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.

Laser‐Induced Graphene Hologram Reconfiguration for Countersurveillance Multisecret Sharing (Laser Photonics Rev. 17(8)/2023)

Laser‐Induced Graphene Hologram Reconfiguration for Countersurveillance Multisecret Sharing (Laser Photonics Rev. 17(8)/2023)

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

Laser‐Induced Graphene Hologram Reconfiguration for Countersurveillance Multisecret Sharing

AbstractSecret sharing, as a sophisticated cryptographic technique, is widely used to protect important messages in the information era. As an important evaluation criterion, being able to provide timely warning and judge the security of the secret once eavesdropping occurs is a highly practical way to minimize losses. Here, the concept of countersurveillance holographic secret sharing based on laser‐induced irreversible hologram reconfiguration of graphene oxides (GO) is demonstrated. The laser‐ and thermal diffusion‐induced reduced graphene oxides (rGO) form two regions with different transmittances, which are defined as rGO superpixels. The rGO superpixels enable synchronous two‐amplitude‐state modulation of the holographic pixels, resulting in hologram reconfiguration. As such, multisecret sharing is realized by introducing a deep‐learning gradient descent algorithm into hologram encoding, which broadens the functionality and information capacity. The results establish a high‐security information delivery platform based on GO and pave the way for an all‐optical on‐chip holographic cryptography strategy.

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 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.

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.

Unordered Multisecret Sharing Based on Generalized Chinese Remainder Theorem

Multisecret sharing schemes have been widely used in the area of information security, such as cloud storage, group authentication, and secure parallel communications. One of the issues for these schemes is to share and recover multisecret from their shareholders. However, the existing works consider the recovery of multisecret only when the correspondences between the secrets and their shares are definite. In this paper, we propose a multisecret sharing scheme to share and recover two secrets among the participants based on the generalized Chinese Remainder Theorem (GCRT), where the multisecret and their shares are unordered. To overcome the leakage of information, we propose an improved scheme including the improved sharing phase and the recovery phase. The improved scheme has not only a more secure performance but also a lower computation complexity. The conditions for recovery failure and success are also explored.

Multi-secret Sharing Model based on Hermite Interpolation Polynomial and Quantum Graph State

With the rise of the Internet plus blockchain, quantum secure communication has become a hot topic of interdisciplinary research. Secret sharing is the key technology to realize blockchain. In this paper, the Hermite interpolation polynomial combined with the idea of homomorphic cryptography is used to construct a multi-secret sharing model based on quantum graph theory. This paper relies on the theory of quantum theory to have mature theoretical and experimental foundations in quantum preparation, storage transmission, and measurement feasibility and overcomes the existing program feasibility problems and potential security problems with classical cryptography. This model is outsourced, verifiable, and extensible and has a high information rate. It can effectively resist external interception, replay, entanglement, tampering attacks and internal forgery, impersonation, deception, and collusion attacks. This paper has carried on a detailed analysis of the model.

Generating logistic chaotic sequence using geometric pattern to decompose and recombine the pixel values

The Secret Sharing Scheme plays a vital role in cryptography which allows to transmit the secret digital information (image, video, audio, handwriting, etc.,) over a communication channel. This cryptographic technique involves encrypting the secret images into noisy shares and transmitted. The transmitted image shares are reconstructed using simple logical computation. In this paper, we propose a secure (n, n)- Multi-Secret-Sharing (MSS) scheme using image scrambling algorithm which is based on the logistic chaotic sequence generated using the secret key which is retrieved from the geometric pattern named as spirograph which drawn by the users with their private values. Also, decomposition and recombination of image pixels which points to change the position and values of the pixels. The experimental results estimate that the standard metrics NPCR, UACI, Entropy, Coefficient Correlation values proves the rigidness of the implemented algorithm.

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.

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 New Reversible Data Hiding in Encrypted Image Based on Multi-Secret Sharing and Lightweight Cryptographic Algorithms

Reversible data hiding in encrypted images (RDHEI) has been introduced for preserving image privacy and data embedding. RDHEI usually involves three parties, namely, the image provider, data hider, and receiver. On the security with key setting, there are three categories: share independent secret keys (SIK), shared one key (SOK), and share no secret keys (SNK). In SIK, the image provider and data hider must respectively and independently share secret keys with the receiver, whereas in SNK, no secret key is shared. However, the literature works proposed SNK-type schemes by using homomorphic encryption (with exorbitant computation cost). In this paper, we address the SOK setting, where only the image provider shares a secret key with the receiver, and the data hider can embed a secret message without any knowledge of this key. To realize our SOK scheme in a simple manner, we propose a new technique by using multi-secret sharing as the underlying encryption, which indeed induces a blow-up issue of the key size. For preserving the efficiency of the key size, we apply a compression by using lightweight cryptographic algorithms. Then, we demonstrate our SOK scheme based on the proposed techniques, and show effectiveness, efficiency, and security by experiments and analysis.

Light Repository Blockchain System with Multisecret Sharing for Industrial Big Data

Blockchain is an emerging technology that promises many exciting applications in various fields, including financial, medical, energy, and logistics management. However, there are still some limitations in the existing blockchain framework that prevents its widespread adoption in the commercial world. One important limitation is the storage requirement, wherein each blockchain node has to store a copy of the distributed ledger. Thus, as the number of transactions increases, this storage requirement grows quadratically, eventually limiting the scalability of a blockchain system. Moreover, the public ledger in a blockchain framework allows anyone in the network to audit the transaction, which may not be favourable in some privacy-sensitive applications. In this paper, a secret-sharing scheme is proposed to reduce the size of the blockchain transactions. Each transaction block is divided into t parts, and the size of each part is 1/t size of transaction block. We use the secret-sharing mechanism to share t parts into n shares. Hence, each node stores not one transaction but one share in the blockchain system. The proposed scheme can eventually reduce the storage cost of a blockchain transaction by 1/t without introducing an additional recovery communication cost; however, robustness is reduced in node failure as a tradeoff. Meanwhile, the proposed scheme was more efficient and secure compared to other state-of-the-art schemes that aim to reduce blockchain storage for industrial big data.

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.