Homomorphic Property Research Articles

Complex cubic intuitionistic fuzzy set applied to subbisemirings of bisemirings using homomorphism

We develop and analyze the concept of complex cubic intuitionistic fuzzy subbisemiring (ComCIFSBS). We investigate ComCIFSBS its characteristics and homomorphic proper-ties. We suggest the ComCIFSBS level sets of bisemiring. A cubic complex intuitionistic fuzzy set subset Ξ of bisemiring B, if and only if each non-empty level set R(t,s), where R = (μ̂ Z · ei2πβ̂ Z , ν̂ Z · ei2πγ̂ Z , μZ · ei2πβZ , νZ · ei2πγZ ) is a ComCIFSBS of B. Let υ be a ComCIFSBS bisemiring B. If Υ is a ComCIFSBS of B × B, then Z is a ComCIFSBS of bisemiring B. Let Z denote the strongest complex intuitionistic fuzzy relation bisemiring B. It is proved that all ComCIFSBSs have homomorphic images as well as homomorphic pre-images. Examples are presented to demonstrate how our findings are applied.

Finite-Timeless Local Observability for Linear Control Systems on Lie Groups

In this work, we introduce finite-timeless observability for linear control systems on Lie groups. Observability problem is to distinguish the elements of the state space by looking the images of the solutions passing through those elements in the output space. For this aim, we define almost indistinguishability and show that it is an equivalence relation. We consider linear control systems on Lie groups, where the output function is a Lie group homomorphism and study properties of the image of almost indistinguishable points from the neutral element. Thus, we relate local observability of this kind of systems to its finite-timeless local observability.

A Stealthy Communication Model for Protecting Aggregated Results Integrity in Federated Learning

Given how quickly artificial intelligence technology is developing, federated learning (FL) has emerged to enable effective model training while protecting data privacy. However, when using homomorphic encryption (HE) techniques for privacy protection, FL faces challenges related to the integrity of HE ciphertexts. In the HE-based privacy-preserving FL framework, the public disclosure of the public key and the homomorphic additive property of the HE algorithm pose serious threats to the integrity of the ciphertext of FL’s aggregated results. For the first time, this paper employs covert communication by embedding the hash value of the aggregated result ciphertext received by the client into the ciphertext of local model parameters using the lossless homomorphic additive property of the Paillier algorithm. When the server receives the ciphertext of the local model parameters, it can extract and verify the hash value to determine whether the ciphertext of the FL’s aggregated results has been tampered with. We also used chaotic sequences to select the embedding positions, further enhancing the concealment of the scheme. The experimental findings demonstrate that the suggested plan passed the Welch’s t-test, the K–L divergence test, and the K–S test. These findings confirm that ciphertexts containing covert information are statistically indistinguishable from normal ciphertexts, thereby affirming the proposed scheme’s effectiveness in safeguarding the integrity of the FL’s aggregated ciphertext results. The channel capacity of this scheme can reach up to 512 bits per round, which is higher compared to other FL-based covert channels.

Security, QoS and energy aware optimization of cloud-edge data centers using game theory and homomorphic encryption: Modeling and formal verification

Privacy and efficient data processing are crucial research areas in the field of outsourcing computing. Thus, the contribution of the paper is twofold. First of all, we develop a secure offloading technique that can process data while preserving privacy. Although RSA and Paillier cryptosystems are highly beneficial for mathematical operations on basic encrypted data due to their homomorphic properties, images are processed using permutation-ordered binary (POB) and Shamir's secret sharing (SSS). Second, a non-cooperative game theory model was formulated to examine the interactions between service providers, characterizing each edge as an M/M/1 system with an infinite queue. Through formal verification using rigorous mathematical reasoning, the suggested strategies for task offloading and resource allocation are shown to be effective in terms of security, quality of service (QoS), and energy consumption. The best-response dynamics approach is used to calculate the final strategy for each participant and assess how fairly resources are allocated. Finally, the potential of our approach is demonstrated numerically, revealing a faster convergence towards attaining Nash equilibrium in a duopoly cloud-edge data center market, granted that the necessary and sufficient conditions are met.

