Threshold Secret Sharing Scheme Research Articles

Lattice-Based Threshold Secret Sharing Scheme and Its Applications: A Survey

As the most popular cryptographic scheme in the post-quantum field, lattices have received extensive attention and research. Not only do they provide quantum-resistant security, they also enable the construction of complex applications. Currently, lattice cryptography schemes based on different difficult problems have been applied in different fields. The threshold secret sharing (TSS) scheme is an important field of cryptography and has important application value and development prospects in key protection, secure multi-party computation, privacy protection, etc. However, with the rapid development of quantum computing, many existing cryptography-underlying technologies are facing huge difficulties and challenges. Therefore, post-quantum TSS has important research significance and value for the future development of cryptography. In this paper, we summarize the existing secret sharing schemes based on lattice-hard problems and the relevant applications of these schemes in the post-quantum realm. We classify existing lattice-based TSS according to different functions and introduce typical solutions. To the best of our knowledge, this is the first review paper on lattice-based TSS 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).

(10,10)-THRESHOLD SECRET-SHARING SCHEME USING EQUIVALENCE CLASSES OF INTEGERS MODULO A PRIME

Introduction: The quest for increasing the security of data in secret-sharing schemes has attracted much attention in the world of cryptography. Several methods have been applied, and the application of the new technique, (n,n)-threshold secretsharing scheme based on equivalence classes, will be a perfect solution. Aims: The aim is to explore and construct strong knowledge in the theory and structure of the secret-sharing scheme on (n,n)- threshold secret-sharing scheme based on equivalence classes; (𝑋) = (𝑦 𝜖 𝑋: (𝑥, 𝑦)𝜖 ℝ) And achieve the following objectives: i. To investigate an (𝑛, 𝑛)-threshold secret-sharing scheme based on the equivalence classes of the prime over ℤ. ii. Investigation of the accuracy of such a scheme. Materials and Methods: The study uses the set of integers modulo a prime and modulo arithmetic on the set of integers. Results: The statistics on the coalition, security analysis, and information-theoretic efficiency are also discussed. Conclusion: The secret sharing scheme on (10,10)-threshold secret-sharing scheme based on equivalence classes of integers modulo a prime is perfect in terms of only qualified coalitions can obtain the secret and it is reliable by means of security. We have used the property of these classes to provide the reconstruction algorithms, and access structures and calculated the number of minimal coalitions of the scheme. This new system is ideal in that the size of the secret is equal to the size of the share.

Verifiable, Secure Mobile Agent Migration in Healthcare Systems Using a Polynomial-Based Threshold Secret Sharing Scheme with a Blowfish Algorithm.

A mobile agent is a software application that moves naturally among hosts in a uniform and non-uniform environment; it starts with one host and then moves onto the next in order to divide data between clients. The mobile paradigm is utilized in a wide assortment of medical care applications such as the medical information of a patient, the recovery of clinical information, the incorporation of information pertaining to their wellbeing, dynamic help, telemedicine, obtaining clinical data, patient administration, and so on. The accompanying security issues have grown in tandem with the complexity and improvements in mobile agent technologies. As mobile agents work in an insecure environment, their security is a top priority when communicating and exchanging data and information. Data integrity, data confidentiality and authentication, on-repudiation, denial of service, and access control, are all key security concerns with mobile agent migration. This paper proposes a Verifiable, Secure Mobile Agent Migration model, based on two polynomials (t, n), and an edge secret imparting plan with Blowfish encryption, to enable secure information transmission in clinical medical care.

FPDA: Fault-Tolerant and Privacy-Enhanced Data Aggregation Scheme in Fog-Assisted Smart Grid

The data aggregation approach in smart grid (SG) is an effective solution to make data available while keeping privacy preserving at the same time. The fault tolerance means decryption can still be carried out successfully even if some smart meters (SMs) are breaking down. It is a challenging issue to design an efficient, fault-tolerant data aggregation scheme with no help of centralized trusted authority (TA) or key update after each fault recovery. Recently, a fault-tolerant data aggregation scheme FESDA (Saleem <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.,</i> 2020) was presented. However, we identify a serious and inherent vulnerability in its fault tolerance. Specifically, given an equivalent ciphertext derived from each SM’s private key aiming at resiting faults, the control center can abuse it to obtain any SM’s reading. An effective attack is launched with both theoretical proof and experimentative verification. Furthermore, to fix it and solve the challenging issue, we first design an extended Shamir’s threshold secret-sharing scheme (tSSS) with master secret security and reusability, allowing SMs to reconstruct subsequent multiple secrets without leaking their original secret shares. Then, if some SMs fail to submit data successfully, the fog node (FN) starts extra request–response interactivities among itself and a limited number of SMs. Finally, a privacy-enhanced aggregation of normal reports can also be achieved. Extensive experiments demonstrate that the majority of computation costs and communication overload to acquire fault tolerance are offload on FNs, while SMs are computationally economical.

