Homomorphic Encryption Scheme 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.

Enhanced privacy-preserving distributed deep learning with application to fog-based IoT

Generally, privacy-preserving distributed deep learning (PPDDL) solutions provided so far present a trade-off between privacy and efficiency/effectiveness, especially, in terms of high communication and run-time costs (i.e. efficiency) and declined accuracy (i.e. effectiveness). Additionally, not much attention has been paid to proposing privacy-preserving solutions that are multi-key compliant, able to extend to new participants and well fit for an unbounded number of participants as well as being post-quantum robust. Also, application of DDL to fog-based IoT needs more attention. To this effect, we present enhanced PPDDL by proposing two solutions (basic and advanced). The basic combines LWE-based additive homomorphic encryption and partial sharing, making it communication cost friendly. The advanced, however, uses a lattice-based fully dynamic multi-key fully homomorphic encryption (FHE) scheme and partial sharing with the additional advantages of being multi-key compliant, able to extend to new participants and well fit for an unbounded number of participants. Furthermore, we put our work in the context of Fog-Based IoT. Extensive experimental evaluations for the basic solution which also best suits the Fog-Based IoT, show that the PPDDL accuracy is maintained, recording accuracy of about 97% for the MNIST dataset. For a much deeper architecture, accuracy could reach about 99%. To assess the generalizability of the accuracy trend observed in the PPDDL, the proposed solution was also evaluated using the CIFAR-10 dataset with interesting results recorded in this study. This paper is innovative as it combines partial sharing and homomorphic encryption in DDL . Solutions are post-quantum robust and communication cost efficient.

Biometric identification on the cloud: A more secure and faster construction

Cloud-assisted biometric identification can benefit data owners with limited resources by offloading their storage and identification tasks to cloud servers with abundant resources. However, the adoption of this computing paradigm is hindered by security and privacy concerns. To solve the dilemma, several privacy-preserving cloud-assisted biometric identification protocols have been proposed. Nevertheless, the existing designs suffer from one or more of the following restrictions: (1) support only for data owner-online query, (2) low security level, and (3) inefficiency. Motivated by these challenges, this paper aims to explore a more secure and efficient construction. Concretely, we initialize the error weighted hashing (EWH)-based data packing technique to replace the time-consuming linear scan search during the identification process. Additionally, to ensure compatibility with the EWH-based search algorithm, we formulate an identity (id)-based scoring strategy and introduce a random split-based data encryption algorithm, which circumvents the costly homomorphic encryption scheme. Within the framework of the two non-colluding servers model, the random split-based one-time pad encryption guarantees provably indistinguishable security against chosen-plaintext attacks. Finally, since only simple hash and xor operations are involved, our novel construction exhibits significantly improved performance compared to prior designs, both in theory and in practice. This superiority is validated through rigorous theoretical analysis and extensive experimental evaluation.

MemFHE: End-to-end Computing with Fully Homomorphic Encryption in Memory

The increasing amount of data and the growing complexity of problems have resulted in an ever-growing reliance on cloud computing. However, many applications, most notably in healthcare, finance, or defense, demand security and privacy, which today’s solutions cannot fully address. Fully homomorphic encryption (FHE) elevates the bar of today’s solutions by adding confidentiality of data during processing. It allows computation on fully encrypted data without the need for decryption, thus fully preserving privacy. To enable processing encrypted data at usable levels of classic security, e.g., 128-bit, the encryption procedure introduces noticeable data size expansion—the ciphertext is much bigger than the native aggregate of native data types. In this article, we present MemFHE, which is the first accelerator of both client and server for the latest Ring-GSW (Gentry et al. [ 17 ])-based homomorphic encryption schemes using Processing in Memory (PIM). PIM alleviates the data movement issues with large FHE encrypted data while providing in situ execution and extensive parallelism needed for FHE’s polynomial operations. While the client-PIM can homomorphically encrypt and decrypt data, the server-PIM can process homomorphically encrypted data without decryption. MemFHE’s server-PIM is pipelined and is designed to provide flexible bootstrapping, allowing two encryption techniques and various FHE security levels based on the application requirements. We evaluate MemFHE for various security levels and compare it with state-of-the-art CPU implementations for Ring-GSW-based FHE. MemFHE is up to 20 k × (265×) faster than CPU (GPU) for FHE arithmetic operations and provides on average 2,007× higher throughput than [ 36 ] while implementing neural networks with FHE.