Secure PUF-Based Authentication Systems.

The Internet of Things faces significant security challenges, particularly in device authentication. Traditional methods of PUF-based authentication protocols do not fully address IoT's unique security needs and resource constraints. Existing solutions like Identity-Based Encryption with Physically Unclonable Functions enhance security but still struggle with protecting data during transmission. We show a new protocol that leverages PUFs for device authentication by utilizing Paillier homomorphic encryption or the plaintext equality test to enhance security. Our approach involves encrypting both the challenge-response pairs (CRPs) using Paillier homomorphic encryption scheme or ElGamal encryption for plaintext equality testing scheme. The verifier does not need access to the plaintext CRPs to ensure that sensitive data remain encrypted at all times and our approach reduces the computational load on IoT devices. The encryption ensures that neither the challenge nor the response can be deciphered by potential adversaries who obtain them during the transmission. The homomorphic property of the Paillier scheme or plaintext equality testing scheme allows a verifier to verify device authenticity without decrypting the CRPs, preserving privacy and reducing the computational load on IoT devices. Such an approach to encrypting both elements of the CRP provides resistance against CRP disclosure, machine learning attacks, and impersonation attacks. We validate the scheme through security analysis against various attacks and evaluate its performance by analyzing the computational overhead and the communication overhead. Comparison of average computational and communication time demonstrates Paillier scheme achieves approximately 99% reduction while the plaintext equality test achieves approximately 94% reduction between them.

Secure computation protocol of Chebyshev distance under the malicious model

Secure multi-party computation of Chebyshev distance represents a crucial method for confidential distance measurement, holding significant theoretical and practical implications. Especially within electronic archival management systems, secure computation of Chebyshev distance is employed for similarity measurement, classification, and clustering of sensitive archival information, thereby enhancing the security of sensitive archival queries and sharing. This paper proposes a secure protocol for computing Chebyshev distance under a semi-honest model, leveraging the additive homomorphic properties of the NTRU cryptosystem and a vector encoding method. This protocol transforms the confidential computation of Chebyshev distance into the inner product of confidential computation vectors, as demonstrated through the model paradigm validating its security under the semi-honest model. Addressing potential malicious participant scenarios, a secure protocol for computing Chebyshev distance under a malicious model is introduced, utilizing cryptographic tools such as digital commitments and mutual decryption methods. The security of this protocol under the malicious model is affirmed using the real/ideal model paradigm. Theoretical analysis and experimental simulations demonstrate the efficiency and practical applicability of the proposed schemes.

Cryptanalysis of a privacy-preserving authentication scheme based on private set intersection

Abstract Continuous and context-aware authentication mechanisms have been proposed as complementary security mechanisms to password-based authentication for computer devices that are handled directly by humans, such as smart phones. Such authentication mechanisms incur some privacy issues as user-dependent features are revealed to the authentication server, which is assumed to be untrusted. Domingo-Ferrer et al. proposed a privacy-preserving protocol for context-aware user authentication on the basis of private set intersection and Paillier homomorphic encryption. This approach enables user authentication based on establishing the number of similarities between sampled user context data and reference context data, without revealing any plaintext data to either party. The authors claim that their scheme is secure against malicious adversaries. In this article, we show that Domingo-Ferrer et al.’s scheme is insecure by means of two undetectable attacks that reveal all user information despite the encryption. The Paillier encryption primitive has a homomorphic property that we observe not only lacks relevance but, indeed, incurs a vulnerability that is exploited in the proposed cryptanalysis. This means that special care needs to be taken considering homomorphic properties of cryptographic primitives used in cryptographic protocols. Our cryptanalysis may therefore have a general interest regarding the design of cryptographic protocols.

