Verifiable Secret Sharing Research Articles

Lightweight Asynchronous Verifiable Secret Sharing with Optimal Resilience

We present new protocols for Asynchronous Verifiable Secret Sharing for Shamir (i.e., threshold t<n\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t<n$$\\end{document}) sharing of secrets. Our protocols:Use only “lightweight” cryptographic primitives, such as hash functions;Can share secrets over rings such as Z/(pk)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {Z}}/(p^k)$$\\end{document} as well as finite fields Fq\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {F}_q$$\\end{document};Provide optimal resilience, in the sense that they tolerate up to t<n/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$t < n/3$$\\end{document} corruptions, where n is the total number of parties;Are complete, in the sense that they guarantee that if any honest party receives their share then all honest parties receive their shares;Employ batching techniques, whereby a dealer shares many secrets in parallel and achieves an amortized communication complexity that is linear in n, at least on the “happy path”, where no party provably misbehaves.

Feldman's Verifiable Secret Sharing for a Dishonest Majority

Verifiable secret sharing (VSS) protocols enable parties to share secrets while guaranteeing security (in particular, that all parties hold valid and consistent shares) even if the dealer or some of the participants are malicious. Most work on VSS focuses on the honest majority case, primarily since it enables one to guarantee output delivery (e.g., a corrupted recipient cannot prevent an honest dealer from sharing their value). Feldman's VSS is a well known and popular protocol for this task and relies on the discrete log hardness assumption. In this paper, we present a variant of Feldman's VSS for the dishonest majority setting and formally prove its security. Beyond the basic VSS protocol, we present a publicly-verifiable version, as well as show how to securely add participants to the sharing and how to refresh an existing sharing (all secure in the presence of a dishonest majority). We prove that our protocols are UC secure, for appropriately defined ideal functionalities.

Universal Adaptive Construction of Verifiable Secret Sharing and Its Application to Verifiable Secure Distributed Data Storage

Universal Adaptive Construction of Verifiable Secret Sharing and Its Application to Verifiable Secure Distributed Data Storage

VSSB-Raft: A Secure and Efficient Zero Trust Consensus Algorithm for Blockchain

To solve the problems of vote forgery and malicious election of candidate nodes in the Raft consensus algorithm, we combine zero trust with the Raft consensus algorithm and propose a secure and efficient consensus algorithm -Verifiable Secret Sharing Byzantine Fault Tolerance Raft Consensus Algorithm (VSSB-Raft). The VSSB-Raft consensus algorithm realizes zero trust through the supervisor node and secret sharing algorithm without the invisible trust between nodes required by the algorithm. Meanwhile, the VSSB-Raft consensus algorithm uses the SM2 signature algorithm to realize the characteristics of zero trust requiring authentication before data use. In addition, by introducing the NDN network, we redesign the communication between nodes and guarantee the communication quality among nodes. The VSSB-Raft consensus algorithm proposed in this paper can make the algorithm Byzantine fault tolerant by setting a threshold for secret sharing while maintaining the algorithm’s complexity to be O(n). Experiments show that the VSSB-Raft consensus algorithm is secure and efficient with high throughput and low consensus latency.

Lightweight and Secure Multi-Message Multi-Receiver Certificateless Signcryption Scheme for the Internet of Vehicles

The Internet of Vehicles (IoV) improves traffic efficiency and enhances driving safety through the real-time collection and analysis of traffic-related data. Numerous secure and privacy-preserving communication protocols have been proposed for the IoV. However, various security threats, privacy leakage, and inefficient communications remain unaddressed. Therefore, a lightweight and secure multi-message multi-receiver certificateless signcryption (LS-MRCLSC) scheme based on elliptic curve cryptography (ECC) is proposed. The proposed scheme guarantees secure communication and promotes messaging efficiency with multi-cast mode. Multiple key generation centers (KGCs) collaborate to generate and update the system master key (SMK) using Feldman’s verifiable secret-sharing (FVSS) algorithm, avoiding the single point of failure (SPoF) problem. Formal security proofs under the random oracle model (ROM) demonstrate that the proposed scheme meets requirements such as data confidentiality, message unforgeability, anonymity, and unlinkability. Performance evaluations confirm that the LS-MRCLSC scheme is better than similar schemes in terms of efficiency, feasibility, and scalability.

