Shamir's Threshold Research Articles

A Blockchain-Based Secure Covert Communication Method via Shamir Threshold and STC Mapping

A Blockchain-Based Secure Covert Communication Method via Shamir Threshold and STC Mapping

A Stealthy Communication Model with Blockchain Smart Contract for Bidding Systems

With the widespread adoption of blockchain technology, its public ledger characteristic enhances transaction transparency but also amplifies the risk of privacy breaches. Attackers can infer users’ real identities and behaviors by analyzing public transaction patterns and address relationships, posing a severe threat to users’ privacy and security, and thus hindering further advancements in blockchain applications. To address this challenge, covert communication has emerged as an effective strategy for safeguarding the privacy of blockchain users and preventing information leakage. But existing blockchain-based covert communication schemes rely solely on the immutability of blockchain itself for robustness and suffer from low transmission efficiency. To tackle these issues, this paper proposes a stealthy communication model with blockchain smart contract for bidding systems. The model initiates by preprocessing sensitive information using a secret-sharing algorithm-the Shamir (t, n) threshold scheme-and subsequently embeds this information into bidding amounts, facilitating the covert transfer of sensitive data. We implemented and deployed this model on the Ethereum platform and conducted comprehensive performance evaluations. To assess the stealthiness of our approach, we employed a suite of statistical tests including the CDF, the Kolmogorov–Smirnov test, Welch’s t-test and K–L divergence. These analyses confirmed that amounts carrying concealed information were statistically indistinguishable from regular transactions, thus validating the effectiveness of our solution in maintaining the anonymity and confidentiality of information transmission within the blockchain ecosystem.

An identity-verifiable quantum threshold group signature scheme based on three-particle GHZ states

With the advancement of the new generation of information technology in recent years, quantum digital signatures have been widely concerned. Among them, quantum threshold group signatures have become a hot research field due to their advantages such as low cost and strong scalability. Therefore, in this paper, we propose an identity-verifiable quantum threshold group signature scheme based on three-particle GHZ states. The characteristics of the scheme are as follows. The signers can reconstruct the key K for signature’s generation and verification by using the Shamir threshold secret sharing scheme. A quantum signature is generated by performing controlled-not operations, von Neumann measurements, and quantum Fourier transform. When the signature is verified, only classical hash values need to be compared, without comparing quantum states. Identity verification is performed between participants by using hash functions. The efficiency of the scheme is improved by using super-dense coding. Security analysis shows that our scheme is unforgeable and undeniable.

EFTA: An Efficient and Fault-Tolerant Data Aggregation Scheme without TTP in Smart Grid

Abstract With the rapid construction and implementation of smart grid, lots of studies have been conducted to explore how to ensure the security of information privacy. At present, most privacy-preserving data aggregation schemes in smart grid achieve privacy data protection through homomorphically encrypted data aggregation. However, these data aggregation schemes tend to rely on a trusted third party (TTP), and fail to efficiently handle the case of a meter failure. Besides, they are less flexible for overall user management, and resistance to collusion attacks needs to be improved. In this paper, we propose an efficient and robust privacy-preserving data aggregation scheme without TTP, called EFTA. Overall, the scheme eliminates the reliance on a TTP, combines with Shamir threshold secret sharing scheme to increase overall fault tolerance, supports flexible and dynamic user management, and effectively defends against entity initiated collusion attacks. According to security and performance analysis results, the scheme proposed in this paper meets the multiple security requirements of smart grid, and is more efficient in terms of overall overhead compared to the existing privacy-preserving data aggregation schemes.

A Practical Multiparty Private Set Intersection Protocol Based on Bloom Filters for Unbalanced Scenarios

Multiparty Private Set Intersection (MPSI) is dedicated to finding the intersection of datasets of multiple participants without disclosing any other information. Although many MPSI protocols have been presented, there are still some important practical scenarios that require in-depth consideration such as an unbalanced scenario, where the server’s dataset is much larger than the clients’ datasets, and in cases where the number of participants is large. This paper proposes a practical MPSI protocol for unbalanced scenarios. The protocol uses the Bloom filter, an efficient data structure, and the ElGamal encryption algorithm to reduce the computation of clients and the server; adopts randomization technology to solve the encryption problem of the 0s in the Bloom filter; and introduces the idea of the Shamir threshold secret-sharing scheme to adapt to multiple environments. A formal security proof and three detailed experiments are given. The results of the experiments showed that the new protocol is very suitable for unbalanced scenarios with a large number of participants, and it has a significant improvement in efficiency compared with the typical related protocol (TIFS 2022).

