Verifiable Secret Sharing Scheme Research Articles

Game-based security proofs for verifiable secret sharing schemes in the standard model

ABSTRACT In a verifiable secret sharing (VSS) scheme, each participant can check cheating by the dealer or the other participants. In this work, we construct a VSS scheme with the strongest level of computational security and prove its security in the standard model. This scheme is secure against active attack and does not use bilinear pairing and hash function.

A Survey on Perfectly Secure Verifiable Secret-sharing

Verifiable Secret-Sharing(VSS) is a fundamental primitive in secure distributed computing. It is used as a building block in several distributed computing tasks, such as Byzantine agreement and secure multi-party computation. In this article, we consider VSS schemes withperfectsecurity, toleratingcomputationally unboundedadversaries. We comprehensively survey the existing perfectly secure VSS schemes in three different communication settings, namely, synchronous, asynchronous, and hybrid setting and provide full details of the existing schemes in these settings. The aim of this survey is to provide a clear knowledge and foundation to researchers who are interested in knowing and extending the state-of-the-art perfectly secure VSS schemes.

Verifiable Secret Sharing Scheme Based on Certain Projective Transformation

The main purpose of verifiable secret sharing scheme is to solve the honesty problem of participants. In this paper, the concept of nonzero k-submatrix and theresidual vector of system of hyperplane intersecting line equations is proposed. Based on certain projective transformations in projective space, a verifiable (t, n)-threshold secret sharing scheme is designed by using the structure of solutions of linear equations and the difficulty of solving discrete logarithm problems. The results show that this scheme can verify the correctness of the subkey provided by each participant before the reconstruction of the master key, and can effectively identify the fraudster. The fraudster can only cheat by guessing and the probability of success is only 1/p. The design of the scheme is exquisite and the calculation complexity is small. Each participant only needs to hold a subkey, which is convenient for management and use. The analysis shows that the scheme in this paper meets the security requirements and rules of secret sharing, and it is a computationally secure and effective scheme with good practical value.

Verifiable Secret Sharing Scheme Based on the Plane Parametric Curve

Verifiable secret sharing is a special kind of secret sharing. In this paper, A secure and efficient threshold secret sharing scheme is proposed by using the plane parametric curve on the basis of the principle of secret sharing. And the performance of this threshold scheme is analyzed. The results reveal that the threshold scheme has its own advantage of one-parameter representation for a master key, and it is a perfect ideal secret sharing scheme. It can easily detect cheaters by single operation in the participants so that the probability of valid cheating is less than 1/p (where p is a large prime).

RSU authentication in vehicular ad hoc networks base on verifiable secret sharing

Vehicular ad hoc networks (VANET) is seen as an effective solution to ensure the driving safety and efficiency. As a key foundation, the road side unit (RSU) connect with each other to form a backbone network in VANET. The authentication of RSUs is the main tasks to prevent the secure communication in VANET suffering from various attacks caused by cunning adversaries. In this paper, we propose a new type of verifiable secret sharing (VSS) scheme based on bivariate polynomial to achieving the RSU authentication in a secret sharing way. Our proposed VSS based authentication includes two phases. In phase 1, the t RSUs that participate in secret reconstruction collaborate to detect whether there exist illegitimate ones; in phase 2, the t legitimate RSUs reveal their shares for secret reconstruction, and the fake shares can be identified. Our VSS facilitates the RSU authentication since (1) any RSUs participate in secret reconstruction can be confirmed legitimate, (2) any fake shares revealed in secret reconstruction can be identified, (3) a globalized group temporary session key will be established after the VSS process. In addition, our VSS scheme is unconditional secure since the security of our VSS is not based on any computational assumption.

A Hybrid-Based Verifiable Secret Sharing Scheme Using Chinese Remainder Theorem

It is not always in the best interests to rely on an individual to have control of entire sensitive information. This has led to the need for secret sharing schemes, which divide secret (key) among many participants or shareholders. To avoid any cheating by any of the shareholders, the need for verifiable secret sharing (VSS) has emerged. In this context, a hybrid approach for VSS scheme is suggested in this paper. The proposed algorithm shares multiple secrets among shareholders, where shareholders are also divided/classified into different levels. Hence, it includes multiple as well as multilevel secret sharing. Secrets can be recovered at intra- or inter-level, where shareholders of higher level can contribute their shares to lower levels. To reduce the complexity, the one-way hash function is used instead of the hard number-theoretic problems. The proposed scheme stands against the dishonest dealer and shareholders. To rule out a typical dishonest strategy of leaking secret information in the valid shares, the concept of dealer leakage resilience is used by reducing the dealer’s powers of selecting random values on his own. The execution is also done using cryptographic libraries. Finally, it is demonstrated that the scheme satisfies the security requirements of VSS.

