Homomorphic Property Research Articles

Analysing RSA and PAILLIER homomorphic Property for security in Cloud

One of the critical goals of advanced cryptography is to protect data privacy. Although protecting sensitive data has always been essential, it has become much more due to the widespread use of cloud services. Conventional encryption schemes have one drawback: data must be decrypted before processing. Best practices have long recommended that data must be secured at rest and in motion when using public cloud services, i.e., we need encryption at the storage as well as at processing levels. Homomorphic encryption is an advanced cryptographic approach in which the processing of encrypted data is possible. In this paper, we have presented the insights required for understanding homomorphic encryption approaches. We examined and compared two partial homomorphic techniques, RSA and Pallier algorithm based on efficiency, base method, and homomorphic property.

Multi-dimensional Security Range Query for Industrial IoT

The Internet of Things (IoT) has allowed for significant advancements in applications not only in the home, business, and environment, but also in factory automation. Industrial Internet of Things (IIoT) brings all of the benefits of the IoT to industrial contexts, allowing for a wide range of applications ranging from remote sensing and actuation to decentralization and autonomy. The expansion of the IoT has been set by serious security threats and obstacles, and one of the most pressing security concerns is the secure exchange of IoT data and fine-grained access control. A privacy-preserving multi-dimensional secure query technique for fog-enhanced IIoT was proposed in light of the fact that most existing range query schemes for fog-enhanced IoT cannot provide both multi-dimensional query and privacy protection. The query matrix was then decomposed using auxiliary vectors, and the auxiliary vector was then processed using BGN homomorphic encryption to create a query trapdoor. Finally, the query trapdoor may be matched to its sensor data using the homomorphic computation used by an IoT device terminal. With the application of particular auxiliary vectors, the spatial complexity might be efficiently decreased. The homomorphic encryption property might ensure the security of sensor data and safeguard the privacy of the user's inquiry mode. The results of the experiments reveal that the computing and communication expenses are modest.

Convergence of Blockchain, k-medoids and homomorphic encryption for privacy preserving biomedical data classification

Data privacy on the Internet of Medical Things (IoMT) remains a critical concern when handling biomedical data. While extant studies focus on cryptography and differential privacy, few of them capture the utility and authenticity of data. As a result, data privacy remains the primary concern when training a machine learning (ML) model with IoMT data from various data sources/owners such as k − medoids. To overcome the above-mentioned issues, this study proposes secure ​k − medoids ​that are implemented together with Blockchain and partial homomorphic cryptosystem (Paillier) to ensure authenticity and protect all entities (i.e., data owner and data analyst) data privacy. The homomorphic property of Paillier is utilized to develop secure building blocks (i.e., secure polynomial operations, secure comparison, and secure biasing operations) to ensure data privacy and eliminate dependency on any third parties. We utilized three different biomedical datasets, and these are (I) Heart Disease Data (HDD), (II) Diabetes Data (DD), and (III) Breast Cancer Wisconsin Data (BCWD). Rigorous security analysis demonstrates that secure ​k − medoids ​protect against sensitive data breaches. It also showed superior performance in both BCWD (Accuracy 97.80%, Precision 96.83%, and Recall 99.80%) and HDD (Accuracy 82.50%, Precision 81.28%, and Recall 80.50%) datasets, respectively. However, similar performance was not reflected in the case of the DD dataset. Furthermore, the study explains why such performance results are observed. In addition, the proposed system has been proven to take less execution time compared to the extant studies.

Deductive systems of pseudo-M algebras

Abstract The class of pseudo-M algebras contains pseudo-BCK, pseudo-BCI, pseudo-BCH, pseudo-BE, pseudo-CI algebras and many other algebras of logic. In this paper, the notion of deductive system in a pseudo-M algebra is introduced and its elementary properties are investigated. Closed deductive systems are defined and studied. The homomorphic properties of (closed) deductive systems are provided. The concepts of translation deductive systems and R-congruences in pseudo-M algebras are introduced and investigated. It is shown that there is a bijection between closed translation deductive systems and R-congruences. Finally, the construction of quotient algebra 𝒜/D of a pseudo-M algebra 𝒜 via a translation deductive system D of 𝒜 is given.