Simple and efficient threshold changeable secret sharing

Shamir's (t, n) threshold secret sharing (SS) is one of the most important cryptographic primitives in various security applications designed to protect highly sensitive information, such as intellectual property and network security. A dealer in a (t, n) threshold SS divides the secret into n shares such that with t or more than t of these shares, the secret can be retrieved; but with less than t of these shares, no information of the secret can be revealed. In order to adapt the dynamic environment in various applications, the threshold changeable SS (TCSS) allows the threshold of the original secret to be dynamically adjusted. Note that Shamir's original SS is unable to achieve this property. In the literature, most existing TCSS schemes are suffering from limitations that either it requires a trusted dealer to generate and distribute new shares, or requires interactions among shareholders to generate new shares. In this paper, we propose a novel idea to construct a dealer-free and non-interactive TCSS based on pairwise keys between users. Research papers related to pairwise key distribution schemes have been published over last 40 years and it has become one of fundamental tools used in design of cryptographic solutions. First, we show that our idea can be used to construct a scheme for anonymously releasing data and a secure multiparty computation scheme. Both schemes are very simple and security analysis can be understood easily. Second, we demonstrate that a TCSS can also be designed based on same approach. Our design of TCSS is novel and it can be applied to convert any existing SS into a TCSS.

SPRA: Scalable policy‐based regulatory architecture for blockchain transactions

AbstractImplementing effective regulation of blockchain transactions has become a research hotspot in recent years. However, most of the current regulatory schemes are customized for specific blockchain applications and lack versatility and scalability. Meanwhile, these schemes cannot guarantee fairness due to the non‐disclosure of regulatory policies and regulatory processes. To address these issues, a scalable policy‐based regulatory architecture (SPRA) is proposed for blockchain transactions that separates regulation and application to provide sufficient scalability. SPRA is a four‐layer model (permission layer, regulation layer, bridge layer, and business layer). A regulatory policy description language (XRPL) is designed to define the regulatory rules and specifications for interoperability between the layers. A decentralized jury mechanism (JuryBC) based on the Shamir threshold secret sharing algorithm and Pedersen commitment is proposed at the regulation layer to avoid regulatory arbitrariness and unfairness. We also construct a secure and efficient regulatory data sharing scheme (RDShare) at the business layer using an attribute‐based encryption algorithm. The key parameters in both JuryBC and RDShare can be specified in the regulatory policy to suit different application scenarios. Finally, the security of the architecture is analyzed and the feasibility and scalability of the architecture through simulation experiments are demonstrated.

A secured blockchain method for multivariate industrial IoT-oriented infrastructure based on deep residual squeeze and excitation network with single candidate optimizer

IoT infrastructures have been growing in recent years across a variety of industrial applications in sustainable smart cities and communities, including smart manufacturing and smart industries. Infrastructure geared towards Internet of Things also includes Cyber-Physical System (CPS). With a distributed environment, CPS has experienced significant success in industrial applications and critical infrastructure. However, there are numerous difficulties in such an environment, including those related to scalability, centralization, communication latency, and security and privacy. Deep residual squeeze and excitation network (DRSEN) with Single Candidate Optimizer-based IoT-oriented infrastructure is used in this manuscript to address these challenges. Blockchain creates a distributed environment for CPS's communication phase, and Software-Defined Networking (SDN) establishes protocols for data forwarding in network. At the application layer of suggested infrastructure, a deep learning-based cloud is used to address communication latency, centralization, and scalability issues. It makes high-performance, affordable computing resources available for smart city applications like smart industrial and smart transportation. The proposed method is implemented in ns-3 tool and the effectiveness is assessed using F-measure, reliability, scalability, accuracy, sensitivity, specificity, and precision. The proposed method provides 35.39%, 23.87% and 20.67% higher reliability, 42.39%, 11.39%, 34.16% and 25.78% higher accuracy, 15.02%, 26.64% and 37.55% higher F-measure compared with existing techniques like Industrial Internet of Things based on Blockchain Secure Device Authentication Solution (IIoT-BC-BASA), Industrial Internet of things based on Blockchain- InterPlanetary File System (IIoT-BC-IPFS), Industrial Internet of Things based on Blockchain- Shamir Threshold Cryptography (IIoT-BC-SHC), Industrial Internet of Things based on Blockchain- software Define Networking (IIoT-BC-SDN) methods, respectively.