Self-Verifiable Attribute-Based Keyword Search Scheme for Distributed Data Storage in Fog Computing With Fast Decryption

Presently many searchable encryption schemes have been proposed for cloud and fog computing, which use fog nodes (or fog servers) to partly undertake some computational tasks. However, these related schemes still retain cloud servers to undertake most computational tasks, which result in large communication costs between edge devices and cloud servers. Therefore, in this paper we propose a self-verifiable attribute-based keyword search scheme for distributed data storage (SV-KSDS) in full fog computing, where each decryption operation on the data required by a user must meet the negotiated decryption rule between fog servers. Our SV-KSDS scheme first provides attribute-based distributed data storage among fog servers through the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(w, \sigma)$ </tex-math></inline-formula> threshold secret-sharing scheme, where fog servers can provide self-verifiable keyword search and data decryption for terminal users. Compared with the data storage in cloud computing, our scheme extends it to the distributed structure while providing fine-grained access control for distributed data storage through attribute-based encryption. The access control policy of our scheme is constructed on linear secret-sharing scheme, whose security is reduced to the decisional bilinear Diffie-Hellman assumption against chosen-keyword attack and the decisional <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${q}$ </tex-math></inline-formula> -parallel bilinear Diffie-Hellman assumption against chosen-plaintext attack in the standard model. Based on theoretical analysis and practical testing, our SV-KSDS scheme generates less computation and communication costs, which further unloads some computational tasks from terminal users to fog servers so as to reduce computing costs of terminal users.

A New Approach to Construct (K, N) Threshold Secret Sharing Schemes Based on Finite Field Extension

With increase in use of internet there is need to keep passwords, secret keys, important information secret. One way to do this is encryption. But it also need key which should be kept secure. Sometimes key is secure. But what will happens if the key is lost, forgotten etc. This problem can be solved using secret sharing. Instead of sharing whole secret, it is divided into pieces and distributed to finite set of pieces and some subset of pieces called access structure of scheme, which can recover secret. Here we propose a new way to construct threshold secret sharing schemes based on finite field extension using Blakley's secret sharing as a base. It is useful in many cryptographic applications and security. Because of finite fields the size of numbers stays within a specified range, doesn't matter how many operations we apply on number.

Two polynomials based (t, n) threshold secret sharing scheme with cheating detection

A two-polynomial based threshold secret sharing (SS) scheme is proposed by Liu et al., where two functions for detection of share cheating are used. It is found that the scheme is weak as the equations formed by at most (t – 1) dishonest participants in term of unknowns are not equivalent to the cheating detection function, and if one polynomial is kept fixed and other with two cheating detection equations are taken, a set of equations with unknowns exist, and are found to be easily solvable. In this paper, we also propose a two-polynomial based (t, n) threshold SS scheme; however, the polynomials are taken in such a way that they have an arbitrary common coefficient and as a result, both the polynomials are to be modified simultaneously for cheating of shares and incorporates higher cheating detection capability. Some analytical proofs and comparison with other schemes in support of our claims are provided.

Threshold changeable secret sharing with secure secret reconstruction

(t,n) threshold secret sharing (SS) is an important cryptographic primitive in which a secret is divided into n shares, and then any t or more shareholders can exchange shares to reconstruct the secret without help of any trusted third party. However, if an illegal participant, without any valid share, impersonates a shareholder to recover the secret with m (m≥t) legal shareholders in a traditional (t,n) threshold SS scheme, it may obtain the secret. Therefore, this paper utilizes a bivariate symmetry polynomial to propose a basic threshold changeable secret sharing (TCSS) scheme which is cheating immune and thwarts the above illegal participant attack. In the basic TCSS scheme, threshold is allowed to increase from t to the exact number of all participants during secret reconstruction. In this way, the secret can be recovered only if all the participants have valid shares. However, each shareholder has to keep t coefficients of its share. Then, an improved TCSS scheme based on both univariate polynomial and bivariate symmetry polynomial is proposed to reduce coefficients of shares for each shareholder.

