Homomorphically Encrypted Arithmetic Operations Over the Integer Ring

e18725 Background: Healthcare data sharing is important for the creation of diverse and large data sets, supporting clinical decision making, and accelerating efficient research to improve patient outcomes. This is especially vital in the case of real world data analysis. However, stakeholders are reluctant to share their data without ensuring patients’ privacy, proper protection of their data sets and the ways they are being used. Homomorphic encryption is a cryptographic capability that can address these issues by enabling computation on encrypted data without ever decrypting it, so the analytics results are obtained without revealing the raw data. The aim of this study is to prove the accuracy of analytics results and the practical efficiency of the technology. Methods: A real-world data set of colorectal cancer patients’ survival data, following two different treatment interventions, including 623 patients and 24 variables, amounting to 14,952 items of data, was encrypted using leveled homomorphic encryption implemented in the PALISADE software library. Statistical analysis of key oncological endpoints was blindly performed on both the raw data and the homomorphically-encrypted data using descriptive statistics and survival analysis with Kaplan-Meier curves. Results were then compared with an accuracy goal of two decimals. Results: The difference between the raw data and the homomorphically encrypted data results, regarding all variables analyzed was within the pre-determined accuracy range goal, as well as the practical efficiency of the encrypted computation measured by run time, are presented in table. Conclusions: This study demonstrates that data encrypted with Homomorphic Encryption can be statistical analyzed with a precision of at least two decimal places, allowing safe clinical conclusions drawing while preserving patients’ privacy and protecting data owners’ data assets. Homomorphic encryption allows performing efficient computation on encrypted data non-interactively and without requiring decryption during computation time. Utilizing the technology will empower large-scale cross-institution and cross- stakeholder collaboration, allowing safe international collaborations. Clinical trial information: 0048-19-TLV. [Table: see text]

With the wide application of cloud computing in multi-tenant, heterogeneous nodes and high-concurrency environments, model parameters frequently interact during distributed training, which easily leads to privacy leakage, communication redundancy, and decreased aggregation efficiency. To realize the collaborative optimization of privacy protection and computing performance, this study proposes the Heterogeneous Federated Homomorphic Encryption Cloud (HFHE-Cloud) model, which integrates federated learning (FL) and homomorphic encryption and constructs a secure and efficient collaborative learning framework for cloud platforms. Under the condition of not exposing the original data, the model effectively reduces the performance bottleneck caused by encryption calculation and communication delay through hierarchical key mapping and dynamic scheduling mechanism of heterogeneous nodes. The experimental results show that HFHE-Cloud is significantly superior to Federated Averaging (FedAvg), Federated Proximal (FedProx), Federated Personalization (FedPer) and Federated Normalized Averaging (FedNova) in comprehensive performance, Homomorphically Encrypted Federated Averaging (HE-FedAvg) and other five baseline models. In the dimension of privacy protection, the global accuracy is up to 94.25%, and the Loss is stable within 0.09. In terms of computing performance, the encryption and decryption time is shortened by about one third, and the encryption overhead is controlled at 13%. In terms of distributed training efficiency, the number of communication rounds is reduced by about one fifth, and the node participation rate is stable at over 90%. The results verify the model's ability to achieve high security and high scalability in multi-tenant environment. This study aims to provide cloud service providers and enterprise data holders with a technical solution of high-intensity privacy protection and efficient collaborative training that can be deployed in real cloud platforms.

Histograms are widely used for summarizing data distributions, detecting anomalies, and improving machine learning models’ accuracy. However, traditional histogram-based methods require access to raw data, raising privacy concerns, particularly in sensitive IoT applications. Encryption-based techniques offer potential solutions; however, they secure the data in transit or storage, requiring decryption during analysis, which exposes raw data to potential privacy risks. In this paper, we propose a method for constructing privacy-preserving histograms directly on homomorphically encrypted IoT data, leveraging the Fast Fully Homomorphic Encryption over the Torus (TFHE) scheme implemented in the Concrete framework. To overcome the challenges posed by homomorphic encryption, we redesign the traditional histogram construction algorithm, optimizing it for secure computation by addressing constraints related to nested loops and conditional statements. As an evaluation use case, we have considered an outlier detection mechanism based on histogram frequency counts, ensuring that all data and computations remain encrypted throughout the process. Our method achieves results consistent with plaintext-based outlier detection while maintaining reasonable computational overhead compared to those reported in the existing literature.

Homomorphic Encryption (HE) allows encrypted data to be processed without decryption, which could maximize the protection of user privacy without affecting the data utility. Thanks to strides made by cryptographers in the past few years, the efficiency of HE has been drastically improved, and machine learning on homomorphically encrypted data has become possible. Several works have explored machine learning based on HE, but most of them are restricted to the outsourced scenario, where all the data comes from a single data owner. We propose HomoPAI, an HE-based secure collaborative machine learning system, enabling a more promising scenario, where data from multiple data owners could be securely processed. Moreover, we integrate our system with the popular MPI framework to achieve parallel HE computations. Experiments show that our system can train a logistic regression model on millions of homomorphically encrypted data in less than two minutes.