An Efficient Privacy-Preserving Aggregation Scheme for Multidimensional Data in IoT

Internet of Things (IoT) enables terminal devices connecting with the Internet and provides various intelligent applications by analyzing devices data. As a typical IoT technique, edge computing provides a three-tier architecture to reduce communications and improve efficiency. Specifically, edge nodes are responsible for collecting and aggregating device data, and then send processed results to the cloud for subsequent analysis. However, the data aggregation function will compromise the privacy of device data. In this article, we proposed an efficient privacy-preserving multidimensional data aggregation scheme for IoT, called PMDA. The scheme uses the Chinese remainder theorem to design a homomorphic encryption method that encryptes a multiple-dimensional small integer vector into one ciphertext and keeps linear homomorphic properties per dimension. Combining with the signature mechanism and the batch verification method, the scheme guarantees nonrepudiation of device data and enhance verification efficiency at edge nodes. Through theoretical analysis, we demonstrate that the proposed scheme can achieve correctness, privacy, authentication, and integrity. After performance evaluation, we demonstrate that our scheme is superior to other schemes in terms of computation and communication costs. In particular, as the message dimension increases, our scheme computation costs almost a tenth of others at the 80-bits security level.

Privacy-preserving association rule mining based on electronic medical system

Privacy protection during collaborative distributed association rule mining is an important research, which has been widely used in market prediction, medical research and other fields. In medical research, Domadiya et al. (Sadhana 43(8):127, 2018) focused on mining association rules from horizontally distributed healthcare data to diagnose heart disease. They claimed they proposed a more effective privacy-preserving distributed association rule mining (PPDARM) scheme. However, a serious security scrutiny of the scheme is performed, and we find it vulnerable to protect the support of the itemsets from any electronic health record (EHR) system, which is the most important parameter Domadiya et al. tried to protect. In this paper, we first present the cryptanalysis of the PPDARM scheme proposed by Domadiya et al. as well as some revised performance analyses. Then a new PPDARM scheme with less interactions is proposed to avert the shortcomings of Domadiya et al., using the homomorphic properties of the distributed Paillier cryptosystem to accomplish the cooperative computation. Our scheme allows the directed authority (miner) to obtain the final results rather than all cooperative EHR systems, in case of semi-honest but pseudo EHR systems. Moreover, security analysis and performance evaluation demonstrate our proposal is efficient and feasible.

Image Encryption Paillier Homomorphic Cryptosystem

With the increasing use of media in communications, both academia and industry pay attention to the content security of digital images. This research presents a Homomorphic cryptosystem-based asymmetric picture encryption technique (Paillier). The algorithm is used for securing images that transmit over public unsecured channels. The Homomorphic property is used in this paper, which is comprised of three steps: key generation, encryption, and decryption. To realize such approach, the encryption cryptosystem must support additional operation over encrypted data. This cryptosystem can be effective in protecting images and supporting the construction of programs that can process encrypted input and produce encrypted output. Index Terms —Homomorphic, Partiall HE, Paillier Homomorphic, Encryption.

Privacy-preserving inpainting for outsourced image

In this article, a framework of privacy-preserving inpainting for outsourced image and an encrypted-image inpainting scheme are proposed. Different with conventional image inpainting in plaintext domain, there are two entities, that is, content owner and image restorer, in our framework. Content owner first encrypts his or her damaged image for privacy protection and outsources the encrypted, damaged image to image restorer, who may be a cloud server with powerful computation capability. Image restorer performs inpainting in encrypted domain and sends the inpainted and encrypted image back to content owner or authorized receiver, who can acquire final inpainted result in plaintext domain through decryption. In our encrypted-image inpainting scheme, with the assist of Johnson–Lindenstrauss transform that can preserve Euclidean distance between two vectors before and after encryption, the best-matching block with the smallest distance to current block can be found and utilized for patch filling in Paillier-encrypted image. To eliminate mosaic effect after decryption, weighted mean filtering in encrypted domain is conducted with Paillier homomorphic properties. Experimental results show that our privacy-preserving inpainting framework can be effectively applied in secure cloud computing, and the proposed encrypted-image inpainting scheme achieves comparable visual quality of inpainted results with some typical inpainting schemes in plaintext domain.

Basic Fundamental Formulas for Wiener Transforms Associated with a Pair of Operators on Hilbert Space

Segal introduce the Fourier–Wiener transform for the class of polynomial cylinder functions on Hilbert space, and Hida then develop this concept. Negrin define the extended Wiener transform with Hayker et al. In recent papers, Hayker et al. establish the existence, the composition formula, the inversion formula, and the Parseval relation for the Wiener transform. But, they do not establish homomorphism properties for the Wiener transform. In this paper, the author establishes some basic fundamental formulas for the Wiener transform via some concepts and motivations introduced by Segal and used by Hayker et al. We then state the usefulness of basic fundamental formulas as some applications.