ICRB: An improved consensus‐based redactable blockchain considering contextual consistency

AbstractBlockchain is a distributed ledger proposed by Satoshi Nakamoto. It has become one of the most important networks for humans in the world. With the rapid development of blockchain technology, an increasing number of criminals are engaging in fraudulent activities, extortion and other financial crimes on the blockchain. Due to the immutability of blockchain, it is difficult for users to recover their losses. Some scholars have proposed the concept of the redactable blockchain. However, most redactable blockchain schemes fail to consider the impact of modification on the contextual economic relationships of the blockchain. We propose an improved redactable blockchain considering contextual consistency. Additionally, we utilize a security deposit mechanism to guarantee financial contextual consistency for the modified blockchain. We distribute users' security deposit account private keys to random users on the blockchain using Verifiable Secret Sharing, Verifiable Random Functions and other cryptographic primitives to achieve decentralized key management and modification. Experiments show that the performance of our scheme is acceptable in realistic situations.

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.

Practical Undeniable Multiparty Drawing-Straw Protocol in Asynchronous Networks for Resource-Constrained Information Systems

The next generation of mobile networks and communications (5G networks) has a very strong ability to compute, store, and so on. Group-oriented applications demonstrate their potential ability in resource-constrained information systems (RISs) towards 5G. The security issues in RIS towards 5G have attracted great attention. For example, how to conduct fair and orderly multiparty communication in an intelligent transportation system (ITS). One of the main challenges for secure group-oriented applications in RIS towards 5G is how to manage RIS communications fairly in multiparty applications. In other words, when the users cannot transmit their messages simultaneously, the order of their communication can cause security concerns in multiparty applications. A feasible solution to the problem is for the group of users to follow a specific order to transmit their messages. Otherwise, some users may take advantage over other users if there has no agreeable order to be followed. In this paper, we propose a novel cryptographic primitive, called multiparty drawing-straw (MDS) protocol, which can be used by a group of users to determine the order of the group to participate in the multiparty applications. Our scheme is based on Pedersen’s verifiable secret sharing (VSS), which is a well-known scheme. Our proposed protocol is fair since the output is uniformly distributed, and this is an attractive feature for secure multiparty applications in RIS towards 5G.

Secure verifiable aggregation for blockchain-based federated averaging

IoT devices’ storage and computation capacities are constantly increasing in recent years, which brings critical challenges in data privacy protection. Federated learning (FL) and blockchain technology are two popular techniques used in IoT data aggregation, where FL enables data training with privacy protection, and blockchain provides a decentralized architecture for data storage and mining. However, very few the state-of-the-art works consider the applicability of the combination of FL and blockchain. In this paper, we adopt the federated averaging algorithm to reduce the communication overhead between the blockchain and end users to achieve higher performance. We also apply the double-mask-then-encrypt approach for end users to submit their local updates in order to protect data privacy. Finally, we propose and implement a non-interactive Public Verifiable Secret Sharing (PVSS) algorithm with Distributed Hash Table (DHT) that solves the user-drop-out problem and improves the communication efficiency between blockchain and end-users. At last, we theoretically analyze the security strengths of the proposed solution and conduct experiments to measure the execution time of PVSS on both the server and clients sides.

Towards self-stabilizing blockchain, reconstructing totally erased blockchain

Blockchains are commonly used for crypto-currency systems, where they publicly store transactions. In a permissioned blockchain, only a few participants (nodes) can push new transactions to the chain. The known boundary on the number of faulty participants – up to f for 3f+1 participants – may be surpassed, causing the underlying consensus algorithm (BFT) to fail. When a malicious adversary compromises or corrupts enough nodes it may lead to the complete corruption of the ledger and even to the destruction of ledger copies the nodes hold. We suggest a reconstruction solution for the blockchain in the event of such an attack. We present a technique using verifiable secret sharing (VSS), making our solution immediate, requires no trust between the different blockchain parties, and provides each user an independent reconstruction. Our solution enables the exposure of an end-user's private key in case of dishonest reconstruction, thus, removing the incentive of such an act.

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.

A Lightweight Verifiable Secret Sharing in Internet of Things

A Lightweight Verifiable Secret Sharing in Internet of Things

Simple Approach to Realizing Verifiable Secret Sharing for Secure Cloud System

In (<i>k, n</i>) threshold secret sharing, a secret is converted into n shares such that any threshold <i>k</i> or more shares allow for the reconstruction of this secret; however, the total storage cost increases. By contrast, asymmetric secret sharing reduces the total shares to be stored. When implementing secret sharing in the cloud, if malicious players submit forged shares during the reconstruction process, the reconstructed value will differ from the original secret. Therefore, a method that quickly verifies the integrity of the restored secret should be developed. Many research papers investigate cheater detection/identification for (<i>k, n</i>) threshold secret sharing. However, most of them require additional information, such as an authenticator. Harn et al. proposed a method for cheat detection using only the shares for (<i>k, n</i>) threshold secret sharing. In this study, we improved and extended the method proposed by Harn et al. to realize the detection and identification of shares forgery (cheating) in asymmetric secret sharing suitable for a cloud system. The proposed method uses the shares generated during asymmetric secret sharing to reconstruct and verify the secret. We also included an attack that assumes a cloud system and shows that most methods cannot work against it. Finally, we discussed the requirements for a secret sharing scheme suitable for the cloud and showed that the proposed method is ideal for use in a cloud environment.