Computationally Secure Verifiable Secret Sharing Scheme for Distributing Many Secrets

Computationally Secure Verifiable Secret Sharing Scheme for Distributing Many Secrets

Space-Efficient Verifiable Secret Sharing Using Polynomial Interpolation

Preserving data confidentiality in clouds is a key issue. Secret Sharing, a cryptographic primitive for the distribution of a secret among a group of n participants designed so that only subsets of shareholders of cardinality 0 <; t ≤ n are allowed to reconstruct the secret by pooling their shares, can help mitigating and minimizing the problem. A desirable feature of Secret Sharing schemes is cheater detection, i.e., the ability to detect one or more malicious shareholders trying to reconstruct the secret by obtaining legal shares from the other shareholders while providing them with fake shares. Verifiable Secret Sharing schemes solve this problem by allowing shareholders verifying the others' shares. We present new verification algorithms providing arbitrary secret sharing schemes with cheater detection capabilities, and prove their space efficiency with regard to other schemes appeared in the literature. We also introduce, in one of our schemes, the Exponentiating Polynomial Root Problem (EPRP), which is believed to be NP-Intermediate and therefore difficult.

Verifiable Rational Secret Sharing Scheme in Mobile Networks

With the development of mobile network, lots of people now have access to mobile phones and the mobile networks give users ubiquitous connectivity. However, smart phones and tablets are poor in computational resources such as memory size, processor speed, and disk capacity. So far, all existing rational secret sharing schemes cannot be suitable for mobile networks. In this paper, we propose a verifiable rational secret sharing scheme in mobile networks. The scheme provides a noninteractively verifiable proof for the correctness of participants’ share and handshake protocol is not necessary; there is no need for certificate generation, propagation, and storage in the scheme, which is more suitable for devices with limited size and processing power; in the scheme, every participant uses her encryption on number of each round as the secret share and the dealer does not have to distribute any secret share; every participant cannot gain more by deviating the protocol, so rational participant has an incentive to abide by the protocol; finally, every participant can obtain the secret fairly (means that either everyone receives the secret, or else no one does) in mobile networks. The scheme is coalition-resilient and the security of our scheme relies on a computational assumption.

Information-theoretical secure verifiable secret sharing with vector space access structures over bilinear groups and its applications

As a basic tool, Verifiable Secret Sharing (VSS) has wide applications in distributed cryptosystems as well as secure multi-party computations. A number of VSS schemes for sharing a secret from a finite field, both on threshold access structures and on general access structures, have been available. In this paper, we investigate the verifiably sharing of a secret that is a random element from a bilinear group on vector space access structures. For this purpose, we present an information-theoretical secure VSS scheme, and then convert it to a modified one with improved efficiency. The performance and the security of the proposed schemes are analyzed in detail. Two examples are given to illustrate the applications of our proposed VSS schemes. One is the secure sharing of an organization’s private key in Boneh and Franklin’s identity-based encryption system, and the other is the distributed key generation and distributed decryption for bilinear ElGamal encryption system, both with vector space access structures.

Privacy Preserving Distributed K-Means Clustering in Malicious Model Using Verifiable Secret Sharing Scheme

In this article, the authors propose an approach for privacy preserving distributed clustering that assumes malicious model. In the literature, there do exist, numerous approaches that assume a semi honest model. However, such an assumption is, at best, reasonable in experimentations; rarely true in real world. Hence, it is essential to investigate approaches for privacy preservation using a malicious model. The authors use the Pederson's Verifiable Secret Sharing scheme ensuring the privacy using additively homomorphic secret sharing scheme. The trustworthiness of the data is assured using homomorphic commitments in Pederson's scheme. In addition, the authors propose two variants of the proposed approach - one for horizontally partitioned dataset and the other for vertically partitioned dataset. The experimental results show that the proposed approach is scalable in terms of dataset size. The authors also carry out experimentations to highlight the effectiveness of Verifiable Secret Sharing scheme against Zero Knowledge Proof scheme.

An Efficient Autonomous Key Management with Verifiable Secret Sharing Schemes for Reduced Communication/Computation Costs in MANET

A primary concern in mobile impromptu networks (MANETs) is security. Not like typical infrastructure based mostly wireless networks like, wireless cellular net-works, Mobile ad hoc Networks (MANET) contains speedily deployable, self organizing and self maintaining capability options. Moreover, they will be shaped on the fly as required. Additional issues for MANET’s security arise as a result of its high quality to its users. A number of key management schemes have been proposed for MANETs. Due to the disadvantages in Shamir secret sharing such as distribute erroneous sub shares based on this that message transmission communication cost is increased. To overcome this Verifiable secret sharing schemes are used here. Existing research in key management can only handle very limited number of nodes and are inefficient, insecure, or unreliable when the nodes increases. Here this paper modifies Autonomous key management scheme is proposed to address both for security and efficiency for key management in Mobile Ad hoc Network (MANET). It also reduces communication and computational cost in Ad-Hoc Network and works for large number of nodes

Multiuser Message Authentication, Application to Verifiable Secret Sharing and Key Management Schemes

Providing authentication for the messages exchanged among a group of users is an important issue in secure group communication. We develop multiuser authentication schemes with perfect protection against colluding malicious users numbering fewer than k, where all the n users are allowed to be senders (simultaneously with being receivers). In our scheme each user is required to store secret information of size 2klog2 q 1 bits, and tags to authenticate messages are of length klog 2 q. We use this to obtain, in the setup in which the participants are allowed to employ previously distributed private keys, a non-interactive verifiable secret sharing scheme for multiple dealers, in which shares reveal no information about the secret, and dealers cannot deal inconsistent shares. We also provide authentication to the group key management schemes proposed by Blundo et al. and Fiat-Naor without incurring extra storage cost.

