General Access Structures Research Articles

On Multi-image Random Grids by Arbitrary Transformations

Random grids are a method for visual secret sharing, whereby a secret image is encoded into a number of shares, each of which is maximally entropic. There has been growing interest in hiding multiple images in a scheme, such that additional images are revealed by stacking the shares in different ways. This paper proposes a metaheuristic method for generating schemes that allow for a wide range of transformations, or even combinations thereof, to reveal an arbitrary number of secret images. Up to 10 multi-secrets are shown in this paper, as well as hiding multiple secrets in a general access structure. To remove noise from these schemes an algorithm is proposed to extract the information from the noise, and in all cases, relative contrasts are given. In one example, six images are hidden in two shares, such that the mean relative contrast under OR-stacking is 0.152, under XOR-stacking 0.278, and with noise removed, it is 0.74. In an example hiding 10 images in two shares, the values are respectively 0.136, 0.206 and 0.679, respectively.

Sharing Visual Secrets Among Multiple Groups With Enhanced Performance

An almost unexplored research topic in visual secret sharing (VSS), i.e., sharing different visual secrets among various groups, is investigated in this article. Generally, multiple groups are cooperated together to encrypt multiple visual secrets, where every group is correlated with a VSS scheme to share one secret and each participant receives only one shadow. Such a cooperative system is referred to as cooperative VSS (CVSS). In this paper, we develop a general construction for CVSS with improved computational overhead. The basis matrices for generating the shadows are easily obtained. To improve the recovered image quality, an efficient XOR-based CVSS (XCVSS) is given. Furthermore, to fulfill the requirement of implementing complex sharing policy, the XCVSS is extended to collaborate general access structure (GAS) VSS schemes together. Theoretical and experimental results and comparisons are illustrated to demonstrate the advantages of the proposed techniques.

Dynamic hierarchical quantum secret sharing with general access structure

Dynamic hierarchical quantum secret sharing with general access structure

Proactive visual cryptographic schemes for general access structures

Proactive visual cryptographic schemes for general access structures

Linear Algebraic Approach to Strongly Secure Ramp Secret Sharing for General Access Structures with Application to Symmetric PIR

Ramp secret sharing is a variant of secret sharing which can achieve better information ratio than perfect schemes by allowing some partial information on a secret to leak out. Strongly secure ramp schemes can control the amount of leaked information on the components of a secret. In this paper, we reduce the construction of strongly secure ramp secret sharing for general access structures to a linear algebraic problem. As a result, we show that previous results on strongly secure network coding imply two linear transformation methods to make a given linear ramp scheme strongly secure. They are explicit or provide a deterministic algorithm while the previous methods which work for any linear ramp scheme are non-constructive. In addition, we present a novel application of strongly secure ramp schemes to symmetric PIR in a multi-user setting. Our solution is advantageous over those based on a non-strongly secure scheme in that it reduces the amount of communication between users and servers and also the amount of correlated randomness that servers generate in the setup.

Equivalence of Non-Perfect Secret Sharing and Symmetric Private Information Retrieval With General Access Structure

We study the equivalence between non-perfect secret sharing (NSS) and symmetric private information retrieval (SPIR) with arbitrary response and collusion patterns. NSS and SPIR are defined with an access structure, which corresponds to the authorized/forbidden sets for NSS and the response/collusion patterns for SPIR. We prove the equivalence between NSS and SPIR in the following two senses. 1) Given any SPIR protocol with an access structure, an NSS protocol is constructed with the same access structure and the same rate. 2) Given any linear NSS protocol with an access structure, a linear SPIR protocol is constructed with the same access structure and the same rate. We prove the first relation even if the SPIR protocol has imperfect correctness and secrecy. From the first relation, we derive an upper bound of the SPIR capacity for arbitrary response and collusion patterns. For the special case of $\mathsf{n}$-server SPIR with $\mathsf{r}$ responsive and $\mathsf{t}$ colluding servers, this upper bound proves that the SPIR capacity is $(\mathsf{r}-\mathsf{t})/\mathsf{n}$. From the second relation, we prove that a SPIR protocol exists for any response and collusion patterns.