CASA: A Compact and Scalable Accelerator for Approximate Homomorphic Encryption

Approximate arithmetic-based homomorphic encryption (HE) scheme CKKS [CKKS17] is arguably the most suitable one for real-world data-privacy applications due to its wider computation range than other HE schemes such as BGV [BGV14], FV and BFV [Bra12, FV12]. However, the most crucial homomorphic operation of CKKS called key-switching induces a great amount of computational burden in actual deployment situations, and creates scalability challenges for hardware acceleration. In this paper, we present a novel Compact And Scalable Accelerator (CASA) for CKKS on the field-programmable gate array (FPGA) platform. The proposed CASA addresses the aforementioned computational and scalability challenges in homomorphic operations, including key-exchange, homomorphic multiplication, homomorphic addition, and rescaling.On the architecture layer, we propose a new design methodology for efficient acceleration of CKKS. We design this novel hardware architecture by carefully studying the homomorphic operation patterns and data dependency amongst the primitive oracles. The homomorphic operations are efficiently mapped into an accelerator with simple control and smooth operation, which brings benefits for scalable implementation and enhanced pipeline and parallel processing (even with the potential for further improvement).On the component layer, we carry out a detailed and extensive study and present novel micro-architectures for primitive function modules, including memory bank, number theoretic transform (NTT) module, modulus switching bank, and dyadic multiplication and accumulation.On the arithmetic layer, we develop a new partially reduction-free modular arithmetic technique to eliminate part of the reduction cost over different prime moduli within the moduli chain of the Residue Number System (RNS). The proposed structure can support arbitrary numbers of security primes of CKKS during key exchange, which offers better security options for adopting the scalable design methodology.As a proof-of-concept, we implement CASA on the FPGA platform and compare it with state-of-the-art designs. The implementation results showcase the superior performance of the proposed CASA in many aspects such as compact area, scalable architecture, and overall better area-time complexities.In particular, we successfully implement CASA on a mainstream resource-constrained Artix-7 FPGA. To the authors’ best knowledge, this is the first compact CKKS accelerator implemented on an Artix-7 device, e.g., CASA achieves a 10.8x speedup compared with the state-of-the-art CPU implementations (with power consumption of only 5.8%). Considering the power-delay product metric, CASA also achieves 138x and 105x improvement compared with the recent GPU implementation.

When cryptography stops data science: Strategies for resolving the conflicts between data scientists and cryptographers

The advent of the digital era and computer-based remote communications has significantly enhanced the applicability of various sciences over the past two decades, notably data science (DS) and cryptography (CG). Data science involves clustering and categorizing unstructured data, while cryptography ensures security and privacy aspects. Despite certain CG laws and requirements mandating fully randomized or pseudonoise outputs from CG primitives and schemes, it appears that CG policies might impede data scientists from working on ciphers or analyzing information systems supporting security and privacy services. However, this study posits that CG does not entirely preclude data scientists from operating in the presence of ciphers, as there are several examples of successful collaborations, including homomorphic encryption schemes, searchable encryption algorithms, secret-sharing protocols, and protocols offering conditional privacy. These instances, along with others, indicate numerous potential solutions for fostering collaboration between DS and CG. Therefore, this study classifies the challenges faced by DS and CG into three distinct groups: challenging problems (which can be conditionally solved and are currently available to use; e.g., using secret sharing protocols, zero-knowledge proofs, partial homomorphic encryption algorithms, etc.), open problems (where proofs to solve exist but remain unsolved and is now considered as open problems; e.g., proposing efficient functional encryption algorithm, fully homomorphic encryption scheme, etc.), and hard problems (infeasible to solve with current knowledge and tools). Ultimately, the paper will address specific solutions and outline future directions to tackle the challenges arising at the intersection of DS and CG, such as providing specific access for DS experts in secret-sharing algorithms, assigning data index dimensions to DS experts in ultra-dimension encryption algorithms, defining some functional keys in functional encryption schemes for DS experts, and giving limited shares of data to them for analytics.

Input–Output History Feedback Controller for Encrypted Control With Leveled Fully Homomorphic Encryption

Protecting the parameters, states, and input/output signals of a dynamic controller is essential for securely outsourcing its computation to an untrusted third party. Although a fully homomorphic encryption scheme allows the evaluation of controller operations with encrypted data, an encrypted dynamic controller with the encryption scheme destabilizes a closed-loop system or degrades the control performance due to overflow. This paper presents a novel controller representation based on input-output history data to implement an encrypted dynamic controller that operates without destabilization and performance degradation. Implementation of this encrypted dynamic controller representation can be optimized via batching techniques to reduce the time and space complexities. Furthermore, this study analyzes the stability and performance degradation of a closed-loop system caused by the effects of controller encryption. A numerical simulation demonstrates the feasibility of the proposed encrypted control scheme, which inherits the control performance of the original controller at a sufficient level.