Data Hiding of Multicompressed Images Based on Shamir Threshold Sharing

Image-based data hiding methods have been used in the development of various applications in computer vision. At present, there are two main types of data hiding based on secret sharing, namely dual-image data hiding and multi-image data hiding. Dual-image data hiding is a kind of secret sharing-based data hiding in the extreme case. During the image transmission and storage process, the two shadow images are visually highly similar. Multi-image data hiding disassembles the cover image into multiple meaningless secret images through secret sharing. Both of the above two methods can easily attract attackers’ attention and cannot effectively guarantee the security of the secret message. In this paper, through the Shamir threshold scheme for secret sharing, the secret message is disassembled into multiple subsecrets that are embedded in the smooth blocks of multiple different images, by substituting the bitmap of block truncation coding. Thus, the shortcomings of the above two data hiding methods are effectively avoided. The proposed method embeds the secret messages in the compressed images, so it satisfactorily balances the visual quality and the embedding capacity. In our method, the shadow images make sense while they are not visually similar. The compression ratio is four, so the embedding capacity of our method has an obvious advantage under the same storage space.

NSSIA: A New Self-Sovereign Identity Scheme with Accountability

Self-sovereign identity (SSI) is a new distributed method for identity management, commonly used to address the problem that users are lack of control over their identities. However, the excessive pursuit of self-sovereignty in the most existing SSI schemes hinders sanctions against attackers. To deal with the malicious behavior, a few SSI schemes introduce accountability mechanisms, but they sacrifice users’ privacy. In addition, the digital identities (static strings or updatable chains) in the existing SSI schemes are as inputs to a third-party executable program (mobile app, smart contract, etc.) to achieve identity reading, storing and proving, and users’ self-sovereignty are weakened. To solve the above problems, we present a new self-sovereign identity scheme to strike a balance between privacy and accountability and get rid of the dependence on the third-party program. In our scheme, one and only individual-specific executable code is generated as a digital avatar-i for each human to interact with others in cyberspace without a third-party program, in which the embedding of biometrics enhances uniqueness and user control over their identity. In addition, a joint accountability mechanism, which is based on the shamir (t, n) threshold algorithm and a consortium blockchain, is designed to restrict the power of each regulatory authority and protect users’ privacy. Finally, we analyze the security, SSI properties and conduct detailed experiments in terms of the cost of computation, storage, and blockchain gas. The analysis results indicate that our scheme resists the known attacks and fulfills all the six SSI properties. Compared with the state-of-the-art schemes, the extensive experiment results show that the cost is larger in server storage, blockchain storage, and blockchain gas, but is still low enough for practical situations.

A Blockchain-Based Shamir’s Threshold Cryptography Scheme for Data Protection in Industrial Internet of Things Settings

The Industrial Internet of Things (IIoT), a typical Internet of Things (IoT) application, integrates the global industrial system with other advanced computing, analysis, and sensing technologies through Internet connectivity. Due to the limited storage and computing capacity of edge and IIoT devices, data sensed and collected by these devices are usually stored in the cloud. Encryption is commonly used to ensure privacy and confidentiality of IIoT data. However, the key used for data encryption and decryption is usually directly stored and managed by users or third-party organizations, which has security and privacy implications. To address this potential security and privacy risk, we propose a Shamir threshold cryptography scheme for IIoT data protection using blockchain: STCChain. Specifically, in our solution, the edge gateway uses a symmetric key to encrypt the data uploaded by the IoT device and stores it in the cloud. The symmetric key is protected by a private key generated by the edge gateway. To prevent the loss of the private key and privacy leakage, we use a Shamir secret sharing algorithm to divide the private key, encrypt it, and publish it on the blockchain. We implement a prototype of STCChain using Xuperchain, and the results show that STCChain can effectively prevent attackers from stealing data as well as ensuring the security of the encryption key.