A perfect secret sharing scheme for general access structures

The secret sharing (SS) scheme has been widely used as the de facto paradigm for group key management in cryptography and distributed computation. An SS scheme for a general access structure (GSS) has drawn more and more attention since it allows flexible access control. However, previous solutions to GSS need to either assign multiple shares to each participant or to solve a complex nonlinear integer programming. In this paper, we propose a novel strategy to address the two problems simultaneously based on the Chinese Remainder Theorem (CRT) for a polynomial ring over a finite field. We classify general access structures satisfying the monotone property into the two families of maximum forbidden subsets and minimum qualified subsets conforming to the security condition and the revealing condition. The moduli used in the scheme are pairwise coprime polynomials and can take the irreducible polynomials. To find the degrees of these polynomials, we only need to solve an integer linear programming (ILP) by minimizing the sum of the degrees of all the moduli. The proposed scheme is inherently a weighted SS scheme and may have no solution which commonly exists in all GSS schemes. To ensure a solution, we put forth a preprocessing algorithm which separates the original access structure into several subaccess structures based on graph theory. The proposed scheme only assigns a share for each participant and achieves perfect security. It has good generalization and provides a universal approach to program the scheme construction for SS schemes with general access structures, threshold access structures and weighted access structures.

Towards cheat-preventing in block-based progressive visual cryptography for general access structures

Existing block-based progressive visual cryptography schemes (BPVCS) that prevent cheating are limited to (2,n) and (k,n) thresholds. They are unsuitable for implementing complex sharing techniques in the actual world. A cheating immune BPVCS for general access structure (GAS) is proposed in this paper. To find the parameters that make up the proposed scheme, a simplified multiple assignment procedure based on integer linear programming is introduced. The secret parts can be decrypted by the members of a qualified set. Participants in a forbidden set, on the other hand, are not allowed to know about the secret. The proposed scheme includes cheat-prevention and progressive recovery capabilities. In addition, to generate meaningful shadows for BPVCS, a modified extended VCS (EVCS) is proposed. Our modified EVCS can solve the cover-interference problem in conventional BPVCS. The effectiveness and benefits of the proposed BPVCS are supported through the experimental findings and comparisons.

Extended XOR-based visual cryptography schemes by integer linear program

XOR-based visual cryptography scheme (XVCS) is a promising branch of VCS since superior visual quality of recovered secret image is provided. To assist the shadow management, meaningful shadow is preferred. However, existing extended XVCSs (EXVCSs) that generate meaningful shadows are confined to the (n,n) threshold. They are not practical for real-world applications. In this paper, we introduce EXVCS for (k,n) threshold and general access structure (GAS) by using integer linear program (ILP) technique. First of all, an approach for implementing the (k,n)-XVCS is given. We associate the (k,n)-XVCS with a minimizing problem, where the constraints in this problem are derived from the contrast and security conditions in (k,n)-XVCS. The ILP technique is adopted to solve this problem for obtaining the best solutions for constructing the base matrices for (k,n)-XVCS. Further, the construction is extended to (k,n)-EXVCS, in which the shadows with meaningful contents are constructed. To realize complicated sharing strategies, a construction of EXVCS for GAS is described as well. The base matrices for XVCS and EXVCS are demonstrated, as well as the pixel expansion and contrast. Comparisons among related methods are illustrated to show the advantages of the proposed schemes.

A (k, n) multi-secret image sharing scheme based on Chinese remainder theorem and Arnold cat map

A multi-secret image sharing (MSIS) scheme is a procedure to break down secret images into numerous shares and distribute each share to each authorized participant. Most existing ( n , n ) schemes face the problem of all-or-nothing that is all the n shares are required to reconstruct a secret image. If a single share is lost, then the secret image will not be recovered. Moreover, the existing ( k , n ) MSIS schemes either require k consecutive shares or general access structure to recover the secret images. The proposed scheme addresses the previous schemes’ issues. It is based on Arnold cat map, Chinese remainder theorem (CRT), and Boolean operation. It is a ( k , n ) threshold scheme where k is the threshold, and n is the number of participants. Arnold cat map is adopted for the randomization of images, and Boolean operation is used for producing public share images. CRT is utilized for the recovery of images. It has high fault tolerance capability as any of the k participants can submit their shares to reconstruct images and consume less computational time due to employing the modular method. Moreover, it can withstand differential as well as statistical attacks.