Fundamental relations and identities of fuzzy hyperalgebras

Inspired by fuzzy hyperalgebras and fuzzy polynomial function (term function), some homomorphism properties of fundamental relation on fuzzy hyperalgebras are conveyed. The obtained relations of fuzzy hyperalgebra are utilized for certain applications, i.e., biological phenomena and genetics along with some elucidatory examples presenting various aspects of fuzzy hyperalgebras. Then, by considering the definition of identities (weak and strong) as a class of fuzzy polynomial function, the smallest equivalence relation (fundamental relation) is obtained which is an important tool for fuzzy hyperalgebraic systems. Through the characterization of these equivalence relations of a fuzzy hyperalgebra, we assign the smallest equivalence relation α i 1 i 2 ∗ on a fuzzy hyperalgebra via identities where the factor hyperalgebra is a universal algebra. We extend and improve the identities on fuzzy hyperalgebras and characterize the smallest equivalence relation α J ∗ on the set of strong identities.

An Unlinkable Authenticated Key Agreement With Collusion Resistant for VANETs

Anonymous authentication is an important step to protect vehicular privacy and security in VANETs. To improve the efficiency of anonymous authentication in multiple security domains, VANETs integrated with blockchain attracts extensive attention. However, the existing blockchain-based authentication schemes cannot effectively achieve anonymity because colluded RSUs or vehicles can achieve linkability via the same retrieved record to destroy anonymity. To address the issue, we propose an unlinkable authenticated key agreement with collusion resistant for VANETs. For the unlinkability of V2R, firstly, a trusted authority generates multiple tickets that hide the vehicle's identity and shares them by the blockchain network. Then, vehicle generates different pseudonyms by homomorphic encryption, and RSU uses different tickets to authenticate them. Meanwhile, in view of the unlinkability of the V2V, anonymous authenticated key agreement based on homomorphic properties is designed to enable vehicles to achieve authentication without retrieving any vehicular information. Security analysis and performance evaluation show that our scheme has strict unlinkability and enhanced anonymity as well as improves the efficiency of V2R and V2V by 10% and 50%, respectively.

Factor generalized BE-semigroups through deductive systems

In this paper, we investigate some properties of homomorphisms and deductive systems of generalized BE-semigroups. In particular, we show that through every deductive system, we may get factor generalized BE-semigroup.

Factoring Continuous Characters Defined on Subgroups of Products of Topological Groups

This study is on the factorization properties of continuous homomorphisms defined on subgroups (or submonoids) of products of (para)topological groups (or monoids). A typical result is the following one: Let D=∏i∈IDi be a product of paratopological groups, S be a dense subgroup of D, and χ a continuous character of S. Then one can find a finite set E⊂I and continuous characters χi of Di, for i∈E, such that χ=∏i∈Eχi∘piS, where pi:D→Di is the projection.

Analysis of Homomorphic Cryptosystems of Benaloh and Paillier for the Construction of an Electronic Voting System

The analysis of the performance of two cryptographic algorithms (Paillier and Benaloh), in order to apply them in the construction of electronic voting systems is carried out. A description of each system and their homomorphic properties is given. Electronic voting systems based on these schemes are described. The requirements for the voting system are formulated and a comparative analysis of the voting systems based on the schemes of Paillier and Benaloh is carried out. The analysis showed that the Paillier scheme is the best and simplest method for building secure electronic voting systems, while the Benaloh scheme is more complex and computationally more time-consuming.

A New View of Homomorphic Properties of BCK-Algebra in Terms of Some Notions of Discrete Dynamical System

In the present manuscript, we introduce the concept of a discrete dynamical system (Ⱬ,Ψ) in BCK-algebra where Ⱬ is a BCK-algebra and Ψ is a homomorphism from Ⱬ to Ⱬ and establish some of their related properties. We prove that the set of all fixed points and the set of all periodic points in BCK-algebra Ⱬ are the BCK-subalgebras. We show that when a subset of BCK-algebra Ⱬ is invariant concerning Ψ. We prove that the set of all fixed points and the set of all periodic points in commutative BCK-algebra Ⱬ with relative cancellation property are the ideals of Ⱬ. We also prove that the set of all fixed points in Ⱬ is an S-invariant subset of a BCK-algebra Ⱬ.

