Verifiable Multi-secret Sharing 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.

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

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

New (k,l,m)-verifiable multi-secret sharing schemes based on XTR public key system

Secret sharing was proposed primarily in 1979 to solve the problem of key distribution. In recent decades, researchers have proposed many improvement schemes. Among all these schemes, verifiable multi-secret sharing (VMSS) schemes are studied sufficiently, which share multiple secrets simultaneously and perceive malicious dealer as well as participants. By pointing out that the schemes presented by Dehkordi and Mashhadi in 2008 cannot detect some vicious behaviors of the dealer, we propose two new VMSS schemes by adding new validity check in the verification phase to overcome this drawback. Our new schemes are based on XTR public key system, and can realize GF(p6) security by computations in GF(p2) without explicit constructions of GF(p6), where p is a prime. Compared with the VMSS schemes using RSA and linear feedback shift register (LFSR) public key cryptosystems, we can achieve the same security level with shorter parameters by using trace function. What's more, our schemes are much simpler to operate than those schemes based on Elliptic Curve Cryptography (ECC). In addition, our two schemes are dynamic and threshold changeable, which means that it is efficient to implement our schemes when participants, secrets or the threshold needs to be changed.

Threshold-Based Post-Quantum Secure Verifiable Multi-Secret Sharing for Distributed Storage Blockchain

Blockchain systems store transaction data in the form of a distributed ledger where each node stores a copy of all data, which gives rise to storage issues. It is well-known that the tremendous storage and distribution of the block data are common problems in blockchain systems. In the literature, some types of secret sharing schemes are employed to overcome these problems. The secret sharing method is one of the most significant cryptographic protocols used to ensure the privacy of the data. The main purpose of this paper is to improve the recent distributed storage blockchain systems by proposing an alternative secret sharing method. We first propose a secure threshold verifiable multi-secret sharing scheme that has the verification and private communication steps based on post-quantum lattice-based hard problems. We then apply the proposed threshold scheme to the distributed storage blockchain (DSB) system to share transaction data at each block. In the proposed DSB system, we encrypt the data block with the AES-256 encryption algorithm before distributing it among nodes at each block, and both its secret key and the hash value of the block are privately shared among nodes simultaneously by the proposed scheme. Thereafter, in the DSB system, the encrypted data block is encoded by the Reed–Solomon code, and it is shared among nodes. We finally analyze the storage and recovery communication costs and the robustness of the proposed DSB system. We observe that our approach improves effectively the recovery communication cost and makes it more robust compared to the previous DSB systems. It also improves extremely the storage cost of the traditional blockchain systems. Furthermore, the proposed scheme brings to the DSB system the desirable properties such as verification process and secret communication without private channels in addition to the known properties of the schemes used in the previous DSB systems. As a result of the flexibility on the threshold parameter of the scheme, a diverse range of qualified subsets of nodes in the DSB system can privately recover the secret values.

New dynamic and verifiable multi‐secret sharing schemes based on LFSR public key cryptosystem

A verifiable multi-secret sharing (VMSS) scheme allows distributors to share multiple secrets simultaneously and can detect fraud by both distributors and participants. After analysing the security of the VMSS schemes proposed by Dehkordi and Mashhadi in 2015, the authors point out that they could not detect the fraudulent behaviour of the dealer. By using the non-homogeneous linear recursion and linear feedback shift rigister (LFSR) public key cryptosystem, they introduce two new VMSS schemes. The proposed schemes can not only overcome the defects mentioned above, but also have shorter private and public key lengths at the same level of security. Besides, the proposed schemes are dynamic.

How to construct a verifiable multi‐secret sharing scheme based on graded encoding schemes

In a verifiable multi-secret sharing scheme, a dealer distributes multiple secrets between a group of participants and also additional information is given that allows each participant to check whether his share is valid. In this study, the authors present a novel verifiable multi-secret sharing (VMSS) scheme with general access structure using monotone span programs, which its security is based on graded encoding schemes. More precisely, they reduce the hardness of graded decision-Diffie–Hellman problem to the computational security of the authors’ scheme in the standard model. To the best of the authors’ knowledge, this is the first study to present a VMSS scheme based on graded encoding schemes.