Algorithmic trading has proliferated the area of quantitative finance for already over a decade. The decisions are made without human intervention using the data provided by brokerage firms and exchanges. There is an emerging intermediate layer of financial players that are placed in between a broker and algorithmic traders. The role of these players is to aggregate market decisions from the algorithmic traders and send a final market order to a broker. In return, the quantitative analysts receive incentives proportional to the correctness of their predictions. In such a setup, the intermediate player - an aggregator - does not provide the market data in plaintext but encrypts it. Encrypting market data prevents quantitative analysts from trading on their own, as well as keeps valuable financial data private. This paper proposes an implementation of a popular trend-following indicator with two different homomorphic encryption libraries - SEAL and HEAAN - and compares it to the trading indicator implemented for plaintext. Then an attempt to implement a trading strategy is presented and analysed. The trading indicator implemented with SEAL and HEAAN is almost identical to that implemented on the plaintext, the percentage error is of 0.14916% and 0.00020% respectively. Despite many limitations that homomorphic encryption imposes on this algorithm's implementation, quantitative finance has a high potential of benefiting from the methods of homomorphic encryption.

While homomorphic encryption (HE) provides strong privacy protection, its high computational cost has restricted its application to simple tasks. Recently, hyperdimensional computing (HDC) applied to HE has shown promising performance for privacy-preserving machine learning (PPML). However, when applied to more realistic scenarios such as batch inference, the HDC-based HE has still very high compute time as well as high encryption and data transmission overheads. To address this problem, we propose HDC with encrypted parameters (EP-HDC), which is a novel PPML approach featuring client-side HE, i.e., inference is performed on a client using a homomorphically encrypted model. Our EP-HDC can effectively mitigate the encryption and data transmission overhead, as well as providing high scalability with many clients while providing strong protection for user data and model parameters. In addition to application examples for our client-side PPML, we also present design space exploration involving quantization, architecture, and HE-related parameters. Our experimental results using the BFV scheme and the Face/Emotion datasets demonstrate that our method can improve throughput and latency of batch inference by orders of magnitude over previous PPML methods ($36.52 \sim 1068 \times$ and $6.45 \sim 733 \times$, respectively) with <1% accuracy degradation.

FedHEONN: Federated and homomorphically encrypted learning method for one-layer neural networks

When users store their data on a cloud, they may concern on whether their data is stored correctly and can be fully retrieved. Proofs of Retrivability (PoR) is a cryptographic concept that allows users to remotely check the integrity of their data without downloading. This check is usually done by attaching data with message authenticators that contain data integrity information. The existing PoR schemes consider only the retrievability of unencrypted data and their message authenticators are usually deterministic. In this paper, we propose a PoR scheme that is built over homomorphic encryption schemes. Our PoR scheme can prove the retrievability of homomorphically encrypted data by generating probabilistic and homomorphic message authenticators. Moreover, the homomorphically encrypted data can be processed by the cloud directly and our PoR scheme can verify the integrity of such outsourced computations over ciphertexts. A prototype of our scheme is implemented to evaluate its performance.

Machine-Learning-as-a-Service has become increasingly popular, with Recommendation-as-a-Service as one of the representative examples. In such services, providing privacy protection for the users is an important topic. Reviewing privacy-preserving solutions which were proposed in the past decade, privacy and machine learning are often seen as two competing goals at stake. Though improving cryptographic primitives (e.g., secure multi-party computation (SMC) or homomorphic encryption (HE)) or devising sophisticated secure protocols has made a remarkable achievement, but in conjunction with state-of-the-art recommender systems often yields far-from-practical solutions. We tackle this problem from the direction of machine learning. We aim to design crypto-friendly recommendation algorithms, thus to obtain efficient solutions by directly using existing cryptographic tools. In particular, we propose an HE-friendly recommender system, refer to as CryptoRec, which (1) decouples user features from latent feature space, avoiding training the recommendation model on encrypted data; (2) only relies on addition and multiplication operations, making the model straightforwardly compatible with HE schemes. The properties turn recommendation-computations into a simple matrix-multiplication operation. To further improve efficiency, we introduce a sparse-quantization-reuse method which reduces the recommendation-computation time by $9\times$ (compared to using CryptoRec directly), without compromising the accuracy. We demonstrate the efficiency and accuracy of CryptoRec on three real-world datasets. CryptoRec allows a server to estimate a user's preferences on thousands of items within a few seconds on a single PC, with the user's data homomorphically encrypted, while its prediction accuracy is still competitive with state-of-the-art recommender systems computing over clear data. Our solution enables Recommendation-as-a-Service on large datasets in a nearly real-time (seconds) level.

