Multi-secret Sharing Scheme Research Articles

A Verifiable Multi-Secret Sharing Scheme Based on ℓ-Intersection Pair of Cyclic Codes

A verifiable multi-secret sharing (VMSS) scheme addresses various security issues, helping in cheating detection and cheater identification. The dimension of the intersection of a given pair of cyclic codes over a finite field [Formula: see text] is represented by [Formula: see text]. In this paper, we propose a VMSS scheme based on an [Formula: see text]-intersection pair of cyclic codes. The proposed scheme is very useful for sharing a large number of secrets. If [Formula: see text] is the number of secrets in a threshold [Formula: see text] scheme, then for [Formula: see text], the computational complexity and the public values required in the reconstruction phase are much less compared to many existing schemes in the literature. Overall, the proposed scheme comprises nearly all the features, like being verifiable, testing participants’ integrity, checking Verifier frauds, and most importantly, it is of multi-use type.

On the Security of a Lattice-Based Multi-Stage Secret Sharing Scheme

In response to the threat posed by quantum computers, Pilaram and Eghlidos proposed the first lattice-based multi-stage secret sharing scheme which is the only post-quantum multi-stage secret sharing scheme. In this paper, we introduce an efficient attack on it and show that any adversary can easily reconstruct unrecovered secrets as long as it collects enough pseudo-secret shares. For the sake of complete, we further list two countermeasures to protect the scheme from such attack.

Conjunctive Hierarchical Multi-Secret Sharing Scheme using Elliptic Curves

Conjunctive Hierarchical Multi-Secret Sharing Scheme using Elliptic Curves

A Verifiable Multi-Secret Sharing Scheme Based on Short Integer Solution

A Verifiable Multi-Secret Sharing Scheme Based on Short Integer Solution

Protected Fair Secret Sharing Based Bivariate Asymmetric Polynomials in Satellite Network

Verifiable secret sharing mainly solves the cheating behavior between malicious participants and the ground control center in the satellite network. The verification stage can verify the effectiveness of secret shares issued by the ground control center to each participant and verify the effectiveness of secret shares shown by participants. We use a lot of difficult assumptions based on mathematical problems in the verification stage, such as solving the difficult problem of the discrete logarithm, large integer prime factorization, and so on. Compared with other verifiable secret sharing schemes designed for difficult problems under the same security, the verifiable secret sharing scheme based on the Elliptic Curve Cryptography (ECC) system has the advantages of less computational overhead and shorter key. At present, the binary polynomial is a single secret scheme and cannot provide effective verification. Therefore, based on a Protected Verifiable Synchronous Multi Secret Sharing (PVS-MSS) scheme, this paper is designed based on bivariate asymmetric polynomials. The advanced verifiable attribute is introduced into the Protected Secret Sharing (PSS) scheme. This paper extends the protected synchronous multi-secret sharing scheme based on bivariate polynomial design. The ECC system constructs the security channel between the ground control center and participants and constructs the verification algorithm. Through the verification algorithm, any participant can verify the consistency and effectiveness of the secret shadow and secret share received from other participants or presented by the secret distribution center. Therefore, no additional key agreement protocol is required; participants do not need to negotiate the session key for encryption; the secret share polynomial can generate the session key between participants and speed up the secret reconstruction process. The verification stage has lower computational complexity than the verifiable scheme constructed by Rivest Shamir Adleman (RSA) and other encryption methods. Chinese Remainder Theorem (CRT) is used to update the secret shadow. The secret shadow does not need to be updated with the change of the scheme shared secret, and the public value update efficiency is higher. Reduce the complexity of sharing secret updates in a synchronous multi-secret sharing scheme.

