Essential secret image sharing scheme with different importance of shadows

In (k, n) secret image sharing (SIS), a scheme encrypts a secret image into n shadow images. Any k or more shadow images can be collaborated together to reveal the secret image. Most of the previous SIS schemes don’t distinguish the importance of shadows. However, in some application environments, some participants are accorded special privileges due to their status or importance. Thus, some shadows may be more important than others. In this paper, we consider the (t, s, k, n) essential SIS (ESIS) scheme. All n shadows are classified into s essential shadows and (n–s) non-essential shadows. When reconstructing the secret image, the (t, s, k, n)-ESIS scheme needs k shadows, which should include at least t essential shadows.     

A Subband Adaptive Filtering Algorithm Employing Dynamic Selection of Subband Filters

In 2007, Wang and Shyu proposed a scalable secret image sharing scheme in which three sharing styles, namely the multisecret, priority, and progressive modes, are designed to encode an image with diverse revealing effects. Their scheme is a (2, n ) sharing method where each generated shadow image is half size of the original image. This letter proposes a general (t,n), 2 ? t ? n, scalable secret image sharing scheme with the same revealing effects. Notably, the size of each generated shadow image is only (2n-t)/n ² times of the original image. The smaller size of the generated shadow images makes their transmission and storage more efficient.     

Quadri-directional searching algorithm for secret image sharing using meaningful shadows

Contrary to conventional protecting data such as cryptographic techniques which encrypt the data with a secret key, secret sharing takes an approach to ensure well protection of transmitted information by allowing a secret message M to be divided into n pieces. Secret message M can be held by n participants to avoid the secret from incidentally or intentionally being lost. In a secret sharing scheme, secret information leaks from shadows, attack on shadow image, and large shadow image issues which has arisen when developing an algorithm. Although existing algorithms provide remedies for such problems, the computational complexity of existing algorithms is still questionable. Therefore, we propose a low computational complexity Quadri-Directional Searching Algorithm (QDSA) for secret image sharing. Experiment results show that the proposed algorithm ensures that generated shares are of high quality and no secret information is leaked from these shares, thus it guarantees high security of our scheme.     

(t,k, n) XOR-based visual cryptography scheme with essential shadows

Visual cryptography scheme (VCS) shares a binary secret image into multiple shadows, only qualified set of shadows can reveal the secret image by stacking operation. However, VCS suffers the problems of low visual quality of the revealed image and large shadow size. A (t, k, n) XOR-based visual cryptography scheme (XVCS) shares the secret image into n shadows including t essentials and n-t non-essentials. A qualified set of shadows contains any k shadows including t essentials. The revealing process is implemented by XOR operation on the involved shadows. In this paper, we propose a construction method for (t, k, n)-XVCS with essential shadows. The secret image can be revealed perfectly, and the shadow size is small compared with VCS. Theoretical analysis and experimental results show the security and effectiveness of the proposed scheme.     

Two-layered structure for optimally essential secret image sharing scheme

This paper presents a two-layered structure for optimally sharing a secret image among s essential and n − s non-essential shared shadows using the (t, s, k, n) essential thresholds, that t essential shared shadows and totally k shared shadows are needed to recover the secret image. The presented two-layered structure includes one user-defined parameter m to determine different kinds of optimal results. m = 1 leads to minimum size of total shared shadows (ST) and size of an essential shared shadow is close to size of a non-essential shared shadow. On the other hand, m = t leads to size of an essential shared shadow being twice of size of a non-essential shared shadow to signify the importance of an essential shared shadow. Moreover, the proposed structure overcomes the threshold fulfillment problem in Chen’s scheme (Chen, 2016). Theoretical analyses and experimental results show that the proposed scheme exhibits secure with optimal sharing ratios among related works.     