Selecting representative objects from a large-scale database is an essential task to understand the database. A skyline query is one of the popular methods for selecting representative objects. It retrieves a set of non-dominated objects. In this paper, we consider a distributed algorithm for computing skyline, which is efficient enough to handle “big data”. We have noticed the importance of “big data” and want to use it. On the other hand, we must take care of its privacy. In conventional distributed algorithms for computing a skyline query, we must disclose the sensitive values of each object of a private database to another for comparison. Therefore, the privacy of the objects is not preserved. However, such disclosures of sensitive information in conventional distributed database systems are not allowed in the modern privacy-aware computing environment. Recently several privacy-preserving skyline computation frameworks have been introduced. However, most of them use computationally expensive secure comparison protocol for comparing homomorphically encrypted data. In this work, we propose a novel and efficient approach for computing the skyline in a secure multi-party computing environment without disclosing the individual attributes’ value of the objects. We use a secure multi-party sorting protocol that uses the homomorphic encryption in the semi-honest adversary model for transforming each attribute value of the objects without changing their order on each attribute. To compute skyline we use the order of the objects on each attribute for comparing the dominance relationship among the objects. The security analysis confirms that the proposed framework can achieve multi-party skyline computation without leaking the sensitive attribute value to others. Besides that, our experimental results also validate the effectiveness and scalability of the proposed privacy-preserving skyline computation framework.

Medical wearable devices monitor health data and, coupled with data analytics, cloud computing, and artificial intelligence (AI), enable early detection of disease. Privacy issues arise when personal health information is sent or processed outside the device. We propose a framework that ensures the privacy and integrity of personal medical data while performing AI-based homomorphically encrypted data analytics in the cloud. The main contributions are: (i) a privacy-preserving cloud-based machine learning framework for wearable devices, (ii) CipherML—a library for fast implementation and deployment of deep learning-based solutions on homomorphically encrypted data, and (iii) a proof-of-concept study for atrial fibrillation (AF) detection from electrocardiograms recorded on a wearable device. In the context of AF detection, two approaches are considered: a multi-layer perceptron (MLP) which receives as input the ECG features computed and encrypted on the wearable device, and an end-to-end deep convolutional neural network (1D-CNN), which receives as input the encrypted raw ECG data. The CNN model achieves a lower mean F1-score than the hand-crafted feature-based model. This illustrates the benefit of hand-crafted features over deep convolutional neural networks, especially in a setting with a small training data. Compared to state-of-the-art results, the two privacy-preserving approaches lead, with reasonable computational overhead, to slightly lower, but still similar results: the small performance drop is caused by limitations related to the use of homomorphically encrypted data instead of plaintext data. The findings highlight the potential of the proposed framework to enhance the functionality of wearables through privacy-preserving AI, by providing, within a reasonable amount of time, results equivalent to those achieved without privacy enhancing mechanisms. While the chosen homomorphic encryption scheme prioritizes performance and utility, certain security shortcomings remain open for future development.

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.

Machine learning servers with mass storage and computing power is an ideal platform to store, manage, and analyze data and support decision-making. However, the main issue is providing security and privacy to the data, as the data is stored in a public way. Recently, homomorphic data encryption has been proposed as a solution due to its capabilities in performing computations over encrypted data. In this paper, we proposed an encrypted all convolutional net that transformed traditional all convolutional net into a net based on homomorphic encryption. This scheme allows different data holders to send their encrypted data to cloud service, complete predictions, and return them in encrypted form as the cloud service provider does not have a secret key. Therefore, the cloud service provider and others cannot get unencrypted raw data. When applied to the MNIST database, privacy-preserving all convolutional based on homomorphic encryption predict efficiently, accurately and with privacy protection.

ReActHE: A homomorphic encryption friendly deep neural network for privacy-preserving biomedical prediction

Homomorphic encryption (HE) enables arithmetic operations to be performed directly on encrypted data. It is essential for privacy-preserving applications such as machine learning, medical diagnosis, and financial data analysis. In popular HE schemes, ciphertext multiplication is only defined for two inputs. However, the multiplication of multiple inputs is needed in many HE applications. In our previous work, a three-input ciphertext multiplication method for the CKKS HE scheme was developed. This paper first reformulates the three-input ciphertext multiplication to enable the combination of computations in order to further reduce the complexity. Thesecond contribution is extending the multiplication to multiple inputs without compromising the noise overhead. Additional evaluation keys are introduced to achieve relinearization of polynomial multiplication results. To minimize the complexity of the large number of rescaling units in the multiplier, a theoretical analysis is developed to relocate the rescaling, and a multi-level rescaling approach is proposed to implement combined rescaling with complexity similar to that of a single rescaling unit. Guidelines and examples are provided on the input partition to enable the combination of more rescaling operations. Additionally, efficient hardware architectures are designed to implement our proposed multipliers. The improved three-input ciphertext multiplier reduces the logic area and latency by 15% and 50%, respectively, compared to the best prior design. For multipliers with more inputs, ranging from 4 to 12, the architectural analysis reveals 29% savings in area and 63% shorter latency, on average, compared to prior work.