A New Multi-stage Secret Sharing Scheme for Hierarchical Access Structure with Existential Quantifier

Multi-stage secret sharing scheme is practical in the case that there is a security system with m ordered checkpoints.It is natural to divide the m checkpoints into m different levels. There are m different secrets, and eachof them with a different importance corresponds to a checkpoint/level. The participants are also divided intom disjoint levels as they do in the hierarchical threshold access structure. Hierarchical threshold access structurewith the existential quantifier ( HTAS∃ ) does not cover the common practice that at least a few numbersof high-ranking participants are required to be involved in any recovery of the secret. The popular schemeswith hierarchical access structure were needed to check many matrices for non-singularity. We propose amulti-stage secret sharing scheme for HTAS∃ , and the tools are based on the linear homogeneous recurrencerelations (LHRRs) and one-way functions. We give the HTAS∃ a modification, so that this hierarchical accessstructure can satisfy the common practice. In our scheme, if the participants are divided into m levels, thereusually has m secrets. But before the (j − 1)-th secret is recovered, the j-th secret cannot be recovered. Ourscheme is a computational secure. The proposed scheme requires a share for each participant and the shareis as long as each secret. Our scheme has high efficiency by comparing with the state-of-the-art hierarchicalsecret sharing schemes.

A novel approach for multilevel multi-secret image sharing scheme

Multi-secret sharing (MSS) is an effective technique that securely encodes multiple secrets to generate shares and distributes them among the participants in such a way that these shares can be used later to reconstruct the secrets. MSS schemes have a considerable advantage over the single-secret sharing schemes for secure multimedia data transmission. This paper presents a novel secret image sharing approach, namely ‘(n, m, l)-Multilevel Multi-Secret Image Sharing (MMSIS) scheme.’ The proposed MMSIS scheme encodes ‘n’ distinct secret images to generate ‘m’ shares and distributes them among ‘m’ participants allocated to ‘l’ distinct levels. The paper proposes two variants of the MMSIS scheme. The first variant is an $$(n,n+1,l)$$ -MMSIS scheme which encodes ‘n’ secret images each having a unique level id $$L_k$$ into $$(n+1)$$ shares. The image shares are then distributed among $$(n+1)$$ participants assigned to ‘ $$l=n$$ ’ different levels. With the increase in level id, the number of shares required to reconstruct the secret image also increases. To reconstruct a secret image of a particular level $$L_k$$ , all the shares at level $$L_k$$ and its preceding levels need to be acquired, which requires the consensus of all participants holding the shares up to level $$L_k$$ . The second variant, namely extended-MMSIS (EMMSIS) scheme is a generalized (n, m, l) version of the former scheme that allows to generate more shares for a specific secret image at a particular level in accordance with the consensus requirements for its reconstruction. The multilevel structure of the scheme makes it useful for multi-secret distribution in a multilevel organizational structure.

A Study on Multisecret-Sharing Schemes Based on Linear Codes

Secret sharing has been a subject of study since 1979. In the secret sharing schemes there are some participants and a dealer. The dealer chooses a secret. The main principle is to distribute a secret amongst a group of participants. Each of whom is called a share of the secret. The secret can be retrieved by participants. Clearly the participants combine their shares to reach the secret. One of the secret sharing schemes is threshold secret sharing scheme. A threshold secret sharing scheme is a method of distribution of information among participants such that can recover the secret but cannot. The coding theory has been an important role in the constructing of the secret sharing schemes. Since the code of a symmetric design is a linear code, this study is about the multisecret-sharing schemes based on the dual code of code of a symmetric design. We construct a multisecret-sharing scheme Blakley’s construction of secret sharing schemes using the binary codes of the symmetric design. Our scheme is a threshold secret sharing scheme. The access structure of the scheme has been described and shows its connection to the dual code. Furthermore, the number of minimal access elements has been formulated under certain conditions. We explain the security of this scheme.

Some Multisecret-Sharing Schemes over Finite Fields

A secret sharing scheme is a method of assigning shares for a secret to some participants such that only some distinguished subsets of these subsets can recover the secret while other subsets cannot. Such schemes can be used for sharing a private key, for digital signatures or sharing the key that can be used to decrypt the content of a file. There are many methods for secret sharing. One of them was developed by Blakley. In this work, we construct a multisecret-sharing scheme over finite fields. The reconstruction algorithm is based on Blakley’s method. We determine the access structure and obtain a perfect and ideal scheme.