A Privacy Preserving Mutual Authentication Scheme Suitable for IoT-Based Medical Systems

The medical system remains among the fastest to adopt the Internet of Things. The reason for this trend is that integration Internet of Things(IoT) features into medical devices greatly improve the quality and effectiveness of service. However, there are many unsolved security problems. Due to medical information is critical and important, authentication between users and medical servers is an essential issue. Recently, Park et al. proposed an authentication scheme using Shamir's threshold technique for IoT-based medical information system and claimed that their scheme satisfies all security requirements and is immune to various types of attacks. However, in this paper, we show that Park et al.'s scheme does not achieve user anonymity, forward security, and mutual authentication and it is not resistant to the DoS attacks and then we introduce an improved mutual authentication scheme based on Elliptic Curve Cryptography (ECC) and Shamir 's secret sharing for IoT-based medical information system.In this paper, we formally analyze the security properties of our scheme via the ProVerif. Moreover, we compare our proposed scheme with other related schemes in terms of security and performance.

Aggregation Encryption Method of Social Network Privacy Data Based on Matrix Decomposition Algorithm

Currently, there are some defects in data aggregation encryption methods, such as low accuracy and efficiency. In this regard, this paper proposes an aggregation encryption method of social network privacy data based on matrix decomposition. Shamir threshold segmentation scheme was used to improve the security of matrix decomposition results, and then re-encrypted network user attributes. For codomain and non-codomain users, private file and key generation technology were used to improve the privacy of users in common domain and non-common domain. Considering the results of matrix decomposition, privacy security and efficient user matching in social networks were implemented. The node information was embedded in the process of data encryption and signature, and the interference factors were classified by cluster as a unit, which can resist the internal attack and improve the operation efficiency. The experimental results show that this method has excellent encryption effect and high privacy data protection processing efficiency.

Dynamic Parameters-Based Reversible Data Transform (RDT) Algorithm in Recommendation System

The protection and processing of the sensitive data in recommendation system are the major concern. Existing literature, used homomorphic encryption (HE), Reversible Data Transform (RDT), differential privacy (DP) and many more schemes to protect user information. Existing RDT scheme require prior sharing of the parameters and an alternative mechanism e.g., Shamir Threshold Protocol or Diffie-hellman algorithm are used to protect the sharing parameters. In this paper, we proposed a chaotic based RDT approach for privacy-preserving data mining (PPDM) in recommendation system. Using this approach, RDT parameter values will be generated locally and because of this, prior sharing of the parameter values for the recovery process will not be necessary. This approach can be used as an alternative to the standard-RDT algorithm where bandwidth and memory are considered important factors. Our results on the Iris data set clearly show that the proposed chaotic RDT shows similar results as standard-RDT. Secondly, in this paper, we explore the usage of the RDT algorithm on real app usage records in the mobile app recommendation (MAR) domain. Thirdly, we tested the application of the RDT algorithm for the standard MovieLens dataset to ensure the validity of results because app usage dataset is publicly not available. Our results show that the proposed RDT algorithm can replace HE if an adaptive recommendation approach is used. Similarly, we can safely use the RDT approach to any data including user rating, health data or app usage frequency to ensure user privacy before delivering it to the recommender-server.

Secure multiparty quantum computation based on Lagrange unitary operator

As an important subtopic of classical cryptography, secure multiparty quantum computation allows multiple parties to jointly compute their private inputs without revealing them. Most existing secure multiparty computation protocols have the shortcomings of low computational efficiency and high resource consumption. To remedy these shortcomings, we propose a secure multiparty quantum computation protocol by using the Lagrange unitary operator and the Shamir (t, n) threshold secret sharing, in which the server generates all secret shares and distributes each secret share to the corresponding participant, in addition, he prepares a particle and sends it to the first participant. The first participant performs the Lagrange unitary operation on the received particle, and then sends the transformed particle to the next participant. Until the last participant’s computation task is completed, the transformed particle is sent back to the server. The server performs Lagrange unitary operation on the received particle by using a secret message, and then measures the transformed particle to obtain the sum of the calculations of multiple participants. Security analysis shows that the proposed protocol can resist intercept-measurement attack, intercept-resend attack, entanglement-swapping attack, entanglement-measurement attack and collusion attack. Performance comparison shows that it has higher computation efficiency and lower resource consumption than other similar protocols.