Comprehensive Work on Interval-valued Fuzzy Translation and Multiplication in Z-subalgebra of Z-algebra

In this paper, we explore interval-valued fuzzy translation and multiplication in z-algebras, delving into their detailed properties through the application of the concepts of fuzzy z- algebras and fuzzy z-subalgebras in z-algebras. Our specific focus is on presenting the notions of int-val-fuz-translation and multiplication, along with elucidating their homomorphism properties within the scope of this work. Additionally, we investigate several results based on in-val-fuz magnified translation in z-subalgebras.

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.

Further results on generalized cellular automata

Given a finite set A and a group homomorphism ϕ : H → G , a ϕ -cellular automaton is a function T : A G → A H that is continuous with respect to the prodiscrete topologies and ϕ -equivariant in the sense that h · T ( x ) = T ( ϕ ( h ) · x ) , for all x ∈ A G , h ∈ H , where · denotes the shift actions of G and H on A G and AH , respectively. When G = H and ϕ = id , the definition of id -cellular automata coincides with the classical definition of cellular automata. The purpose of this paper is to expand the theory of ϕ -cellular automata by focusing on the differences and similarities with their classical counterparts. After discussing some basic results, we introduce the following definition: a ϕ -cellular automaton T : A G → A H has the unique homomorphism property (UHP) if T is not ψ-equivariant for any group homomorphism ψ : H → G , ψ ≠ ϕ . We show that if the difference set Δ ( ϕ , ψ ) is infinite, then T is not ψ-equivariant; it follows that when G is torsion-free abelian, every non-constant T has the UHP. Furthermore, inspired by the theory of classical cellular automata, we study ϕ -cellular automata over quotient groups, as well as their restriction and induction to subgroups and supergroups, respectively.

An Electronic Voting Scheme with Privacy Protection

Privacy protection is one of the key focuses of electronic voting technology, and the privacy information of voting participants is particularly important, such as their personal identity information and election voting results. Protecting the privacy information of participants can ensure the fairness and trustworthiness of voting activities. When designing and implementing electronic voting systems, privacy protection issues must be fully considered. In this paper, an electronic voting scheme based on ElGamal homomorphic encryption properties is proposed. The scheme utilizes the feature of homomorphic encryption to encrypt the voting results of participants and decrypt the voting results to obtain the final data. This scheme can to some extent improve the anonymity of voting participants and ensure the security of voting data by the vote counting center.

Research on transparent management of economic transactions using blockchain technology

Abstract The data asset trading market is gradually emerging with the development of the digital economy, making the development of a safe and effective data asset trading management system an important research direction. This paper uses blockchain technology to create a transparent management system for economic transactions. A PHRP algorithm is proposed to guarantee the security of the transaction, addressing the privacy protection issue involved in the transaction process. The PHRP algorithm calculates the actual transaction amount by encrypting both the input and output amounts, utilizing the additive homomorphic property. It also ensures the undeniability and integrity of the transaction by encrypting and committing random numbers. The relevant test results show that the transaction privacy protection scheme based on the PHRP algorithm can better meet the requirements of the economic transaction management system. Users’ satisfaction with the system constructed in this paper in terms of perceived usefulness and perceived ease of use scored high on average, 4.23 and 4.17, respectively, and expressed average for security, for which this paper proposes relevant improvement strategies.

New tag-based signatures and their applications on linearly homomorphic signatures

Tag-based signature schemes can be efficiently converted into digital signature schemes using a generic transformation. However, there is no signature scheme that admits k>1 fold tag-collisions in the lattice environment as pointed by Ducas and Micciancio (2014). This work answers this problem in the stateful case. We use homomorphic hash functions and hash functions of tags to construct a SIS-based stateful tag-based signature (STS) scheme that admits k>1 fold tag-collisions. Messages are encoded prior to the signing procedure such that any k sequentially signed messages with the same tag form a basis for a vector subspace. The security analysis adopts a new abstraction called vector-space oriented partition. With the same technique, two STS schemes based on the CDH and the RSA assumptions, respectively, are proposed.As an application of our STS schemes, we show that those having field (or quasi-field) as message space can be converted into linearly homomorphic signature (LHS) schemes. Therefore, we immediately obtain CDH/RSA-based LHS scheme in the standard model under the same weaker assumption. Our LHS schemes can be viewed as “removing the restriction on the homomorphic property” from the related STS schemes. They have similar public key and signature sizes as the existing counterparts.