Weighted visual secret sharing for general access structures based on random grids

The traditional visual secret sharing (VSS) schemes share a secret image into multiple shares, and all the shares have the same importance. However, it is occasionally necessary to differentiate participants based on their different levels of importance in certain applications. In previous works, some weighted VSS schemes were implemented only for the (k,n) threshold access structure and were not applicable to other access structures. In this paper, a weighted VSS scheme is proposed for general access structures (GAS) based on random grids (RG). For the different qualified sets of shares, the amount of information we get about the secret image is different because the total weight of the shares participating in the recovery process is different. Moreover, both OR and XOR operations can be applied to recover the secret image, which can extend the applications of our scheme. For the same minimal qualified set, we can obtain better visual quality by stacking (XOR-ing) more shares. In addition, we can obtain the lossless secret image by performing the XOR operation on all shares. More importantly, our scheme is suitable for GAS; however, it has certain limitations in the weight assignment of participants for the non-threshold access structures. Finally, experiments and comparisons demonstrate the effectiveness of our scheme.

Multi Secret Image Sharing Scheme of General Access Structure with Meaningful Shares

A Multi Secret Image sharing scheme can share several secret images among certain participators securely. Boolean-based secret sharing schemes are one kind of secret sharing method with light-weighted computation compared to the previous complex algebraic-based methods, which can realize the sharing of multi secret images. However, the existing Boolean-based multi secret sharing schemes are mostly restricted to the particular case of (2, n) and (n, n), only few Boolean-based multi secret sharing schemes study the general access structure, and the shares are mostly meaningless. In this paper, a new Boolean-based multi secret sharing scheme with the general access structure is proposed. All the shares are meaningful, which can avoid attracting the attention of adversaries, and the secret images can be recovered in a lossless manner. The feasibility of the scheme is proven, the performance is validated by the experiments on the gray images, and the analysis of the comparison with other methods is also given out.

Strong security of linear ramp secret sharing schemes with general access structures

A secret sharing scheme is a cryptographic technique to protect a secret from loss and leakage by dividing it into shares. A ramp secret sharing scheme can improve efficiency in terms of the information ratio by allowing partial information about the secret which is composed of several sub-secrets to leak out. The notion of strong security has been introduced to control the amount of information on every subset of the sub-secrets that unauthorized sets can obtain. However, there have been proposed few methods to construct strongly secure schemes for general access structures. Furthermore, all existing methods need strong assumptions, which lead to a loss of efficiency and a limitation of access structures. In this paper, we show that any ramp secret sharing scheme which is linear over a sufficiently large field can be transformed into a strongly secure scheme with the same access structure preserving the information ratio. Since our method only requires linearity, our strongly secure schemes can realize arbitrary access structures and achieve smaller information ratio than the previous schemes.

A Common General Access Structure Construction Approach in Secret Image Sharing

(k, n) threshold is a special case of the general access structure (GAS) in secret image sharing (SIS), therefore GAS is more extensive than (k, n) threshold. Most of conventional SIS, including visual secret sharing (VSS), polynomial-based SIS, linear congruence (LC)-based SIS, etc., were proposed with only (k, k) threshold or (k, n) threshold other than GAS. This article introduces a common GAS construction approach in SIS with on pixel expansion from existing (k, k) threshold or (k, n) threshold SIS. The authors input classic SIS methods to test the efficiency and feasibility of the proposed common GAS construction approach. Experiments are presented to indicate the efficiency of the approach by illustrations and analysis.

Multiple secret image sharing with general access structure

Boolean-operation-based secret image sharing (BSIS), which aims to encode a secret image into some shared images and discloses the original secret image later, has drawn more and more attention in academia. Since Chen and Wu pioneer in proposing the Boolean-operation-based multiple secret image sharing (BMSIS) scheme, there more and more BMSIS schemes proposed in the literature. In order to remove the limitation that in the existing BMSIS schemes, this paper presents Boolean-operation-based multiple-secret image sharing with general access structure for secret reconstruction. Compared with the existing related BMSIS schemes with the property of all-or-nothing reconstruction, the proposed scheme achieves a milestone, i.e., secrets can be reconstructed by the pre-defined access structure. Hence, the secret reconstruction no longer needs to collect all share images. Furthermore, distinct combinations of shares have the ability to disclose the secrets defined in the qualified set. The theoretical analysis and the experimental results demonstrate the proposed scheme does work.

