The advantages in both computation and communication expand with the size of deep learning models.

Privacy Preserving Image Encryption with Optimal Deep Transfer Learning Based Accident Severity Classification Model.

Effective accident management acts as a vital part of emergency and traffic control systems. In such systems, accident data can be collected from different sources (unmanned aerial vehicles, surveillance cameras, on-site people, etc.) and images are considered a major source. Accident site photos and measurements are the most important evidence. Attackers will steal data and breach personal privacy, causing untold costs. The massive number of images commonly employed poses a significant challenge to privacy preservation, and image encryption can be used to accomplish cloud storage and secure image transmission. Automated severity estimation using deep-learning (DL) models becomes essential for effective accident management. Therefore, this article presents a novel Privacy Preserving Image Encryption with Optimal Deep-Learning-based Accident Severity Classification (PPIE-ODLASC) method. The primary objective of the PPIE-ODLASC algorithm is to securely transmit the accident images and classify accident severity into different levels. In the presented PPIE-ODLASC technique, two major processes are involved, namely encryption and severity classification (i.e., high, medium, low, and normal). For accident image encryption, the multi-key homomorphic encryption (MKHE) technique with lion swarm optimization (LSO)-based optimal key generation procedure is involved. In addition, the PPIE-ODLASC approach involves YOLO-v5 object detector to identify the region of interest (ROI) in the accident images. Moreover, the accident severity classification module encompasses Xception feature extractor, bidirectional gated recurrent unit (BiGRU) classification, and Bayesian optimization (BO)-based hyperparameter tuning. The experimental validation of the proposed PPIE-ODLASC algorithm is tested utilizing accident images and the outcomes are examined in terms of many measures. The comparative examination revealed that the PPIE-ODLASC technique showed an enhanced performance of 57.68 dB over other existing models.

Outsourced Privacy-Preserving kNN Classifier Model Based on Multi-Key Homomorphic Encryption

Outsourced Privacy-Preserving kNN Classifier Model Based on Multi-Key Homomorphic Encryption

Encryption with User Authentication Model for Internet of Medical Things Environment

Internet of Medical Things (IoMT) enabled e-healthcare has the potential to greately improve conventional healthcare services significantly. However, security and privacy become major issues of IoMT because of the restricted processing abilities, storage, and energy constraints of the sensors. Therefore, it leads to infeasibility of developing traditional cryptographic solutions to the IoMT sensors. In order to ensure security on sensitive medical data, effective encryption and authentication techniques need to be designed to assure security of the patients and healthcare service providers. In this view, this study designs an effective metaheuristic optimization based encryption with user authentication (EMOE-UA) technique for IoMT environment. This work proposes an EMOE-UA technique aims to accomplish mutual authentication for addressing the security issues and reducing the computational complexity. Moreover, the EMOE-UA technique employs optimal multikey homomorphic encryption (OMKHE) technique to encrypt the IoMT data. Furthermore, the improved social spider optimization algorithm (ISSOA) was employed for the optimal multikey generation of the MKHE technique. The experimental result analysis of the EMOE-UA technique takes place using benchmark data and the results are examined under various aspects. The simulation results reported the considerably better performance of the EMOE-UA technique over the existing techniques.

Verifiable Privacy-Preserving Scheme Based on Vertical Federated Random Forest

Presently, under the condition of privacy preserving, vertical federated learning (VFL) has played an important role in training the machine learning (ML) models in the application scenarios, such as medical prediction, fraud detection, in which the data is distributed vertically. Random forest (RF) is one of the most widely used ML methods in VFL, which has the advantages of strong predictive performance, availability, and the ability to parallel tasks. However, current research on privacy preserving of vertical federated RF is limited, and none of them can achieve the application level of security, that is, in a system where users are dynamically changing, not only privacy can be preserved, but also data integrity can be verified. Therefore, we propose a verifiable privacy-preserving scheme (VPRF) based on vertical federated RF, in which the users are dynamic change. First, we design homomorphic comparison and voting statistics algorithms based on multikey homomorphic encryption for privacy preservation. Then, we propose a multiclient delegated computing verification algorithm to make up for the disadvantage that the above algorithms cannot verify data integrity. Finally, we used the data sets in UCI ML warehouse to evaluate the proposed scheme. The experiment results indicate that our scheme is more efficient than the existing ones that can achieve the same security level.