Recoverable Private Key Scheme for Consortium Blockchain Based on Verifiable Secret Sharing

Recoverable Private Key Scheme for Consortium Blockchain Based on Verifiable Secret Sharing

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).

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.

Publicly verifiable threshold secret sharing based onthree‐dimensional‐cellularautomata

AbstractSecret sharing schemes are being widely used to distribute a secret between various participants so that an authorized subset of participants belonging to appropriate access structures can reconstruct this secret. However, a dealer might get corrupted by adversaries and may influence this secret sharing or the reconstruction process. Verifiable secret sharing (VSS) overcomes this issue by adding a verifiability protocol to the original secret sharing scheme. This article proposes a computationally secure publicly verifiable secret sharing scheme based on the three‐dimensional cellular automata (3D‐CA). Unlike the more widely used linear secret sharing schemes or secret sharing scheme based on the Chinese remainder theorem, our proposed scheme performs the secret sharing using 3D‐CA. The secret is considered one of the initial configurations of the 3D‐CA, and the following configurations are devised to be the shares distributed among the participants. Update mechanisms and various rules make it hard for an adversary to corrupt or duplicate a share. To make it even more efficient, we have added a verifiability layer such that a dealer posts a public share and private share to each shareholder. The verifiability layer reduces the interaction between dealer and participants and hence increases the security. The randomness of the shares has been calculated using the National Institute of Standards and Technology statistical test suite.

Practical and Provably Secure Distributed Aggregation: Verifiable Additive Homomorphic Secret Sharing

Often clients (e.g., sensors, organizations) need to outsource joint computations that are based on some joint inputs to external untrusted servers. These computations often rely on the aggregation of data collected from multiple clients, while the clients want to guarantee that the results are correct and, thus, an output that can be publicly verified is required. However, important security and privacy challenges are raised, since clients may hold sensitive information. In this paper, we propose an approach, called verifiable additive homomorphic secret sharing (VAHSS), to achieve practical and provably secure aggregation of data, while allowing for the clients to protect their secret data and providing public verifiability i.e., everyone should be able to verify the correctness of the computed result. We propose three VAHSS constructions by combining an additive homomorphic secret sharing (HSS) scheme, for computing the sum of the clients’ secret inputs, and three different methods for achieving public verifiability, namely: (i) homomorphic collision-resistant hash functions; (ii) linear homomorphic signatures; as well as (iii) a threshold RSA signature scheme. In all three constructions, we provide a detailed correctness, security, and verifiability analysis and detailed experimental evaluations. Our results demonstrate the efficiency of our proposed constructions, especially from the client side.

Broadcast Complexity and Adaptive Adversaries in Verifiable Secret Sharing

Verifiable secret sharing (VSS) is one of the basic problems in the theory of distributed cryptography and has an important role in secure multiparty computation. In this case, it is tried to share a confidential data as secret, between multiple nodes in a distributed system, in the presence of an active adversary that can destroy some nodes, such that the secret can be reconstructed with the participation of certain size of honest nodes. A dynamic adversary can change its corrupted nodes among the protocol. So far, there is not a formal definition and there are no protocols of dynamic adversaries in VSS context. Also, another important question is, would there exist a protocol to share a secret with a static adversary with at most 1 broadcast round? In this paper, we provide a formal definition of the dynamic adversary. The simulation results prove the efficiency of the proposed protocol in terms of the runtime, the memory usage, and the number of message exchanges. We show that the change period of the dynamic adversary could not happen in less than 4 rounds in order to have a perfectly secure VSS, and then we establish a protocol to deal with this type of adversary. Also, we prove that the lower bound of broadcast complexity for the static adversary is (2,0)-broadcast rounds.

Verifiable Self-Selecting Secret Sharing Based on Elliptic Curves

In distributed systems, as any network architecture, cryptography has a vital role in communication security, and sharing a secret represents a jump in this field where the secret depends on a group instead of a single person. In this article, the authors propose a method to share a multi secrets matrix represented by an image, that could be reconstructed without any loss by an access structure over a distributed system. The presented approach has a verifiable property, where each candidate possesses the advantage to verify the validity of his shadow. The security level of the scheme is based on elliptic curve discrete logarithm problem and the opportunity of allowing each side to generate a private sub-secret key for the sharing. The benefit of this method is justified by the absence of information loss and a lower timing results.