On the Contrast in Visual Cryptography Schemes

A visual cryptography scheme is a method to encode a secret image SI into shadow images called shares such that certain qualified subsets of shares enable the ``visual' recovery of the secret image. The ``visual' recovery consists of xeroxing the shares onto transparencies, and then stacking them. The shares of a qualified set will reveal the secret image without any cryptographic computation. In this paper we analyze the contrast of the reconstructed image in k out of n visual cryptography schemes. (In such a scheme any k shares will reveal the image, but no set of k-1 shares gives any information about the image.) In the case of 2 out of n threshold schemes we give a complete characterization of schemes having optimal contrast and minimum pixel expansion in terms of certain balanced incomplete block designs. In the case of k out of n threshold schemes with we obtain upper and lower bounds on the optimal contrast. Received 27 September 1996 and revised 13 February 1998     

A Novel （n, n） Secret Image Sharing Scheme Based on Sudoku

Recently, Chang et al. proposed a Sudoku-based secret image sharing scheme. They utilized the Sudoku grid to generate meaningful shadow images, and their scheme satisfied all essential requirements. Based on Chang et al.'s scheme, we propose a novel (n, n) secret image sharing scheme based on Sudoku. In the proposed scheme, a secret image can be shared among n different cover images by generating n shadow images, and the secret image can be reconstructed without distortion using only these n shadow images. Also, the proposed scheme can solve the overflow and underflow problems. The experimental results show that the visual quality of the shadow images is satisfactory. Furthermore, the proposed scheme allows for a large embedding capacity.     

Scalable user-friendly image sharing

Image sharing addresses a fault-tolerant protection mechanism for important images. In a typical image sharing scheme, the generated shadow images usually have a noise-like appearance that conceals the secret image completely, but this makes them difficult to identify and manage. This paper proposes a scalable user-friendly image sharing scheme in which each generated shadow image looks like a shrunken replica of the original image. The scheme provides an easy-to-identify interface for managing the shadow images. Compared with previous user-friendly image sharing schemes, the proposed method can reconstruct the original image without any loss and still has the small-size shadow images. A notable feature is that the qualities of generated shadow images are scalable in the proposed scheme, which allows the quality of the shadow images to be adjusted according to the requirements of diverse applications.     

XOR-based visual cryptography scheme with essential shadows

Visual cryptography scheme with essential shadows (EVCS) is of great significance since it provides different levels of the importance to shadows. In this paper, we propose a general construction method for (t, s, k, n)-VCS with essential shadows based on XOR operation ((t, s, k, n)-EXVCS), which originates from the partition of access structure. The secret image is encrypted into s essential shadows and n-s non-essential shadows. Any k shadows including at least t essentials can cooperate to decode the secret image and the decoding process is implemented by XOR operation on the involved shadows. Our scheme achieves perfectly reconstruction of secret image in the revealed image and the less size of shadows and revealed images. The experiments are conducted to testify the feasibility and practicability of the proposed scheme.     

多重门限的图像秘密共享方案

 针对传统的基于视觉密码的图像秘密共享方案存在像素扩张导致其只能共享小尺寸的秘密图像、信息隐藏效率较低的问题,提出一种能够提高信息隐藏容量的(t,k,n)多重门限图像秘密共享方案.该方案利用秘密图像信息控制视觉密码方案中共享矩阵的选取,从而实现秘密图像在视觉密码方案中的隐藏.在秘密图像恢复的第一阶段,任意t个参与者直接叠加其影子图像后可以视觉解密出低质量的秘密图像信息;在第二阶段,任意k个参与者可以从影子图像中提取出隐藏的信息,并通过计算恢复出精确的灰度秘密图像.相对于传统的视觉密码方案,本文方案在不影响视觉密码恢复图像的视觉质量前提下,可以隐藏更多的秘密图像信息,而像素扩张尺寸较小.     