Threshold Homomorphic Encryption From Provably Secure NTRU

Abstract Homomorphic Encryption (HE) supports computation on encrypted data without the need to decrypt, enabling secure outsourcing of computing to an untrusted cloud. Motivated by application scenarios where private information is offered by different data owners, Multi-Key Homomorphic Encryption (MKHE) and Threshold Homomorphic Encryption (ThHE) were proposed. Unlike MKHE, ThHE schemes do not require expensive ciphertext extension procedures and are therefore as efficient as their underlying single-key HE schemes. In this work, we propose a novel NTRU-type ThHE scheme which caters to the computation scenarios with pre-defined participants. In addition to inheriting the simplicity of NTRU scheme, our construction has no expensive relinearization and correspondingly no costly evaluation keys. Controlling noise to make it increase linearly and then using a wide key distribution, our scheme is immune to the subfield lattice attacks and its security follows from the hardness of the standard R-LWE problem. Finally, based on the {0,1}-linear secret sharing and noise flooding techniques, we design a single round distributed threshold decryption protocol, where the decryption is able to be completed even when only given a subset (say $t$-out-of-$k$) of partial decryptions. To the best of our knowledge, our construction is the first NTRU-type ThHE scheme.

TrustGWAS: A full-process workflow for encrypted GWAS using multi-key homomorphic encryption and pseudorandom number perturbation.

The statistical power of genome-wide association studies (GWASs) is affected by the effective sample size. However, the privacy and security concerns associated with individual-level genotype data pose great challenges for cross-institutional cooperation. The full-process cryptographic solutions are in demand but havenot been covered, especially the essential principal-component analysis (PCA). Here, we present TrustGWAS, a complete solution for secure, large-scale GWAS, recapitulating gold standard results against PLINK without compromising privacy and supporting basic PLINK steps including quality control, linkage disequilibrium pruning, PCA, chi-square test, Cochran-Armitage trend test, covariate-supported logistic regression and linear regression, and their sequential combinations. TrustGWAS leverages pseudorandom number perturbations for PCA and multiparty scheme of multi-key homomorphic encryption for all other modules. TrustGWAS can evaluate 100,000 individuals with 1 million variants and complete QC-LD-PCA-regression workflow within 50 h. We further successfully discover gene loci associated with fasting blood glucose, consistent with the findings of the ChinaMAP project.

FogDedupe: A Fog-Centric Deduplication Approach Using Multi-Key Homomorphic Encryption Technique

The advancements in communication technologies and a rapid increase in the usage of IoT devices have resulted in an increased data generation rate. Storing, managing, and processing large quantities of unstructured data generated by IoT devices remain a huge challenge to cloud service providers (CSP). To reduce the storage overhead, CSPs implement deduplication algorithms on the cloud storage servers. It identifies and eliminates the redundant data blocks. However, implementing post-progress deduplication schemes does not address the bandwidth issues. Also, existing convergent key-based deduplication schemes are highly vulnerable to confirmation of file attacks (CFA) and can leak confidential information. To overcome these issues, FogDedupe, a fog-centric deduplication framework, is proposed. It performs source-level deduplication on the fog nodes to reduce the bandwidth usage and post-progress deduplication to improve the cloud storage efficiency. To perform source-level deduplication, a distributed index table is created and maintained in the fog nodes, and post-progress deduplication is performed using a multi-key homomorphic encryption technique. To evaluate the proposed FogDedupe framework, a testbed environment is created using the open-source Eucalyptus v.4.2.0 software and fog project v1.5.9 package. The proposed scheme tightens the security against CFA attacks and improves the storage overhead by 27% and reduces the deduplication latency by 12%.

