Multi-secret Sharing Scheme Research Articles

Multi secret sharing with unexpanded meaningful shares

Traditional Visual Cryptography (VC) facilitates a technique to protect only one secret image using single set of shares. Recent researches enhance the capabilities of traditional VC by providing the feature of Multi Secret Sharing (MSS), where more than one secret image can be protected at a time. In MSS different secret images are revealed by the stacking of same set of shares at different angles. Most of the existing state of art researches on MSS have common problem of pixel expansion and random pattern of the shares. Due to pixel expansion, there is wastage of the storage space and transmission time, moreover random pattern of the shares increases the vulnerability for cryptanalysis. In this paper a novel Multi Secret Sharing scheme with unexpanded as well as meaningful shares has been proposed to protect two secret images at a time. In the proposed approach the recovery probability of black pixels of the secret images in the decoded images is always 1 while that of white pixels, it is 0.25. Therefore the contrast of the decoded images is obtained as 25 % which is same as in most of the earlier researches with pixel expansion & random shares. Experiments confirm that all meaningful shares fulfill the contrast and security conditions. Secret images can be easily decoded by only human visual system without any computation at receiver end.

Efficient and secure multi secret sharing schemes based on boolean XOR and arithmetic modulo

Multi Secret Sharing (MSS) scheme is an efficient method of transmitting more than one secret securely. In (n, n)-MSS scheme n secrets are used to create n shares and for reconstruction, all n shares are required. In state of the art schemes n secrets are used to construct n or n + 1 shares, but one can recover partial secret information from less than n shares. There is a need to develop an efficient and secure (n, n)-MSS scheme so that the threshold property can be satisfied. In this paper, we propose three different (n, n)-MSS schemes. In the first and second schemes, Boolean XOR is used and in the third scheme, we used Modular Arithmetic. For quantitative analysis, Similarity metrics, Structural, and Differential measures are considered. A proposed scheme using Modular Arithmetic performs better compared to Boolean XOR. The proposed (n, n)-MSS schemes outperform the existing techniques in terms of security, time complexity, and randomness of shares.

(t, n) Multi-Secret Sharing Scheme Based on Bivariate Polynomial

In a (t, n) secret sharing scheme (SS), a dealer divides the secret into n shares in such way that any t or more than t shares can reconstruct the secret but fewer than t shares cannot reconstruct the secret. The multi-SS is an extension of the (t, n) SS in which shares can be reused to reconstruct multiple secrets. Thus, the efficiency of the multi-SS is better than the efficiency of the (t, n) SS. In this paper, we propose the first multi-SS using a bivariate polynomial. Our design is unique in comparing with all existing multi-SSs. Shares generated using a bivariate polynomial can not only be used to reconstruct multiple secrets but also be used to establish pairwise keys between any pair of shareholders. The pairwise keys can protect exchange information in the secret reconstruction to prevent outsiders from obtaining the recovered secrets. All existing multi-SSs require additional key establishment to accomplish this.

XOR based continuous-tone multi secret sharing for store-and-forward telemedicine

Traditional k out of n visual cryptography scheme has been proposed to encrypt single secret image into n shares where only k or more shares can decode the secret image. Many existing schemes on visual cryptography are restricted to consider only binary images as secret which are not appropriate for many important applications. Store-and-Forward telemedicine is one such application where medical images are transmitted from one site to another via electronic medium to analyze the patient's clinical health status. The main objective of Store-and-Forward telemedicine is to provide remote clinical services via two-way communication between the patient and the healthcare provider using electronic medical image, audio and video means. In this paper, a new XOR based Continuous-tone Multi Secret Sharing scheme suitable for store-and-forward telemedicine is proposed to securely transmit the medical images. It also eliminates basic security constraints of VC like pixel expansion in shares/recovered secret images, random pattern of shares, explicit codebook requirement, lossy recovery of secret and limitation on number of secret and shares. Proposed approach is n out of n multi secret sharing scheme which is able to transmit n secret images simultaneously. All secrets could be revealed only after some computations with all n shares and one master share. Master share has been created with the secret key at encoding phase and it can be regenerated at the time of decoding using same secret key. Here all shares are meaningful in continuous-tone which may provide confidentiality to medical images during transmission. Proposed approach not only preserves all basic characteristics of traditional VC but also increases the capacity of secret image sharing. From the experiments we found that irrespective of visible contents of the shares, the probability of getting back the pixel values of respective original secret images at the receiver end is very high.