Outsourcing Hierarchical Threshold Secret Sharing Scheme Based on Reputation

Secret sharing is a basic tool in modern communication, which protects privacy and provides information security. Among the secret sharing schemes, fairness is a vital and desirable property. To achieve fairness, the existing secret sharing schemes either require a trusted third party or the execution of a multiround protocol, which are impractical. Moreover, the classic scheme requires expensive computing in the secret verification phase. In this work, we provide an outsourcing hierarchical threshold secret sharing (HTSS) protocol based on reputation. In the scheme, participants from different levels can fairly reconstruct the secret, and the protocol only needs to run for one round. A cloud service provider (CSP) uses powerful computing resources to help participants complete homomorphic encryption and complex verification operations, and the CSP cannot be aware of any valuable information. The participants can obtain the secret with a small number of operations. To avoid collusion, we suppose that participants have their own reputation value, and they are punished or rewarded according to their behavior. The reputation value of a participant who deviates from the protocol will decrease; therefore, the participant will choose a cooperative strategy to obtain better payoffs. Lastly, our scheme is proved to be secure, and experiments indicate that our scheme is feasible and efficient.

Tightly coupled multi-group threshold secret sharing based on Chinese Remainder Theorem

(t,n)-Threshold secret sharing ((t,n)-SS) scheme is a fundamental cryptographic primitive. As a special (t,n)-SS, a Multi-Level threshold Secret Sharing scheme (MLSS) divides shares into different levels. Shares at higher levels can be used at lower ones but shares of lower levels are invalid at higher ones. However, MLSS is limited in applications and vulnerable to Illegal Participant (IP) attack and t-Share Capture (SC) attack. Therefore, the paper first extends the notion of MLSS to multi-group threshold secret sharing (MGSS) to accommodate wider application scenarios. In order to cope with the 2 attacks, the paper then proposes a tightly coupled MGSS scheme based on Chinese Remainder Theorem. In the scheme, a shareholder, with only one private share, is allowed to participate in secret reconstruction of different groups. Moreover, when sufficient shareholders collaborate to recover the secret in a group, they first form a tightly coupled subgroup by constructing a randomized component each so that the secret can be recovered only if each participant has valid share and actually participates in secret reconstruction. Analyses show that the proposed scheme is capable of thwarting IP and SC attacks. Besides, the scheme is more flexible and popular in applications compared with MLSS scheme.

Intelligent conditional collaborative private data sharing

With the advent of distributed systems, secure and privacy-preserving data sharing between different entities (individuals or organizations) becomes a challenging issue. There are several real-world scenarios in which different entities are willing to share their private data only under certain circumstances, such as sharing the system logs when there is indications of cyber attack in order to provide cyber threat intelligence. Therefore, over the past few years, several researchers proposed solutions for collaborative data sharing, mostly based on existing cryptographic algorithms. However, the existing approaches are not appropriate for conditional data sharing, i.e., sharing the data if and only if a pre-defined condition is satisfied due to the occurrence of an event. Moreover, in case the existing solutions are used in conditional data sharing scenarios, the shared secret will be revealed to all parties and re-keying process is necessary. In this work, in order to address the aforementioned challenges, we propose, a “conditional collaborative private data sharing” protocol based on Identity-Based Encryption and Threshold Secret Sharing schemes. In our proposed approach, the condition based on which the encrypted data will be revealed to the collaborating parties (or a central entity) could be of two types: (i) threshold, or (ii) pre-defined policy. Supported by thorough analytical and experimental analysis, we show the effectiveness and performance of our proposal.

A collaborative secret sharing scheme based on the Chinese Remainder Theorem.

Secret sharing (SS) can be used as an important group key management technique for distributed cloud storage and cloud computing. In a traditional threshold SS scheme, a secret is shared among a number of participants and each participant receives one share. In many real-world applications, some participants are involved in multiple SS schemes with group collaboration supports thus have more privileges than the others. To address this issue, we could assign multiple shares to such participants. However, this is not a bandwidth efficient solution. Therefore, a more sophisticated mechanism is required. In this paper, we propose an efficient collaborative secret sharing (CSS) scheme specially tailored for multi-privilege participants in group collaboration. The CSS scheme between two or among more SS schemes is constructed by rearranging multi-privilege participants in each participant set and then formulated into several independent SS schemes with multi-privilege shares that precludes information leakage. Our scheme is based on the Chinese Remainder Theorem with lower recovery complexity and it allows each multi-privilege participant to keep only one share. It can be formally proved that our scheme achieves asymptotically perfect security. The experimental results demonstrate that it is efficient to achieve group collaboration, and it has computational advantages, compared with the existing works in the literature.

A Weighted Threshold Secret Sharing Scheme for Remote Sensing Images Based on Chinese Remainder Theorem

Abstract: The recent advances in remote sensing and computer techniques give birth to the explosive growth of remote sensing images. The emergence of cloud storage has brought new opportunities for storage and management of massive remote sensing images with its large storage space, cost savings. However, the openness of cloud brings challenges for image data security. In this paper, we propose a weighted image sharing scheme to ensure the security of remote sensing in cloud environment, which takes the weights of participants (i.e. cloud service providers) into consideration. An extended Mignotte sequence is constructed according to the weights of participants, and we can generate image shadow shares based on the hash value which can be obtained from gray value of remote sensing images. Then we store the shadows in every cloud service provider, respectively. At last, we restore the remote sensing image based on the Chinese Remainder Theorem. Experimental results show the proposed scheme can effectively realize the secure storage of remote sensing images in the cloud. The experiment also shows that no matter weight values, each service providers only needs to save one share, which simplifies the management and usage, it also reduces the transmission of secret information, strengthens the security and practicality of this scheme. Keywords: Remote sensing image, security, cloud, storage, weighted threshold.