Elliptic code-based oblivious polynomial evaluation

Oblivious polynomial evaluation (OPE) constitutes a crucial element in various two-party computation protocols, including private set intersection, data mining, and oblivious keyword search. Consequently, the development of an efficient OPE protocol is of paramount significance. Leveraging the homomorphic properties of encryption algorithms offers an effective avenue for constructing such a protocol. In this paper, we propose an elliptic code-based symmetric homomorphic encryption scheme that incorporates concepts introduced by Armknecht et al. We also provide parameter selection tailored to various security levels. This encryption scheme accommodates arbitrary additions and a finite number of multiplication operations. Expanding on our encryption scheme, we introduce three practical and straightforward OPE protocols that are fully compatible with our encryption framework. We complement these protocols with a comprehensive security analysis. Our protocols not only achieve a high level of security but also exhibit efficiency, requiring only two message transmissions for the entire OPE process. Furthermore, our protocols can concurrently compute function values at multiple evaluation points, whether for distinct functions or the same function.

General construction of compressive integrity auditing protocol from strong homomorphic encryption scheme

General construction of compressive integrity auditing protocol from strong homomorphic encryption scheme

Enhancement in Homomorphic Encryption Scheme of Cloud Computing to Isolate DOS Attack

Enhancement in Homomorphic Encryption Scheme of Cloud Computing to Isolate DOS Attack

FFBP Neural Network Optimized with Woodpecker Mating Algorithm for Dynamic Cluster-based Secure Routing in WSN

Feed Forward Back Propagation Neural Network (FFBPNN) Optimized with Woodpecker Mating Algorithm is proposed in this manuscript for Dynamic Cluster-Based Secure Routing in Wireless Sensor Networks (FFBPNN-WMA-ECHC-WSN). The proposed method contains three different stages: first stage is dynamically clustered sensor network formation based on FFBPNN, second stage is Key generation for data encryption and decryption using Elliptic Curve-based Hill Cipher (ECHC), third stage is Homomorphic encryption scheme, which is used to deliver the aggregated data in-time. Woodpecker Mating Algorithm (WMA) is proposed to optimize the parameter values of FFBPNN. The proposed FFBPNN-WMA ECHC-WSN method was implemented in NS2 tool and its efficiency is evaluated under some metrics, like alive nodes, packet drop, network lifetime, delay, throughput, and energy consumption, Packet Delivery Ratio (PDR). The performance of FFBPNN-WMA-ECHC-WSN method provides lower delay 99.01%, 98.34%, 95.23% and 97.45%, and higher throughput 97.25%, 90.12%, 89.39% and 95.47% compared with existing models, such as EHCERA-SDT-WSN, DSA-ECC-PSO-SDT-WSN, IPECC-PDF-ABC-SDT-WSN and IBFA-LDCSN-BSHHO-SDT-WSN, respectively.

Parallel Accelerating Number Theoretic Transform for Bootstrapping on a Graphics Processing Unit

The bootstrapping procedure has become the main bottleneck affecting the efficiency of all known fully homomorphic encryption (FHE) schemes. The state-of-the-art scheme for efficient bootstrapping, which is called fully homomorphic encryption over the torus (TFHE), accelerates polynomial multiplication by leveraging number theoretic transform (NTT) and implementing NTT in parallel on a GPU. Unfortunately, almost none of the recent advancements in NTT take full advantage of a GPU, leading to the need for more time. With this in mind, in this work, a novel faster number theoretic transform based on a GPU is proposed, in which matrix multiplication is used to implement a decomposed small-point NTT. When implementing matrix multiplication, we introduce a merging preprocessing method to merge multiple inputs of the small-point NTT, aiming to effectively minimize the count of modulo operations. Subsequently, when the merged result is multiplied by rotation factors, we use logical left shift rather than arithmetic multiplication to improve the computational efficiency. Our scheme can easily be used to realize a 1024-point NTT and the results of the experiments show that the speedup ratio of our method over the butterfly algorithm is about 2.49.

Privacy Protection Based on Special Identifiers of Intersection Base Computing Technology

Private Set Intersection Cardinality (PSI-CA) and Private Set Union Cardinality (PSU-CA) are two cryptographic primitives whereby two or more parties are able to obtain the cardinalities of the intersection and the union of their respective private sets, and the privacy of their sets is preserved. In this paper, we propose a new privacy protection intersection cardinality protocol, which can quickly deal with set inequality and asymmetry problems and can obtain 100% correct results, and, in terms of efficiency, we are much faster than using the polynomial method. Our protocol adopts the Paillier addition homomorphic encryption scheme and applies the identifier guidance technology, using identifier determination, to the semi-homomorphic encryption ciphertext environment, excluding a large number of different options and quickly finding the base of the intersection of two sides.

Secure State Estimation for Artificial Neural Networks With Unknown-But-Bounded Noises: A Homomorphic Encryption Scheme.

