Search Results (58)

Quantum secret sharing (QSS) faces inherent limitations in scaling to multi-user networks due to excess noise introduced by highly asymmetric beam splitters (HABSs) in chain-structured topologies. To overcome this challenge, we propose an optical frequency comb-based continuous-variable QSS (OFC CV-QSS) scheme that establishes parallel frequency channels between users and the dealer via OFC-generated multi-wavelength carriers. By replacing the chain-structured links with dedicated frequency channels and integrating the Chinese remainder theorem (CRT) with a decentralized architecture, our design eliminates excess noise from all users using HABS while providing mathematical- and physical-layer security. Simulation results demonstrate that the scheme achieves a more than 50% improvement in maximum transmission distance compared to chain-based QSS, with significantly slower performance degradation as users scale to 20. Numerical simulations confirm the feasibility of this theoretical framework for multi-user quantum networks, offering dual-layer confidentiality without compromising key rates. Full article

Multi-Key Fully Homomorphic Encryption (MKFHE) offers a powerful solution for secure multi-party computations, where data encrypted under different keys can be jointly computed without decryption. However, existing MKFHE schemes still face challenges such as large parameter sizes, inefficient evaluation key generation, complex homomorphic multiplication processes, and limited scalability in multi-hop scenarios. In this paper, we propose an enhanced multi-hop MKFHE scheme based on the Brakerski-Gentry-Vaikuntanathan (BGV) framework. Our approach eliminates the need for an auxiliary Gentry-Sahai-Waters (GSW)-type scheme, simplifying the design and significantly reducing the public key size. We propose novel algorithms for evaluation key generation and key switching that simplify the computation while allowing each party to independently precompute and share its evaluation keys, thereby reducing both computational overhead and storage costs. Additionally, we combine the tensor product and key switching processes through homomorphic gadget decomposition, developing a new homomorphic multiplication algorithm and achieving linear complexity with respect to the number of parties. Furthermore, by leveraging the Polynomial Chinese Remainder Theorem (Polynomial CRT), we design a ciphertext packing technique that transforms our BGV-type MKFHE scheme into a batched scheme with improved amortized performance. Our schemes feature stronger multi-hop properties and operate without requiring a predefined maximum number of parties, offering enhanced flexibility and scalability compared to existing similar schemes. Full article

Secret sharing is a robust data protection technique that secures sensitive information by partitioning it into multiple shares, such that the original data can only be reconstructed when a sufficient number of shares are combined. While this method has seen remarkable progress in the realm of images, its exploration and application in 3D models remain in their early stages. Given the growing prominence of 3D models in multimedia applications, ensuring their security and privacy has emerged as a critical area of research. At present, secret sharing approaches for 3D models predominantly rely on the vertex coordinates of the model as the basis for embedding and reconstructing secret messages. However, due to the limited quantity of vertex coordinates, these methods face significant constraints in embedding capacity, thereby limiting the potential of 3D models in secure data sharing. In contrast, the vertex indices of polygons, characterized by higher information density and greater structural flexibility, present a promising alternative medium for embedding secret shares. Building on this premise, the present study investigates the feasibility of leveraging shared vertex indices as a foundation for message embedding. It highlights the advantages of this approach in enhancing both the embedding capacity and the overall security of 3D models. By integrating the Chinese Remainder Theorem into vertex index-based sharing, the proposed method strengthens existing algorithms, offering improved model protection and enhanced embedding security. Experimental evaluations reveal that, compared to traditional vertex coordinate-based methods, incorporating vertex indices into secret sharing techniques significantly increases embedding efficiency while bolstering the security of 3D models. This study not only introduces an innovative approach to safeguarding 3D model data but also paves the way for the broader application of secret sharing techniques in the future. Full article