Reversible data hiding in encrypted color images using cross-channel correlations

In recent years, the increasing requirements in cloud storage and cloud computing have made it necessary to encrypt digital images for privacy protection. Meanwhile, many reversible data hiding (RDH) algorithms in the encrypted domain have been proposed. However, most of these algorithms are for gray-level images, and the intrinsic cross-channel correlations of color images cannot be utilized to improve the embedding capacity. In this paper, we propose a novel data hiding method for encrypted color images. In the encryption stage, the homomorphic property of encryption is achieved by basic modular addition. During the data hiding process, the cross-channel correlations between R, G and B channels are generated in encrypted domain, and data hiding is performed by the difference histogram shifting. Analysis and experiments demonstrate that the proposed method is secure and the RDH performance is superior.

A Privacy-Preserving Misbehavior Detection System in Vehicular Communication Networks

5 G based vehicular communication networks support various traffic safety and infotainment use cases and rely on the periodic exchange of information. However, these messages are susceptible to several attacks which can be detected using misbehavior detection systems (MDS). MDS utilizes trust score, feedback score and other evaluation schemes to identify abnormal behavior of the vehicles. However, the trust and feedback scores used in MDS may violate the location, trajectory, or identity privacy of the vehicle. In this paper, we propose a privacy-preserving misbehavior detection system that can detect or identify misbehavior without violating the privacy of the vehicle. In the proposed method, encrypted weighted feedbacks sent from vehicles are combined using additive homomorphic properties without violating the privacy of the information. The decryption of the aggregate feedback is done securely at the trusted authority which updates the reputation score of the vehicle according to the decrypted aggregate feedback score. We have also performed comprehensive security analysis and have shown the correctness and resilience of the proposed schemes against various attacks. In addition, we have done extensive performance analysis and have shown that the computation cost of the proposed scheme is better compared to the existing schemes.

Privacy-Preserving Similarity Search With Efficient Updates in Distributed Key-Value Stores

Privacy-preserving similarity search plays an essential role in data analytics, especially when very large encrypted datasets are stored in the cloud. Existing mechanisms on privacy-preserving similarity search were not able to support secure updates (addition and deletion) efficiently when frequent updates are needed. In this article, we propose a new mechanism to support parallel privacypreserving similarity search in a distributed key-value store in the cloud, with a focus on efficient addition and deletion operations, both executed with sublinear time complexity. If search accuracy is the top priority, we further leverage Yao's garbled circuits and the homomorphic property of Hash-ElGamal encryption to build a secure evaluation protocol, which can obtain the top-R most accurate results without extensive client-side post-processing. We have formally analyzed the security strength of our proposed approach, and performed an extensive array of experiments to show its superior performance as compared to existing mechanisms in the literature. In particular, we evaluate the performance of our proposed protocol with respect to the time it takes to build the index and perform similarity queries. Extensive experimental results demonstrated that our protocol can speedup the index building process by up to 800x with 2 threads and the similarity queries by up to -7x with comparable accuracy, as compared to the state-of-the-art in the literature.

Large deviations built on max-stability

In this paper, we show that the basic results in large deviations theory hold for general monetary risk measures, which satisfy the crucial property of max-stability. A max-stable monetary risk measure fulfills a lattice homomorphism property, and satisfies under a suitable tightness condition the Laplace Principle (LP), that is, admits a dual representation with affine convex conjugate. By replacing asymptotic concentration of probability by concentration of risk, we formulate a Large Deviation Principle (LDP) for max-stable monetary risk measures, and show its equivalence to the LP. In particular, the special case of the asymptotic entropic risk measure corresponds to the classical Varadhan–Bryc equivalence between the LDP and LP. The main results are illustrated by the asymptotic shortfall risk measure.

E-Voting using Blockchain

A vote gives a citizen of a democratic country the power to elect a representative which forms a government which is of the people, by the people, and for the people. Voting forms one of the fundamental pillars of modern democracy. Conducting a transparent, verifiable, and unbiased election is a challenging task for the election commission. Earlier ballot papers were used for conducting elections but it has to face many issues like booth capturing or damaging of ballot papers of the booths where there were fewer chances of winning for a candidate. Currently, EVMs are used for conducting the election in India but there are many reports that EVMs are not fully tamperproof. EVM is not a universal acceptance across the world. Blockchain is a distributed tamperproof technology which can help in conducting election transparent and tamperproof. Here in this paper, an approach for voting using blockchain and Paillier encryption is proposed. It implies the tamperproof property of blockchain and additive homomorphic property of Paillier encryption to build a voting architecture that will make the election process trans-parent and tamperproof. Next, algorithms for registration, voting, and result declaration has been mentioned along with the results of Paillier encryption for voting.