A Novel Message Authentication Scheme With Absolute Privacy for the Internet of Things Networks

With the rapid development and massive deployment of the Internet of things (IoT) networks, security related issues in the IoT networks have been paid more and more attention to. Among all the security concerns, message authentication is critical in preventing the unauthorized messages from being transmitted in the IoT networks. Many message authentication schemes have been proposed based on the public-key cryptosystem, where the key management is simple and scalable. Identity based cryptosystem is a special type of public-key cryptosystem and can further ease the process of the key management since the public keys can be obtained easily. In this paper, we devise an efficient message authentication with enhanced privacy (IMAEP) scheme using the identity based signature. Our proposed scheme can provide both unconditional privacy as well as the enhanced privacy under full key exposure attack. Our proposed scheme can also provide existential unforgeability under the adaptive chosen-message-and-identity attack. Compared with the scheme that has the same level of anonymity and security, our proposed scheme has much lower computational overhead, and can provide extra unconditional privacy. Next we propose an extended IMAEP (EIMAEP) scheme for the general access structures where the message is signed by a group of users instead of one user. We also conduct comprehensive analysis and demonstrate that the EIMAEP scheme can achieve the same level of privacy and unforgeability as the IMAEP scheme.

Multi-Receiver Authentication Scheme for General Access Structure

Authentication is an important primitive of cryptography. With the rapid progress of network communication, the urgent data needs to ensure it integrity and privacy, therefore, the authentication of multi-receiver has a significant impact on the development of network interaction. R. Safavi-Nalni and H. Wang showed that authentication scheme based on Reed-Solomon code is unconditionally secure and allows multiple messages to be authenticated, but the number of receiver to verify is less than $q$ , where the messages are in $\mathbb {F}_{q}$ . In 2014, the secure multi-receiver authentication scheme base on linear code was proposed, however, this scheme can not realize any a given access structure. In this paper, we present a multi-receiver authentication scheme to realize any a given ideal access structure, and demonstrate that our scheme is unconditionally secure and allows $r$ messages to be authenticated with each receiver own private key.

Major Developments in Visual Cryptography

Visual cryptography is a cryptographic mechanism that gets applied in visual information protection for secured transfer of data. The encryption makes the decryption a mechanical operation.The secret image gets converted into several share images. The share images are distorted/ noisy images which will give the correct image only when placed in the right combination. This paper reviews various visual encryption and decryption mechanism with the safe transmission of information from the literature. This paper about visual cryptography discusses, general access structure, halftone, colour, progressive, region incrementing, extended visual cryptography, colour extended visual cryptography, XOR and OR visual cryptography and the applications of visual cryptography. The applications discussed here are banking security, steganography, crime records, intelligence communication, multilayered Id cards and fingerprint records. The paper provides an overview of advances in VCS where each technique overcomes the problem(s) faced in the other manner.

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.

An efficient Boolean based multi-secret image sharing scheme

The purpose of this paper is to develop an algorithm for sharing k secret images to n participants in such a way that each participant gets a single share image by encoding all k images. Any qualified subgroup of t : t ≤ n of those n participants can reconstruct the kith secret image only by combining their share images if they are qualified to reconstruct the kith secret image. Most of the existing literature solves this problem for the cases where t = 2 or t = n making it a very restrictive scheme. In this article, we aim to design a multi-secret image sharing scheme based on XOR operation where t is not restricted to be 2 or n. We have used n random matrices of the same size as the secret image size as private share to generate r (where r is the number of qualified subgroups) share images as public share using XOR operations. The proposed scheme is computationally lightweight and lossless due to XOR operation only. It does not involve any pixel expansion. The experimental results with a very low correlation coefficient between share and secret images confirm that share image does not reveal anything about secret image. The scheme is secure against differential attack as a higher value of Number of Changing Pixel rate (NPCR) confirms that. The current proposal is based on a general access structure, and hence any secret image can be reconstructed by a qualified group of t or more shares where t need not be 2 or n only.