This paper explores advancements in the Gentry-Sahai-Waters (GSW) fully homomorphic encryption scheme (FHE), addressing challenges related to message data range limitations and ciphertext size constraints. We leverage the well-known parallelizing technology—the Chinese Remainder Theorem (CRT)—to tackle the message decomposition, significantly expanding the allowable input message range to the entire plaintext space. This approach enables unrestricted message selection in the GSW scheme and supports parallel homomorphic operations without intermediate decryption. Additionally, we adapt existing ciphertext compression techniques, such as the PVW-like scheme, to reduce the memory overhead associated with ciphertexts. Our experimental results demonstrate the effectiveness of combining the proposed CRT-based decomposition with the PVW-like compression in increasing the upper bound of message values and improving the scheme’s capacity for consecutive homomorphic operations. However, compression introduces a trade-off, necessitating a reduced message range due to error accumulation in successive HE operations. This research contributes to enhancing the practicality and efficiency of the GSW encryption scheme for complex computational scenarios while managing the balance between expanded message range, computational complexity, and storage requirements. Full article

In optical networks, designing optical orthogonal codes (OOCs) with appropriate parameters is essential for enhancing the overall system performance. They are divided into two categories, constant-weight OOCs (CW-OOCs) and variable-weight OOCs (VW-OOCs), based on the number of distinct Hamming weights present in their codewords. This paper introduces a method for constructing VW-OOCs of length $kp$ by using the structure of an integer ring and the Chinese Remainder Theorem. In particular, we present some specific VW-OOCs with weights of 3, 4, or 5. The results demonstrate that certain optimal VW-OOCs can be obtained with parameters that are not covered in the existing literature. Full article

Vehicular ad-hoc networks (VANETs) can significantly improve the level of urban traffic management. However, the sender unlinkability has become an intricate issue in the field of VANETs’ encryption. As the sender signcrypts a message, the receiver has to use the sender’s identity or public key to decrypt it. Consequently, the sender can be traced using the same identity or public key, which poses some security risks to the sender. To address this issue, we present an unlinkable and revocable signcryption scheme (URSCS), where an efficient and powerful signcryption mechanism is adopted for communication. The sender constructs a polynomial to generate a unique session key for each communication, which is then transmitted to a group of receivers, enabling the same secret message to be sent to multiple receivers. Each time a secret message is sent, a new key pair is generated, and an anonymization mechanism is introduced to conceal the true identity of the vehicle, thus preventing malicious attackers from tracing the sender through the public key or the real identity. With the introduction of the identification public key, this scheme supports either multiple receivers or a single receiver, where the receiver can be either road side units (RSUs) or vehicles. Additionally, a complete revocation mechanism is constructed with extremely low communication overhead, utilizing the Chinese remainder theorem (CRT). Formal and informal security analyses demonstrate that our URSCS scheme meets the expected security and privacy requirements of VANETs. The performance analysis shows that our URSCS scheme outperforms other represented schemes. Full article

With the rapid development of the information age, smart meters play an important role in the smart grid. However, there are more and more attacks on smart meters, which mainly focus on the identity authentication of smart meters and the security protection of electricity consumption data. In this paper, an efficient lightweight smart meter authentication scheme is proposed based on the Chinese Remainder Theorem (CRT), which can realize the revocation of a single smart meter user by publishing a secret random value bound to the smart meter identity. The proposed scheme not only protects the security of smart meter electricity consumption data by using encryption, but also resists identity attacks from both internal and external adversaries by using hash functions and timestamps. Experiment shows that the proposed scheme has lower computation overhead and communication overhead than other authentication schemes and is more suitable for smart meter authentication. Full article

Federated learning (FL) is increasingly challenged by security and privacy concerns, particularly vulnerabilities exposed by malicious participants. There remains a gap in effectively countering threats such as model inversion and poisoning attacks in existing research. To address these challenges, this paper proposes the Effective Private-Protected Federated Learning Aggregation Algorithm (EPFed), a framework that utilizes a blockchain platform, homomorphic encryption, and secret sharing to fortify the data privacy and computational efficiency in a federated learning environment. EPFed works by establishing “trust groups” through the unique integration of a Chinese Remainder Theorem-based secret sharing scheme with Paillier homomorphic encryption, streamlining secure model parameter exchange and aggregation while minimizing the computational load. Our performance-driven aggregation strategy leverages local performance metrics to safeguard against malicious contributions, ensuring both the integrity and efficiency of the learning process. The evaluations demonstrate that EPFed achieves a remarkable accuracy rate of 92.5%, thereby confirming the advanced nature of the proposed solution in addressing the pressing challenges of FL. Full article