Secure and efficient multi-key aggregation for federated learning

Federated learning (FL) is a distributed machine learning framework that aims to provide privacy for local datasets while learning a global machine learning model. However, the updates exchanged in FL may indirectly reveal information about the local training datasets. To protect the confidentiality of updates, various solutions using cryptographic schemes such as secret sharing, differential privacy, and homomorphic encryption have been developed. The solutions using secret sharing often have high communication costs, while those using differential privacy require a trade-off between accuracy and privacy. Homomorphic encryption has been used to address these challenges to reduce communication costs and provide provable security. However, existing solutions based on homomorphic encryption require clients to use the same public-private key pair, which may lead to local updates disclosure. To address the existing challenges, we propose a secure and efficient multi-key aggregation protocol (MKAgg) that utilizes homomorphic encryption. The protocol allows clients to drop out at any point during the process. We construct MKAgg based on a two-server model and adopt a proxy re-encryption scheme with additively homomorphic properties to implement secure and efficient ciphertext transformation and calculation. We provide security proof to demonstrate that our MKAgg protocol meets the required security standards. Furthermore, we perform an efficiency analysis of MKAgg and evaluate its performance on various datasets. The results affirm that MKAgg is both effective and efficient for aggregation in the multi-key setting. We then apply MKAgg in FL and develop a multi-key privacy-preserving neural network scheme called MKPNFL. We analyze the security of MKPNFL and conduct tests using real-world datasets. The results demonstrate that MKPNFL is secure and practical for real-world applications.

Generalized commutativity of intuitionistic fuzzy finite state machine

Concepts of generalized commutative intuitionistic fuzzy finite state machines and generalized switching intuitionistic fuzzy finite state machines are proposed in this paper, and properties of these two kinds of intuitionistic fuzzy finite state machines are investigated. By using the conditions associated with generalized commutativity, a kind of congruences of intuitionistic fuzzy finite state machines is defined. Homomorphic properties of generalized commutative intuitionistic fuzzy finite state machine are also discussed. Moreover, products of generalized commutative intuitionistic fuzzy finite state machines and products of generalized switching intuitionistic fuzzy finite state machines are studied, and some related properties are proved.

Homomorphic additive lightweight block cipher scheme for securing IoT applications

Recent emerging systems and applications may be able to process encrypted data to preserve user privacy. However, designing an efficient Homomorphic Encryption (HE) algorithm that can achieve good performance and robustness against attacks is primordial to better respond to real-time requirements and tiny devices. Unfortunately, existing homomorphic asymmetric schemes suffer from high computational complexity, storage, and communication overhead. On the other hand, homomorphic symmetric approaches suffer from a low level of security, and a big majority of them suffer from weaknesses in defending against known plain-text/cipher-text attacks. In this paper, an efficient symmetric homomorphic block cipher scheme is proposed to allow the performing of addition and average operations over cipher-texts. It defines a simple round function that should be iterated for nr≥2 iterations. Moreover, the dynamic key approach is used in this solution to reach a high level of security. To the best of our knowledge, it is a new symmetric additive homomorphic block cipher structure, and it defines three novel variants of addition round keys and two novel variants of the diffusion matrix. Furthermore, the proposed solution is analyzed in detail and evaluated in terms of security and performance levels. In comparison with well-known asymmetric additive HE schemes such as Paillier, BGN (Boneh, Goh, Nissim), BCP (Bresson, Catalano, Pointcheval), and ElGamal ECC (Elliptic Curve ), the obtained results prove that the proposed solution reaches a good balance between both performance and security levels. Therefore, the proposed solution can be applied on limited devices and especially for real-time scenarios that require the additive homomorphic property and the average calculation over cipher-texts.