Threshold verifiable multi‐secret sharing based on elliptic curves and Chinese remainder theorem

In this study, the authors propose a new protocol to share secret shadows for verifiable ( t , n ) secret sharing (VSS) schemes. Unlike traditional VSS schemes, whose communications between the dealer and the participants require a secure channel, the authors’ new scheme relies on the elliptic curve cryptosystem and the Chinese remainder theorem operates over a public channel. The security of the secret shadows and the verification algorithm are based on the hardness of the elliptic curve discrete logarithm problem. They also extend the proposed scheme to an efficient verifiable multi-secret sharing (VMSS) scheme, particularly when the number of secrets is more than the threshold. As a result, their scheme is a multi-use and efficient VMSS on the public channel which provides the same level of security as traditional VMSS schemes with much shorter keys.

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.

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.

A Lightweight Public Verifiable Multi Secret Sharing Scheme Using Short Integer Solution

In this paper we introduce a multi secret sharing (MSS) scheme based on lattice conception. Lattice constitutes the core of many cryptographic constructions. The advantage of using lattice, which our scheme will inherit, is twofold: first is that the hardness of lattice problems is well understood. We will show that breaking our scheme leads to a solution for the robust Short Integer Solution problem. Hence, the presented scheme's security is guaranteed by leveraging lattice based conceptions. Second advantage is that working with lattice is simple and, consequently, execution is fast. A main problem with previous schemes is that they mostly are based on numerical assumptions which are slow and need much throughput. Inheriting simplicity and fastness make our scheme an excellent choice to implement in facilities with limit computational power and resources. In secret sharing schemes, typically in any protocol, dishonest participants and dealer can cheat during execution. To mitigate these concerns we augment our scheme with verifiability properties, say verifiable and public verifiable secret sharing. Verifiability prevents the dealer to share wrong shares and public verifiability forces participants to submit their sub-shares correctly. In MSS schemes, releasing some public values which are used in recovering step is inevitable. At the end, a comprehensive comparison by a table in the conclusion section shows that the presented scheme has minimum number of public values among MSS schemes.

A Secure and Verifiable Multi Secret Sharing Scheme for Encrypting Two Secret Images into Two Shares

A Secure and Verifiable Multi Secret Sharing Scheme for Encrypting Two Secret Images into Two Shares

A (n,t,n) Verifiable Multi-secret Sharing Scheme with Secure Secret Reconstruction

In a verifiable multi-secret sharing scheme, multiple secrets can be shared in one process and the shares can be verified. We propose a novel verifiable multi-secret sharing scheme in this paper. The scheme has the following advantages: (i) A mutually trusted dealer is no longer needed to distribute shares; (ii) shares can be verified by shareholders both in the secret generation and reconstruction phases; and (iii) any adversary without providing a valid share cannot recover the real secrets in the secret reconstruction phase. A secret sharing scheme with above-mentioned advantages is also described as a stepping stone, before we propose the multi-secret sharing scheme. We give the definition of a

A New Verifiable Multi-secret Sharing Scheme Realizing Adversary Structure

In some practical applications of secret sharing schemes, such as Byzantine Quorum systems and secure multi-party protocols, the adversary can corrupt subsets of participants at the same time and exploits their shares to recover the secret. In these applications, the system can be described directly by corruptible subsets of participants (so-called adversary structure). A secret sharing scheme realizing adversary structure is a tool for these applications. It is a method of sharing a secret among a finite set of participants in such a way that only certain pre-specified subsets of participants cannot recover the secret. In this paper, we propose a verifiable multi-secret sharing scheme based on one-way hash function that realizes adversary structure, in which each participant has only one reusable shadow. In this scheme, the participant set and the adversary structure can be changed without refreshing any participant's secret shadow and new secrets can be shared. The security of the proposed scheme is based on the properties of the one-way hash function. Our scheme has the advantages of better verifiability and fewer shadows preserves by every participant respect to other schemes realizing adversary structures.

A (k,t,n) Verifiable Multi-secret Sharing Scheme Based on Adversary Structure

A (n,t, n) secret sharing scheme is to share a secret among n group members, where each member also plays a role of a dealer, and any t shares can be used to recover the secret. In this paper, we propose a strong (k,t, n) verifiable multi-secret sharing scheme, where any k out of n participants operate as dealers. The scheme realizes both threshold structure and adversary structure simultaneously, and removes a trusted third party. The secret reconstruction phase is performed using an additive homomorphism for decreasing the storage cost. Meanwhile, the scheme achieves the pre-verification property in the sense that any participant doesn’t need to reveal any information about real master shares in the verification phase. We compare our proposal with the previous (n,t, n) secret sharing schemes from the perspectives of what kinds of access structures they achieve, what kinds of functionalities they support and whether heavy storage cost for secret share is required. Then it shows that our scheme takes the following advantages: (a) realizing the adversary structure, (b) allowing any k out of n participants to operate as dealers, (c) small sized secret share. Moreover, our proposed scheme is a favorable candidate to be used in many applications, such as secure multi-party computation and privacy preserving data mining, etc.