This article is concerned with the secure state estimation problem for artificial neural networks (ANNs) subject to unknown-but-bounded noises, where sensors and the remote estimator are connected via open and bandwidth-limited communication networks. Using the encoding-decoding mechanism (EDM) and the Paillier encryption technique, a novel homomorphic encryption scheme (HES) is introduced, which aims to ensure the secure transmission of measurement information within communication networks that are constrained by bandwidth. Under this encoding-decoding-based HES, the data being transmitted can be encrypted into ciphertexts comprising finite bits. The emphasis of this research is placed on the development of a secure set-membership state estimation algorithm, which allows for the computation of estimates using encrypted data without the need for decryption, thereby ensuring data security throughout the entire estimation process. Taking into account the unknown-but-bounded noises, the underlying ANN, and the adopted HES, sufficient conditions are determined for the existence of the desired ellipsoidal set. The related secure state estimator gains are then derived by addressing optimization problems using the Lagrange multiplier method. Lastly, an example is presented to verify the effectiveness of the proposed secure state estimation approach.

Secure multi-party computation in deep learning : Enhancing privacy in distributed neural networks

Ensuring data privacy while applying Deep Learning (DL) on distributed datasets represents an essential task in the current period of critical data security. Data privacy and accuracy of models are typically impacted by traditional methods. Data privacy is of the most tremendous significance in distributed data settings, and the current research presents a novel model for DL termed Secure Multi-Party Computation (SMPC). The accuracy of the mathematical models and confidentiality of the data are frequently compelled to coexist in conventional methods. In order to enable collaborative DL without compromising private information, the recommended system uses the Paillier Homomorphic Encryption Scheme (PHES). By using innovative cryptographic methods, this decentralized method secures the confidentiality of data without utilizing a Trusted Authority (TA). By performing a thorough assessment of the CIFAR-10 and IMDB datasets, the present study demonstrates that the system the author uses is simple and scalable and that it offers accuracy on par with conventional methods. By presenting an approach for achieving a balance between the two competing demands of data security and computational performance, this method signifies a vast advance forward with a confidentiality DL.

Concise and Efficient Multi-Identity Fully Homomorphic Encryption Scheme

Concise and Efficient Multi-Identity Fully Homomorphic Encryption Scheme

A Retrospective Analysis on Fully Homomorphic Encryption Scheme

A Retrospective Analysis on Fully Homomorphic Encryption Scheme

Enhancing data privacy in wireless sensor network using homomorphic encryption

From environmental monitoring to healthcare, WSN are essential. The extensive use of these networks to gather sensitive data requires strong data privacy mechanisms. Cryptographic homomorphic encryption may solve this problem. This study uses CKKS encryption and ciphertext packing to improve Wireless Sensor Network data privacy. CKKS is a fully homomorphic encryption scheme that allows complex data operations. This makes it ideal for data analytics and computations. Ciphertext packing improves computational efficiency, making this combination a good choice for data protection in WSN environments with limited resources. Performance efficiency is crucial to evaluation. This parameter evaluates CKKS encryption with ciphertext packing’s computational resource and execution time efficiency. This study examines how this approach affects WSN node and network performance, revealing its feasibility and practicality in real-world situations. The Data Security parameter highlights CKKS encryption with ciphertext packing’s data security. This comprehensive assessment determines data confidentiality and integrity in the Wireless Sensor Network. The system’s ability to withstand data breaches and unauthorized access is crucial for protecting sensitive data. Any WSN solution must consider energy consumption. This parameter evaluates data encryption and processing energy usage, taking sensor node energy constraints into account. The assessment of CKKS encryption with ciphertext packing in WSN sheds light on its potential to improve data confidentiality while addressing WSN challenges. This research strengthens WSN data protection efforts and lays the groundwork for future advances in this vital field.

A retrospective analysis on fully homomorphic encryption scheme

A retrospective analysis on fully homomorphic encryption scheme

A new public key cryptosystem based on the non-commutative ring R

In this paper, we present a new public cryptosystem based on one of the most problems  (word problem, solving a non-linear system problem, integer factorization problem and discrete logarithm problem,...) is the conjugal classical problem (CCP) over a non commutative ring. In generally this cryptosystem is very difficult to solve for decipher. Firstly, by using the elliptic curve over the finite ring Fq[e],  where e4 = e3,  with  q = pd and p is prime number greater than or equal to 5, d ϵ ℕ*  [12] we define the non-commutative ring R. Secondly, by using the protocol of Diffie-Hellman [4] we have proposed a novel encryption scheme on R and we study the problem CCP over it. Precisely, we will make a new fully homomorphic encryption scheme over the ring R based on the two difficult problems; conjugal classical problem and discrete logarithm problem.