Universal Share for Multisecret Image Sharing Scheme Based on Boolean Operation

Conventional secret sharing schemes require complex computation. Visual secret sharing (VSS) scheme encrypts a secret into two or more meaningless images, called as shares. Shares are stacked together to decrypt a secret using human visual system. In recent years, concept of universal share is introduced to share multiple gray images. A company organizer uses this unique share to recover multiple images. However, utilization of complex numerical computation makes such system inappropriate for VSS. In this letter, we overcome this complexity issue and propose a Boolean-based light-weight computation scheme to share multiple secrets using universal share. The proposed Boolean-based multisecret sharing (MSS) scheme encodes n secret images into a universal share and n meaningless shares, and reconstructs lossless secret images. To provide threshold security, the proposed scheme uses random universal share generating function to generate a distinct universal share from base universal share for each secret image. Moreover, to enhance limited sharing capacity of the Boolean-based MSS scheme, we propose a modified Boolean-based MSS 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.

How to Fairly Share Multiple Secrets Stage by Stage

A multi-stage secret sharing scheme (MSSS) allows a dealer to share multiple secrets among a set of participants, in such a way that any authorized subset of participants can reconstruct the secrets stage-by-stage. In this paper, for the first time we propose an efficient MSSS based on the non-homogeneous linear feedback shift register (NHLFSR). According to the properties of NHLFSRs, this scheme has few public information, a new simple distribution, and various techniques for the reconstruction phase.

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

Optimal Improvement Ratios of Multi-Secret Sharing Schemes Can Be Achieved

Secret sharing schemes (SSS) deal with activities relative to the secure distribution of a secret among a group of participants who then securely reconstruct the secret by collecting the shares which are held by individuals in qualified sets. A multi-secret sharing scheme (MSSS) is an extension of this where multiple secrets are shared simultaneously and where the performance is estimated using both the maximum improvement and average improvement ratios. In 2003, Crescenzo calculated a lower bound of maximum and average improvement ratios for a MSSS and proposed some special MSSS which achieve the lower bound of the maximum improvement ratio. Wang and Juan deployed a more flexible MSSS to achieve the optimal maxi-mum improvement ratio 2006. This paper provides evidence such that the optimal maximum improvement ratio and the optimal average improvement ratio may both be achieved through even simpler and more flexible MSSS through even simpler and more flexible multi-secret sharing schemes for any arbitrary n and m .

Multisecret-sharing schemes and bounded distance decoding of linear codes

ABSTRACTError-correcting codes are used to correct errors when messages are transmitted through a noisy communication channel. Bounded distance decoding (i.e. decoding up to the error-correcting capacity) is a method of correcting errors that guarantees unique decoding. Secret sharing is a cryptographic protocol that allows a secret known from a person called the dealer to be distributed to n participants. No single participant knows the secret but some special subsets of participants called coalitions can. In this paper, we present a multisecret-sharing scheme based on an error-correcting code where secret reconstruction is made by using bounded distance decoding of the code. This scheme is ideal in the sense that the size of each secret equals the size of any share. Its security improves on that of multisecret-sharing schemes.

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.

An Efficient Lattice Based Multi-stage Secret Sharing Scheme

In this paper, we construct a lattice based (t, n) threshold multi-stage secret sharing (MSSS) scheme according to Ajtai's construction for one-way functions. In an MSSS scheme, the authorized subsets of participants can recover a subset of secrets at each stage while other secrets remain undisclosed. In this paper, each secret is a vector from a t-dimensional lattice and the basis of each lattice is kept private. A t-subset of n participants can recover the secret(s) using their assigned shares. Using a lattice based one-way function, even after some secrets are revealed, the computational security of the unrecovered secrets is provided against quantum computers. The scheme is multi-use in the sense that to share a new set of secrets, it is sufficient to renew some public information such that a new share distribution is no longer required. Furthermore, the scheme is verifiable meaning that the participants can verify the shares received from the dealer and the recovered secrets from the combiner, using public information.

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.