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

A (k, n)-Threshold Progressive Visual Secret Sharing without Expansion

Visual cryptography (VC) encrypts a secret image into n shares (transparency). As such, we cannot see any information from any one share, and the original image is decrypted by stacking all of the shares. The general (k, n)-threshold secret sharing scheme (SSS) can similarly encrypt and decrypt the original image by stacking at least k (≤ n) shares. If one stack is fewer than k shares, the secret image is unrecognizable. Another subject is progressive visual secret sharing, which means that when more shares are progressively stacked, the combined share becomes clearer. In this study, we constructed an advanced scheme for (k, n)-threshold SSS that can be encrypted in VC for any positive integers n ≥ k ≥ 2 through the method of combination, and the size of each share is the same as that of the original image. That is, no pixel expansion is required. Our scheme is novel, and the results from the theoretical analysis and simulation reveal that our scheme exhibits favorable contrast to that of other related schemes.

Computing on quantum shared secrets

A (k,n)-threshold secret-sharing scheme allows for a string to be split into n shares in such a way that any subset of at least k shares suffices to recover the secret string, but such that any subset of at most k-1 shares contains no information about the secret. Quantum secret-sharing schemes extend this idea to the sharing of quantum states. Here we propose a method of performing computation on quantum shared secrets. We introduce a (n,n)-quantum secret sharing scheme together with a set of protocols that allow quantum circuits to be evaluated on the shared secret without the need to decode the secret. We consider a multipartite setting, with each participant holding a share of the secret. We show that if there exists at least one honest participant, no group of dishonest participants can recover any information about the shared secret, independent of their deviations from the protocol.

Threshold Secret Sharing Scheme for Compartmented Access Structures

In the realm of visual cryptography, secret sharing is the predominant method of transmission and reception of secure data. Most of the (n, n) secret sharing schemes suffer from one common flaw — locking of information when the all- n number of receivers are not available for some reason. This paper proposes a new method of compartmented secret sharing scheme where some threshold number of equally privileged from each compartment can retrieve data. This scheme rules out regeneration of secret image at the single compartment thereby eliminating the danger of misusing secret image. The key features of this scheme are: better visual quality of the recovered image with no pixel expansion; non-requirement of half toning of color images; less computational complexity by reconstructing secret through XORing and simple addition of all share images. This scheme is highly beneficial in applications where data has to be stored securely in a database and in cloud computing to synchronize information passed to different groups or clusters from a single host.

Dynamic threshold secret reconstruction and its application to the threshold cryptography

Shamir's (t,n) secret sharing scheme (SS) is based on a univariate polynomial and is the most cited SS in the literature. The secret in a (t,n) SS can be recovered either by exactly t or more than t shareholders. Most SSs only consider when there are exactly t shareholders participated in the secret reconstruction. In this paper, we examine security issues related to the secret reconstruction if there are more than t shareholders participated in the secret reconstruction. We propose a dynamic threshold SS based on a bivariate polynomial in which shares generated by the dealer can be used to reconstruct the secret but having a larger threshold which is equivalent to the exact number of participated shareholders in the process. In addition, we extend the proposed scheme to enable shares which can also be used to establish pairwise keys to protect the reconstructed secret from non-shareholders. Shamir's SS has been used in conjunction with other public-key algorithms in most existing threshold algorithms. Our proposed SS can also be applied to the threshold cryptography to develop efficient threshold algorithms.

Designing Robust LMCA-based Threshold Secret Sharing Scheme for Digital Images Using Multiple Configurations Assignment

In this paper, we present a new (t,n)-threshold secret images sharing scheme based on linear memory cellular automata (LMCA). While all existing LMCA-based sharing scheme are not robust, the proposed one provides full robustness property. Precisely, any subset of t participants can collude to recover the shared secret, in contrast to existing LMCA-based schemes when this is possible only for participants having consecutive shares. To achieve robustness, produced shares are constructed using subsets of different LMCA’s configurations instead of using single ones. The subsets are defined according to an assignments matrix that is generated using a specific heuristic. The proposed scheme is shown to be robust, and its security is experimentally evaluated with respect to the problem of secret color image sharing. Obtained results illustrate the secrecy of the produced shares, while comparison gives an accurate evaluation with respect to existing schemes.