DHSA: efficient doubly homomorphic secure aggregation for cross-silo federated learning

Secure aggregation is widely used in horizontal federated learning (FL), to prevent the leakage of training data when model updates from data owners are aggregated. Secure aggregation protocols based on homomorphic encryption (HE) have been utilized in industrial cross-silo FL systems, one of the settings involved with privacy-sensitive organizations such as financial or medical, presenting more stringent requirements on privacy security. However, existing HE-based solutions have limitations in efficiency and security guarantees against colluding adversaries without a Trust Third Party. This paper proposes an efficient Doubly Homomorphic Secure Aggregation (DHSA) scheme for cross-silo FL, which utilizes multi-key homomorphic encryption (MKHE) and seed homomorphic pseudorandom generator (SHPRG) as cryptographic primitives. The application of MKHE provides strong security guarantees against up to \(N-2\) participates colluding with the aggregator, with no TTP required. To mitigate the large computation and communication cost of MKHE, we leverage the homomorphic property of SHPRG to replace the majority of MKHE computation by computationally friendly mask generation from SHPRG, while preserving the security. Overall, the resulting scheme satisfies the stringent security requirements of typical cross-silo FL scenarios, at the same time providing high computation and communication efficiency for practical usage. We experimentally demonstrate that our scheme brings a speedup to 20\(\times \) over the state-of-the-art HE-based secure aggregation and reduces the traffic volume to approximately 1.5\(\times \) inflation over the plain learning setting.

Optimized relinearization algorithm of the multikey homomorphic encryption scheme

Multikey homomorphic encryption (MKHE) supports arbitrary homomorphic evaluation on the ciphertext of different users and thus can be applied to scenarios involving multiusers (e.g., cloud computing and artificial intelligence) to protect user privacy. CDKS19 is the current most efficient MKHE scheme, and its relinearization process consumes most of the time of homomorphic evaluation. In this study, an optimized relinearization algorithm of CDKS19 is proposed. This algorithm reorganizes the evaluation key during the key generation process, decreases the complexity of relinearization, and reduces the error growth rate during homomorphic evaluation. First, we reduce the scale of the evaluation key by increasing its modulus instead of using a gadget vector to decompose the user's public key and extend the ciphertext of homomorphic multiplication. Second, we use rescaling technology to optimize the relinearization algorithm; thus, the error bound of the ciphertext is reduced, and the homomorphic operation efficiency is improved. Lastly, the average-case error estimation on the variances of polynomial coefficients and the upper bound of the canonical embedding map are provided. Results show that our scheme reduces the scale of the evaluation key, the error variance, and the computational cost of the relinearization process. Our scheme can effectively perform the homomorphic multiplication of ciphertexts.

Optimal Multikey Homomorphic Encryption with Steganography Approach for Multimedia Security in Internet of Everything Environment

Recent developments of semiconductor and communication technologies have resulted in the interconnection of numerous devices in offering seamless communication and services, which is termed as Internet of Everything (IoE). It is a subset of Internet of Things (IoT) which finds helpful in several applications namely smart city, smart home, precise agriculture, healthcare, logistics, etc. Despite the benefits of IoE, it is limited to processing and storage abilities, resulting in the degradation of device safety, privacy, and efficiency. Security and privacy become major concerns in the transmission of multimedia data over the IoE network. Encryption and image steganography is considered effective solutions to accomplish secure data transmission in the IoE environment. For resolving the limitations of the existing works, this article proposes an optimal multikey homomorphic encryption with steganography approach for multimedia security (OMKHES-MS) technique in the IoE environment. Primarily, singular value decomposition (SVD) model is applied for the separation of cover images into RGB elements. Besides, optimum pixel selection process is carried out using coyote optimization algorithm (COA). At the same time, the encryption of secret images is performed using poor and rich optimization (PRO) with multikey homomorphic encryption (MKHE) technique. Finally, the cipher image is embedded into the chosen pixel values of the cover image to generate stego image. For assessing the better outcomes of the OMKHES-MS model, a wide range of experiments were carried out. The extensive comparative analysis reported the supremacy of the proposed model over the rennet approaches interms of different measures.