A Multisecret-Sharing Scheme Based on LCD Codes

Secret sharing is one of the most important cryptographic protocols. Secret sharing schemes (SSS) have been created to that end. This protocol requires a dealer and several participants. The dealer divides the secret into several pieces ( the shares), and one share is given to each participant. The secret can be recovered once a subset of the participants (a coalition) shares their information. In this paper, we present a new multisecret-sharing scheme inspired by Blakley’s method based on hyperplanes intersection but adapted to a coding theoretic situation. Unique recovery requires the use of linear complementary (LCD) codes, that is, codes in which intersection with their duals is trivial. For a given code length and dimension, our system allows dealing with larger secrets and more users than other code-based schemes.

New Multi-secret Sharing Scheme based on Superincreasing Sequence for Level-Ordered Access Structure

A new multi-secret sharing scheme (MSSS) that uses a superincreasing sequence and realizes level-ordered access structure (LOAS) is proposed. The novelty of the scheme is that not only a single share for all the secrets is sufficient but also the secrets can be changed without renewing the shares of the participants. The proposed scheme has low communication cost and less overhead for the participant.

The least-squares solutions in linear codes based multisecret-sharing approach

The theory of generalised inverses of matrices has been applied in many areas since 1950. Some of them are Markov chains, robotics differential equations, etc. Especially, the applications over finite fields of this theory have an important role in cryptography and coding theory. In this work, we study a new multisecret-sharing scheme by using the generalised inverses of matrices and least-squares solutions in linear codes. We determine the access structure. Its security improves on that of multisecret-sharing schemes.

A CSA-Secure Multi-Secret Sharing Scheme in the Standard Model

In a multi-stage secret sharing (MSSS) scheme, a dealer D share secrets among the participants in such a way that secrets are reconstructed one by one in different stages. Recently, we proposed a secure MSSS in the standard model. In this paper, we present another MSSS scheme that has shorter public outputs and better security relation with the underlying symmetric encryption in the standard model.

A Proactive Multi Stage Secret Sharing Scheme for Any Given Access Structure

In proactive secret sharing schemes, the secret shares are periodically renewed without modifying the secret such that an adversary is unable to get any information about the secret shares unless he is able to obtain a certain number of secret shares in a short time interval. In this paper, using monotone span programs (MSP) we devise a new linear multi-secret sharing (LMSS) scheme which is also multi-stage. We also give a new general method to construct proactive and multi-use linear multi-secret sharing schemes based on MSP. An important advantage of our method compared to the others is that it does not need private channels between each pair of participants or an encryption scheme between them. Finally, we prove that our new scheme satisfies the definition of a perfect LMSS scheme.

A NEW SECRET SHARING SCHEME ADVERSARY FUZZY STRUCTURE BASED ON AUTOMATA

In this paper,we introduce a new verifiable multi-use multi-secretsharing scheme based on automata and one-way hash function. The scheme has theadversary fuzzy structure and satisfy the following properties:1) The dealer can change the participants and the adversary fuzzy structure without refreshing any participants' real-shadow. 2) The scheme is based on the inversion of weakly invertible finite automata and its security depends on the properties of the one-way hash functions.3) The scheme does not encounter time-consuming computationslike discrete logarithm problem.4) The validity of the transmitted data can be verified by the combiner and participants.5) Every participant has only one reusable real-shadow,whereas the most of other existing schemes have more than one shadow.In addition, the proposed scheme which is based on automata has all the properties of a perfect scheme.Finally, the comparisonsamong other schemes and our scheme prove the efficiency of our scheme.