3D Object Watermarking from Data Hiding in the Homomorphic Encrypted Domain

For over a decade, 3D objects are an increasingly popular form of media. It has become necessary and urgent to secure them during their transmission or archiving. In this article, we propose a new method to obtain a watermarked 3D object from high-capacity data hiding in the encrypted domain. Based on the homomorphic properties of the Paillier cryptosystem, our proposed method allows us to embed several secret messages in the encrypted domain with a high-capacity. These messages can be extracted in the plain-text domain after the 3D object decryption. To the best of our knowledge, we are the first to propose a data hiding method in the encrypted domain where the high-capacity watermark is conserved in the plain-text domain after the 3D object is decrypted. The encryption and the data hiding in the encrypted domain are format compliant and without size expansion, despite the use of the Paillier cryptosystem. Each time a new message is embedded in the encrypted domain, flags are added in order to indicate which blocks are still available for the embedding of additional messages. After the decryption of a watermarked encrypted 3D object, our method produces a watermarked 3D object which is visually very similar to the original 3D object. From the decrypted watermarked 3D object, we can then extract all the embedded messages directly in the plain-text domain, without the need for an auxiliary file. Moreover, large keys are used, rending our method secure for real-life applications.

On the Characterization of Antineutrosophic Subgroup

This article gives some essential scopes to study the characterizations of the antineutrosophic subgroup and antineutrosophic normal subgroup. Again, several theories and properties have been mentioned which are essential for analyzing their mathematical framework. Moreover, their homomorphic properties have been discussed.

A Novel Digital Signature Scheme for Advanced Asymmetric Encryption Techniques

Digital signature schemes are practical mechanisms for achieving message integrity, authenticity, and non-repudiation. Several asymmetric encryption techniques have been proposed in the literature, each with its proper limitations. RSA and El Gamal prove their robustness, but are unsuitable in several domains due to their computational complexity. Other asymmetric encryption schemes have been proposed to provide a cloud homomorphic encryption service, where the researchers focused only on how to ensure the homomorphic property. This paper proposes a new digital signature scheme dedicated to a family of encryption techniques. The proposal consists of two parts: the first focused on the secret key, and the second focused on the public key. Signature validity checking was performed by multiplying these two parts to reform again the sender’s public key, then comparing the result with the decrypted message. The validation of the decrypted message guarantees data integrity, where the signer public key is used to ensure authenticity. The proposed scheme takes a shorter execution time for the entire signature operation, including signing and verification, compared to other modern techniques. The analysis showed its robustness against private key recovery and forgery attacks. The implementation results of the proposed scheme showed promising performance in terms of complexity and robustness. The results confirmed that the proposed scheme is efficient and effective for signature generation and verification.

Decentralized privacy-preserving truth discovery for crowd sensing

Truth discovery is an efficient technique for tackling data conflict problems in crowd sensing for distributed data collection. As the sensory data to be collected may include sensitive information about users, privacy-preserving truth discovery has attracted significant attention in recent years. Most existing studies apply a centralized architecture based on a cryptographic system, which may be vulnerable to single-point attacks and also has a very high computational cost. In this paper, we propose DPriTD, a decentralized privacy-preserving framework for truth discovery in crowd sensing. The proposed approach leverages the additively homomorphic property of Shamir's Secret Sharing scheme to protect user's privacy. DPriTD provides a strict privacy guarantee for crowd sensing applications. Because each sensitive data point, considered to be a secret, is split into a batch of shares, and the secret cannot be recovered unless a sufficient number of shares are aggregated, DPriTD achieves effective truth discovery while protecting sensitive data from collusion attacks. Furthermore, DPriTD is independent of a centralized server and can perform reliably when not all participants are online in real time. It thus enhances the robustness of a crowd sensing system. Extensive experiments conducted on real-world datasets demonstrate the high performance of our method compared with existing mechanisms.