Publicly verifiable multi‐secret sharing scheme from bilinear pairings

In a verifiable multi-secret sharing (VMSS) scheme, multiple secrets are shared among participants during one sharing process in such a way that some qualified subsets of them can recover these secrets. Verifiable property means that one participant may verify his/her own share, but cannot check the validity of the other participants’ shares. Verifiable property is deficient for some specific applications such as electronic voting and revocable electronic cash. Publicly verifiable property is more applicable than verifiable property because the shares can be verified by any party. In this study, an efficient publicly verifiable multi-secret sharing (PVMSS) scheme using bilinear pairings is proposed. Under the computational Diffie–Hellman and modified bilinear Diffie–Hellman assumptions, the authors demonstrate that the proposed scheme is a secure PVMSS scheme.

A Finite Equivalence of Verifiable Multi-secret Sharing

Abstract We give an abstraction of verifiable multi-secret sharing schemes that is accessible to a fully mechanized analysis. This abstraction is formalized within the applied pi-calculus by using an equational theory which characterizes the cryptographic semantics of secret share. We also present an encoding from the equational theory into a convergent rewriting system, which is suitable for the automated protocol verifier ProVerif. Based on that, we verify the threshold certificate protocol in ProVerif.

On Novel Verifiable Multi-Secret Sharing Scheme

On Novel Verifiable Multi-Secret Sharing Scheme

A Note On a Threshold Verifiable Multi-Secret Sharing Scheme

In a verifiable multi-secret sharing (VMSS) scheme, multiple secrets can be shared by one sharing process. In 2008, Massoud and Mashhadi proposed a threshold VMSS scheme. They claimed that the scheme had efficient verifiable property that was better than the scheme proposed by Shao and Cao. In this paper, we analyse their scheme and point out that it cannot identify whether the dealer and the participants are honest or not. We further improve their scheme to make it satisfy verifiable property. It notes that the verifiable property in our improved scheme is information-theoretic secure which is more secure than the computationally secure verifiable property of previous schemes.

A New Verifiable Multi-secret Sharing Scheme Based on Bilinear Maps

In a (t, n)-threshold multi-secret sharing scheme, several secrets are shared among n participants in such a way that any t (or more) of them can reconstruct the secrets while a group of (t ? 1) can not obtain any information. Therefore, when such schemes are used to distribute sensitive information over a network, fault tolerance property is achieved since even if n ? t of the nodes go out of function, the remaining t nodes suffice to recover the information. In 2009, Wang et al. proposed a verifiable (t, n)-threshold multi-secret sharing scheme (WTS) based on elliptic curves in which the secrets can change periodically [Wireless Pers. Commun., Springer-Verlage, doi: 10.1007/s11277-009-9875-0] . In this paper, we propose a verifiable (t, n)-threshold multi-secret sharing scheme based on bilinear maps. Our scheme does not require a secure channel and participants can verify the shares pooled in the reconstruction phase. Our proposed scheme is multi-use such that in order to change the secrets, it is sufficient to renew some public information. Furthermore, the proposed scheme is flexible to the threshold value. Therefore, our proposed scheme has all the merits of (WTS), however, we achieve two major improvements. First when the secrets are to be changed, we require to publish fewer public values. This reduction can be very important in certain applications such as steganographic use of secret sharing schemes. The second is that (WTS) is designed with the assumption that the number of secrets (m) is equal to the threshold t so that the case m > t is handled by repeating the scheme $${\left\lceil \frac{m}{t}\right\rceil}$$ times. However, in designing the scheme we do not assume any restrictions on the number of secrets.

A new efficient (t, n) verifiable multi-secret sharing (VMSS) based on YCH scheme

A verifiable multi-secret sharing scheme (VMSS) is a multi-secret sharing scheme with the verifiable property. This paper presents a new efficient verifiable multi-secret sharing based on YCH [C.-C. Yang, T.-Y. Chang, M.-S. Hwang, A (t,n) multi-secret sharing scheme, Appl. Math. Comput. 151 (2004) 483–490] scheme and the intractability of the discrete logarithm (DL). And it just needs few public values and low modular exponentiation operation.