A Publicly Verifiable Multi-Secret Sharing Scheme With Outsourcing Secret Reconstruction

A publicly verifiable secret sharing (PVSS) scheme enjoys the public verification and the lower cost of communication than VSS scheme. However, the existing PVSS schemes cannot be applied in the scenarios of the devices with low computation ability and do not share the multiple secrets among all participants efficiently. In this paper, an efficient publicly verifiable multi-secret sharing scheme with outsourcing secret reconstruction is proposed. Each participant only spends a small amount of computational cost to recover multiple secrets because of the expensive burden of computation and verifiability is outsourced to the cloud service provider (CSP). Moreover, the CSP knows no information of the secrets, and the participants have the abilities to verify the returned result. We also prove that our scheme is secure under the hardness assumption of the discrete logarithm problem and the modified generalized bilinear inversion problem.

Provably secure verifiable multi‐stage secret sharing scheme based on monotone span program

In multi-secret sharing (MSS) scheme, a dealer distributes multiple secrets among a set of participants, each of them according to an access structure. In this study, the authors propose a novel linear MSS with computational verifiability that provide many functions for practical applications in comparison with the previous works focusing on MSS schemes in the general scenario. This scheme has the same advantages as previous schemes; moreover, it is verifiable and multi-use secret sharing. Furthermore, in this scheme the secret reconstruction is according to the dealer's preassigned order. Also, they prove the security of the authors’ scheme in the standard model.

A novel approach for sharing multiple color images by employing Chinese Remainder Theorem

Conventional approaches for encryption are unsuitable for simultaneously achieving reliability and confidentiality. Threshold-based secret sharing scheme deals with the problem of sharing a secret information into a group of n users and secret can be recovered only when a sufficient users come together, we can reconstruct a secret information from t, where t<n. There is a requirement to evolve a secure secret sharing scheme so that the reconstruction is possible only when all shares are available. In this paper, we propose a secure (n,n)-Multi Secret Sharing (MSS) scheme using Chinese Remainder Theorem (CRT). The proposed scheme shares secret information among n users and for recovery all n users are needed, if one of the user is absent then we could not reconstruct the secret information. The proposed scheme does not reveals the partial secret information, as the randomness in shares is more. The proposed scheme outperforms the existing techniques in terms of randomness and security.

An Efficient Threshold Verifiable Multi-Secret Sharing Scheme Using Generalized Jacobian of Elliptic Curves

‎In a (t,n)-threshold secret sharing scheme‎, ‎a secret s is distributed among n participants such that any group of t or more participants can reconstruct the secret together‎, ‎but no group of fewer than t participants can do‎. In this paper, we propose a verifiable (t,n)-threshold multi-secret sharing scheme based on Shao and Cao‎, ‎and the intractability of the elliptic curve discrete logarithm problem (ECDLP) by using generalized Jacobian of elliptic curves‎. ‎The proposed scheme has all the benefits of Shao and Cao‎, ‎however‎, ‎our scheme no need to a secure channel‎. ‎Furthermore‎, ‎we exploit the techniques via elliptic curves to perform the scheme‎. ‎This can be very important‎ ‎because the hardness of discrete logarithm problem on elliptic curves increases security of the proposed scheme‎.

Efficient multisecret sharing scheme using new proposed computational security model

SummaryA multisecret sharing (MSS) is a method for sharing a set of secrets among some participants. They can recover each of these secrets without endangering the other secrets. Two kinds of security models have been proposed for MSS schemes. These models are categorized into 2 types. The first security model is unconditional security. This approach decreases the efficiency of MSS schemes. Therefore, the second type of security, which is more relaxed, appeared. This approach is called computational security. In this paper, with 2 examples, we will show that the current definition of computational security does not satisfy all of our expectations from a secure MSS scheme. In fact, in these examples, recovering a secret leaks information to the other secrets while these schemes are considered secure in view of the computational security. After determining the shortcomings of the current security definition, we propose a new definition for computational security and present an MSS scheme that enjoys rigorous proof of security in terms of the new definition. In addition, a complete comparison in terms of share size, number of public values, and required operations for recovering a secret between our scheme and previous schemes indicates that the presented scheme is efficient.