A verifiable multiparty quantum key agreement based on bivariate polynomial

Based on a point-to-point quantum key distribution protocol and classical key distribution technologies, the concept of quantum-classical key and a new multi-party quantum-classical key agreement protocol is proposed in this paper. The distributor and any one of the participants use quantum key distribution protocol to negotiate subkey, then each of the participants shares his subkey with other participants using Shamir threshold secret sharing scheme, thus each participant will sort these subkeys and his own subkey in order, and eventually get this quantum-classical key. In this protocol, a pair of function values of binary polynomials are used to ensure the authentication of sub-shares and information among participants, and Lagrange interpolation formula of unary polynomials is used to ensure the recovery of subkeys. Security analysis shows that this protocol is secure, practical and effective.

Elliptic Curve based Collaborative Group Key Management for Cloud Data Sharing in Ciphertext Policy Attribute based Encryption

Ciphertext policy attribute based encryption (CPABE) is one of cryptographic procedure that coordinates data information encryption with authenticated admission management for guaranteeing data information security in Cloud. The cloud computing where the application administrations using the Internet. In numerous applications, especially in Group Communication in cloud data information offering to various clients data information proprietors require to conceal undisclosed data information like encryption key. The effective key management system conventions are essential for giving security to this data information. Since, it is extremely difficult to provide security to group's secret data information particularly with various mechanisms of assurance. The effectiveness issue of CP-ABE is as yet accessible that corrupt the computation overhead on the grounds that bilinear pairing is exorbitant in such huge numbers of utilizations of ABE, so by supplanting the bilinear pairing utilized in the attribute coordinating with straightforward scalar multiplication on Elliptic Curves, accordingly diminishing the general computation just as communication overhead. And plan another key dispersion can considered in order to legitimately renounce a client or a characteristic without refreshing the other clients' keys during the property repudiation phase. By utilizing the Shamir's Threshold secret sharing designs access structure to develop the expressiveness of the entrance arrangement. Security and execution examination demonstrate that in this plan improving the general effectiveness just as guarantee the security of the cloud data information

A Multi-party Quantum Key Agreement Protocol Based on Shamir’s Secret Sharing

Quantum networks can extend the advantages of quantum key distribution protocols to more than two remote participants. Based on Shamir threshold secret sharing scheme, a new quantum key agreement protocol on a quantum network with any number of participants is proposed. First, each participant and distributor negotiate a sub-secret key using a kind of quantum key distribution protocol, and then each of these participants, as distributor, shares these sub-secret keys with other participants using Shamir threshold secret sharing scheme. Furthermore, each participant combines all these shared sub-secret keys and his own sub-secret key in sequence to form secret key, and sends the hash function values of this secret key to the master distributor to authenticate, finally they obtain the security key. Our scheme is practical and secure, and it can also prevent fraudulent from participants.

A fully dynamic secret sharing scheme

Based on the homogeneous linear recursive equation and the Elliptic curve cryptography (ECC), a fully dynamic secret sharing scheme is proposed for the general access structure of the participants. The participants choose their own shadows by themselves. When the shared secrets are updated, the access structure is changed, and other participants are added to or deleted from the existed group, but the shadow of each participant remains unchanged. Each participant should only maintain a shadow to share the multiple secrets. Compared with the existing popular dynamic schemes, the key construction of the proposed scheme is simpler and the proposed scheme has a completely dynamic characteristic, so that it has the potential to extend its practical application scenarios. That is, the proposed scheme can improve the performances of the key management and the distributed system. The security of the scheme is based on the Shamir threshold scheme, the computational Diffie–Hellman problem (CDHP) and the discrete logarithm problem (DLP).

N个Shamir门限秘密共享方案组合的通用可验证性设计

N个Shamir门限秘密共享方案组合的通用可验证性设计