Improved Multi-secret Sharing Scheme Based on One-Way Function

The weakness He-Dawson’s threshold multi-secret sharing scheme is presented and analyzed. By using the one-way function thought in the He-Dawson scheme, a new multi-use and multi-secret sharing scheme is proposed. The improved scheme is multi-time-use of once secret shares distribution and can resist conspiring attack. Furthermore, the new scheme is multi-secret sharing, group secrets can be reconstructed in free order and different group secret is corresponding to different threshold value which can meet with different practical application. At last, the security and efficiency of the new proposed multi-secret sharing scheme are analyzed. DOI : http://dx.doi.org/10.11591/telkomnika.v12i6.5481 Full Text: PDF

Improved Multi-secret Sharing Scheme Based on One-Way Function

Improved Multi-secret Sharing Scheme Based on One-Way Function

A Multi-Secret Sharing Scheme with Many Keys Based on Hermite Interpolation

A secret sharing scheme is one of cryptographies. A threshold scheme, which is introduced by Shamir in 1979, is very famous as a secret sharing scheme. We can consider that this scheme is based on Lagrange's interpolation formula. A secret sharing scheme has one key. On the other hand, a multi-secret sharing scheme has more than one keys; that is, a multi-secret sharing scheme has p (≥2) keys. Dealers distribute shares of keys among n participants. Gathering t (≤n) participants, keys can be reconstructed. In this paper, we give a scheme of a (t,n) multi-secret sharing based on Hermite interpolation, in the case of p≤t.

An Ideal Multi-secret Sharing Scheme Based on Connectivity of Graphs

Secure communication has become more and more important for many modern communication applications. In a secure communication, every pair of users need to have a secure communication channel (each channel is controlled by a server) In this paper, using monotone span programs we devise an ideal linear multi-secret sharing scheme based on connectivity of graphs. In our proposed scheme, we assume that every pair of users, $$p$$ p and $$q$$ q , use the secret key $$s_{pq} $$ s p q to communicate with each other and every server has a secret share such that a set of servers can recover $$s_{pq} $$ s p q if the channels controlled by the servers in this set can connect users, $$p$$ p and $$q$$ q . The multi-secret sharing scheme can provide efficiency for key management. We also prove that the proposed scheme satisfies the definition of a perfect multi-secret sharing scheme. Our proposed scheme is desirable for secure and efficient secure communications.

Data Privacy Preservation in Wireless Sensor Networks Based on Multi-Secret Sharing Scheme

The Internet of things is widespread concerned by the whole society now. As an important component of the Internet of things, wireless sensor network has wide application prospect in various fields such as medical and health, military defense. The traditional data privacy protection technology of PKI system used in the WSN networks has its own weakness. This paper presents the secret key sharing mechanism to protect data privacy. The secret key, remote node and base station used to communicate, was divided into multiple secrets. The multiple secrets were distributed in the nodes which connect directly to the base station node. Only through collect more than threshold number of multi-secret that can decrypt the communication data between the base station and the remote node. To be safer, we used digital watermarking technology to protect the data transmission between the base station and the aggregate node. These techniques combined with the data slice, homomorphism encryption technology to protect data privacy, construct a safe and efficient wireless sensor networks.

New results and applications for multi-secret sharing schemes

In a multi-secret sharing scheme (MSSS), $$\ell $$ l different secrets are distributed among the players in some set $$\mathcal{P }=\{P_1,\ldots ,P_n\}$$ P = { P 1 , ? , P n } , each one according to an access structure. The trivial solution to this problem is to run $$\ell $$ l independent instances of a standard secret sharing scheme, one for each secret. In this solution, the length of the secret share to be stored by each player grows linearly with $$\ell $$ l (when keeping all other parameters fixed). Multi-secret sharing schemes have been studied by the cryptographic community mostly from a theoretical perspective: different models and definitions have been proposed, for both unconditional (information-theoretic) and computational security. In the case of unconditional security, there are two different definitions. It has been proved that, for some particular cases of access structures that include the threshold case, a MSSS with the strongest level of unconditional security must have shares with length linear in $$\ell $$ l . Therefore, the optimal solution in this case is equivalent to the trivial one. In this work we prove that, even for a more relaxed notion of unconditional security, and for some kinds of access structures (in particular, threshold ones), we have the same efficiency problem: the length of each secret share must grow linearly with $$\ell $$ l . Since we want more efficient solutions, we move to the scenario of MSSSs with computational security. We propose a new MSSS, where each secret share has constant length (just one element), and we formally prove its computational security in the random oracle model. To the best of our knowledge, this is the first formal analysis on the computational security of a MSSS. We show the utility of the new MSSS by using it as a key ingredient in the design of two schemes for two new functionalities: multi-policy signatures and multi-policy decryption. We prove the security of these two new multi-policy cryptosystems in a formal security model. The two new primitives provide similar functionalities as attribute-based cryptosystems, with some advantages and some drawbacks that we discuss at the end of this work.