The federated learning on large-scale mobile terminals and Internet of Things (IoT) devices faces the issues of privacy leakage, resource limitation, and frequent user dropouts. This paper proposes an efficient secure aggregation method based on multi-homomorphic attributes to realize the privacy-preserving aggregation of local models while ensuring low overhead and tolerating user dropouts. First, based on EC-ElGamal, the homomorphic pseudorandom generator, and the Chinese remainder theorem, an efficient random mask secure aggregation method is proposed, which can efficiently aggregate random masks and protect the privacy of the masks while introducing secret sharing to achieve tolerance of user dropout. Then, an efficient federated learning secure aggregation method is proposed, which guarantees that the computation and communication overheads of users are only O(L); also, the method only performs two rounds of communication to complete the aggregation and allows user dropout, and the aggregation time does not increase with the dropout rate, so it is suitable for resource-limited devices. Finally, the correctness, security, and performance of the proposed method are analyzed and evaluated. The experimental results indicate that the aggregation time of the proposed method is linearly related to the number of users and the model size, and it decreases as the number of dropped out users increases. Compared to other schemes, the proposed method significantly improves the aggregation efficiency and has stronger dropout tolerance, and it improves the efficiency by about 24 times when the number of users is 500 and the dropout rate is 30%. Full article

Conditional Privacy Preserving Authentication (CPPA) schemes are an effective way of securing communications in vehicular ad hoc networks (VANETs), as well as ensuring user privacy and accountability. Cryptanalysis plays a crucial role in pointing out the vulnerabilities in existing schemes to enable the development of more resilient ones. In 2019, Zhang proposed a CPPA scheme for VANET security (PA-CRT), based on identity batch verification (IBV) and Chinese Remainder Theorem (CRT). In this paper, we cryptanalyze Zhang’s scheme and point out its vulnerability to impersonation and repudiation attacks. In 2023, Zhang’s scheme was cryptanalyzed by Tao; however, we point out flaws in Tao’s cryptanalysis due to invalid assumptions; hence, we propose countermeasures to Tao’s attacks. Furthermore, in 2021, Xiong proposed a Certificateless Aggregate Signature (CLAS) scheme which is also cryptanalyzed in this paper. Finally, we analyze the causes and countermeasures by pointing out the vulnerabilities in each scheme that enabled us to launch successful attacks and proposing changes that would fortify these schemes against similar attacks in the future. Full article

A new information theoretic condition is presented for reconstructing a discrete random variable X based on the knowledge of a set of discrete functions of X. The reconstruction condition is derived from Shannon’s 1953 lattice theory with two entropic metrics of Shannon and Rajski. Because such a theoretical material is relatively unknown and appears quite dispersed in different references, we first provide a synthetic description (with complete proofs) of its concepts, such as total, common, and complementary information. The definitions and properties of the two entropic metrics are also fully detailed and shown to be compatible with the lattice structure. A new geometric interpretation of such a lattice structure is then investigated, which leads to a necessary (and sometimes sufficient) condition for reconstructing the discrete random variable X given a set $\{X_1,\dots ,X_n\}$ of elements in the lattice generated by X. Intuitively, the components $X_1,\dots ,X_n$ of the original source of information X should not be globally “too far away” from X in the entropic distance in order that X is reconstructable. In other words, these components should not overall have too low of a dependence on X; otherwise, reconstruction is impossible. These geometric considerations constitute a starting point for a possible novel “perfect reconstruction theory”, which needs to be further investigated and improved along these lines. Finally, this condition is illustrated in five specific examples of perfect reconstruction problems: the reconstruction of a symmetric random variable from the knowledge of its sign and absolute value, the reconstruction of a word from a set of linear combinations, the reconstruction of an integer from its prime signature (fundamental theorem of arithmetic) and from its remainders modulo a set of coprime integers (Chinese remainder theorem), and the reconstruction of the sorting permutation of a list from a minimal set of pairwise comparisons. Full article