A New PVSS Scheme with a Simple Encryption Function

A Publicly Verifiable Secret Sharing (PVSS) scheme allows anyone to verify the validity of the shares computed and distributed by a dealer. The idea of PVSS was introduced by Stadler in [18] where he presented a PVSS scheme based on Discrete Logarithm. Later, several PVSS schemes were proposed. In [2], Behnad and Eghlidos present an interesting PVSS scheme with explicit membership and disputation processes. In this paper, we present a new PVSS having the advantage of being simpler while offering the same features.

Verifiable secret sharing based on the Chinese remainder theorem

ABSTRACTA (t,n) secret sharing scheme (SS) enables a dealer to divide a secret into n shares in such a way that (i) the secret can be recovered successfully with t or more than t shares, and (ii) the secret cannot be recovered with fewer than t shares. A verifiable secret sharing scheme (VSS) has been proposed to allow shareholders to verify that their shares are generated by the dealer consistently without compromising the secrecy of both shares and the secret. So far, there is only one secure Chinese remainder theorem‐based VSS using the RSA assumption. We propose a Chinese remainder theorem‐based VSS scheme without making any computational assumptions, which is a simple extension of Azimuth–Bloom (t,n) SS. Just like the most well‐known Shamir's SS, the proposed VSS is unconditionally secure. We use a linear combination of both the secret and the verification secret to protect the secrecy of both the secret and shares in the verification. In addition, we show that no information is leaked when there are fewer than t shares in the secret reconstruction. Copyright © 2013 John Wiley &amp; Sons, Ltd.

Publicly Verifiable Secret Sharing Scheme with Provable Security against Chosen Secret Attacks

Secret sharing is an important aspect of key management in wireless ad hoc and sensor networks. In this paper, we define a new secure model of secret sharing, use the Lagrange interpolation and the bilinear cyclic groups to construct an efficient publicly verifiable secret sharing scheme on the basis of this model, and show that this scheme is provably secure against adaptively chosen secret attacks (CSAs) based on the decisional bilinear Diffie-Hellman (DBDH) problem. We find that this scheme has the following properties: (a) point-to-point secure channels are not required in both the secret distribution phase and the secret reconstruction phase; (b) it is a noninteractive secret sharing system in that the participants need not communicate with each other during subshadow verification; and (c) each participant is able to share many secrets with other participants despite holding only one shadow.

Publicly Verifiable Secret Sharing Scheme Based on the Chinese Remainder Theorem

Publicly verifiable secret sharing schemes based on Lagrange interpolation utilize public cryptography to encrypt transmitted data and the validity of their shares can be verified by everyone, not only the participants. However, they require O(klog2k) operations during secret reconstruction phase. In order to reduce the computational complexity during the secret reconstruction phase we propose a non-interactive publicly verifiable secret sharing scheme based on the Chinese Remainder Theorem utilizing ElGamal cryptosystem to encrypt data, whonly requires O(k) operations during secret reconstruction phase. Theoretical analysis proves the proposed scheme achieves computation security and is more efficient.

Efficient Verifiable Secret Sharing Scheme over Bilinear Groups

Efficient Verifiable Secret Sharing Scheme over Bilinear Groups

Unconditionally Secure Verifiable Secret Sharing Scheme

Abstract A (t, n) secret sharing scheme permits a secret to be divided into n shares in such a way that any t or more than t shares can reconstruct the secret, but fewer than t shares cannot reconstruct the secret. Verifiable secret sharing (VSS) has been proposed to allow each shareholder to verify the validity of his own share, but not other shareholders' shares. In this paper, we propose an efficient verifiable secret sharing scheme based on Shamir's (t, n) secret sharing scheme. Our proposed scheme can protect the secret and all shares unconditionally in the verification process. Our proposed solution can be used as an important cryptographic tool to design protocols for other related problems of secret sharing.

Efficient VSS free of computational assumption

VSS (verifiable secret sharing) is an important security mechanism in distributed computing. It is a secret sharing technique, where each distributed share holder can verify that he obtains a share of a unique secret. Two properties are important in VSS: efficiency and security, where the security of VSS includes two requirements, bindingness and hidingness. In any application of VSS, high efficiency is desired. In applications with critical security requirements, bindingness and hidingness are desired to be achieved without any computational assumption on hard mathematical problems. No existing VSS scheme is efficient enough in both computation and communication for cost-sensitive applications, especially in the popular ubiquitous and distributed computing environment. When security is required without any hard computational assumption, efficient VSS is even more difficult. To overcome this drawback in VSS, a new secret sharing protocol is proposed in this paper. It does not need any assumption or condition like hardness of computational problems to achieve bindingness and hidingness. Especially, its privacy is information-theoretic instead of statistical in most existing VSS schemes. It is very efficient in both computation and communication and costs much less than the existing VSS schemes. Therefore, it improves the efficiency of VSS and achieves the strongest security in VSS.