In the dynamic landscape of electronic commerce, the robustness of platforms is a critical determinant of operational continuity and trustworthiness, necessitating innovative approaches to fault tolerance. This study pioneers an advanced strategy for enhancing fault tolerance in e-commerce systems, utilizing non-positional numbering systems (NPNS) inspired by the mathematical robustness of the Chinese Remainder Theorem (CRT). Traditional systems rely heavily on positional numbering, which, despite its ubiquity, harbors limitations in flexibility and resilience against computational errors and system faults. In contrast, NPNS, characterized by their independence, equitability, and residue independence, introduce a transformative potential for system architecture, significantly increasing resistance to disruptions and computational inaccuracies. Our discourse extends beyond theoretical implications, delving into practical applications within contemporary e-commerce platforms. We introduce and elaborate on new terminologies, concepts, and a sophisticated classification system for fault-tolerance mechanisms within the framework of NPNS. This nuanced approach not only consolidates understanding but also identifies underexplored pathways for resilience in digital commerce infrastructure. Furthermore, this research highlights the empirical significance of adopting NPNS, offering a methodologically sound and innovative avenue to safeguard against system vulnerabilities. By integrating NPNS, platforms can achieve enhanced levels of redundancy and fault tolerance, essential for maintaining operational integrity in the face of unforeseen system failures. This integration signals a paradigm shift, emphasizing proactive fault mitigation strategies over reactive measures. Conclusively, this study serves as a seminal reference point for subsequent scholarly endeavors, advocating for a shift towards NPNS in e-commerce platforms. The practical adaptations suggested herein are poised to redefine stakeholders’ approach to system reliability, instigating a new era of confidence in e-commerce engagements. Full article

In this paper, a study is carried out related to improving the reliability and fault tolerance of Fog Computing systems. This work is a continuation of previous studies. In the past, we have developed a method of fast operation for determining the sign of a number in the Residue Number System based on the Akushsky Core Function. We managed to increase the efficiency of calculations by using the approximate rank of a number. However, this result is not final. In this paper, we consider in detail the methods and techniques of the Akushsky Core Function. During research, it was found that the so-called weights can be equal to random variables. Based on the data obtained, we have developed a method for determining the optimal weights for the Akushsky Core Function. The result obtained allows you to obtain a performance advantage due to the preliminary identification of optimal weights for each set of moduli. Full article

Secure online consultations can provide convenient medical services to patients who require experts from different regions. Moreover, this process can save time, which is critical in emergency cases, and cut medical costs. However, medical services need a high level of privacy protection that advances the difficulty of a construction method. It is a good idea to construct a virtual private chain through public networks by means of cryptology and identity verification. For this purpose, novel protocols are proposed to finish the package layout, secure transmission, and authorization. By mining the special characteristics of this application, two different kinds of encryption channels were designed to support the proposed protocol to ensure the secure transmission of data. And Hash values and multiple checking were employed in the transmission package to find the incompleteness of data related to network errors or attacks. Besides the secure communication of medical information, the Extended Chinese Remainder Theorem was utilized to finish the approval during a change in committee in emergency situations. Finally, example case was used to verify the effectiveness of the total methods. Full article

As resources provided by single unmanned aerial vehicles (UAVs) are limited, we propose a cross-platform UAV swarm key management scheme for task scenarios in denied environments. In denied environments where the communication link is open and the UAV nodes may go invalid, secure communication is often at stake. To solve this problem, we propose a key management scheme which, based on the Chinese remainder theorem (CRT) and the Hash function, constructs a swarm key by combining the local key and the session key to reduce the overhead of individual UAV nodes in the swarm. Meanwhile, the swarm head node constructs broadcast messages according to the key update needs, which reduces the overhead of the member nodes, improves the efficiency of key updating, and fulfills the key establishment and updating of the UAV swarm. Experiments show that our proposed scheme has forward and backward security and can defend against collusion attacks and replay attacks; our method was compared with other methods on the MIRACL cryptographic library in Visual Studio 2019, and it was found that our method has a lower computing and communication overhead, provides a solution to cross-platform key management of UAV swarms in denied environments, and ensures safe communication of UAVs in the swarm. Full article