基于多项式秘密共享的图像密文域可逆信息隐藏

针对密文域可逆信息隐藏在多用户场景下算法嵌入率低、载体图像容灾性能较弱等问题,该文提出一种基于多项式秘密共享的图像密文域可逆信息隐藏方案。通过将图像分割成多幅影子图像并存储在不同的用户端,可以增强图像的容灾性,为了实现额外信息在图像重构前后提取的可分离性,该方案包括两种嵌入算法：算法1在图像分割的过程中,将额外信息嵌入多项式的冗余系数中得到含有额外信息的影子图像,该算法支持在图像重构之后提取额外信息;算法2针对图像分割后的任一影子图像,利用秘密共享的加法同态特性实施嵌入,该算法支持直接从影子图像中提取额外信息。实验在不同门限方案和影子图像压缩率的条件下进行测试,当压缩率为50%时,(3, 4)门限方案的嵌入率达4.18 bpp(bit per pixel),(3, 5)门限方案的嵌入率达3.78 bpp。结果表明,两种嵌入算法分别支持从影子图像与重构图像中提取额外信息,实现了方案的可分离性;与现有方案相比,所提算法嵌入率较高、计算复杂度较低,具有较强的实用性。     

Secret key sharing scheme based on the theory of algebraic semigroups

How to distribute a secret key information to n authorized departments, denoted as: S1, S2,…, Sn, respectively. For every autherized department Si(i = 1,2,… ,n), there are qi authorized persons, and every authorized person has the same secret key information as that of any other authorized persons in the same authorized department. The secret key information can be reconstructed completely from the secret key information of any k authorized persons, if there is at least one authorized person included for every authorized department. But other cases, the secret key information cannot be reconstructed completely. In this paper, based on the algebraic semigroup theory, a secret key sharing scheme is proposed, which can satisfy the demand.     

Constructions of general (k,n) reversible AMBTC-based visual cryptography with two decryption options

In this paper, a general method of $(k\text{,}n)$ threshold Reversible Absolute moment block truncation coding Visual Cryptography Scheme (RAVCS) is introduced for sharing a binary secret image into multiple absolute moment block truncation coding (AMBTC) shadows. A $(k\text{,}k)$ RAVCS is firstly proposed to encode a secret by referencing one ABMTC image. Then, the proposed $(k\text{,}k)$ RAVCS is adopted to share the same secret into multiple groups of shadows by referencing multiple images. Those multiple groups of shadows are distributed to participants according to a matrix generated by the proposed shadow distribution algorithms. When any k or more participants share their shadows, the secret image is revealed by OR or XOR decryption. Further, those AMBTC shadows can be losslessly reverted to their original forms. Sufficient theoretical analysis and extensive experimental results are provided in this paper, showing the effectiveness and advantages of the proposed method.     

一种无损多秘密分享视觉密码方案

针对分享多幅秘密图像存在信息损失的问题,该文给出(n, n)无损多秘密分享视觉密码的定义,在此基础上基于环状共享份设计了一种(n, n)多秘密视觉密码方案,使秘密图像的信息损失为零。实验结果表明,该方案不仅实现了在多个参与者之间分享多幅秘密图像,而且秘密图像能够完全恢复。     

基于马赛克技术的秘密图像共享

在传统的秘密图像共享算法中,通常产生类似噪声的影子图像,极易引起攻击者的注意。针对这一问题,文中根据马赛克技术提出了一种产生有意义的影子图像算法。通过图像相似度的比较,可将秘密图像共享到载体图像中,得到含有秘密图像信息的马赛克图像。然后采用可逆信息隐藏的技术将图像块的位置序列隐藏到马赛克图像中,得到完整的影子图像。通过文中所提算法产生的影子图像,既可避免攻击者的注意又能恢复出无损的秘密图像。     

MPLS security: an approach for unicast and multicast environments

Multi-Protocol Label Switching (MPLS) network architecture does not protect the confidentiality of data transmitted. This paper proposes a mechanism to enhance the security in MPLS networks by using multi-path routing combined with a modified (k, n) threshold secret sharing scheme. An Internet Protocol (IP) packet entering MPLS ingress router can be partitioned into n shadow (share) packets, which are then assigned to maximally node disjoint paths across the MPLS network. The egress router at the end will be able to reconstruct the original IP packet if it receives any k share packets. The attacker must therefore tap at least k paths to be able to reconstruct the original IP packet that is being transmitted, while receiving k???1 or less of share packets makes it hard or even impossible to reconstruct the original IP packet. In this paper, we consider the multicast case in addition to the unicast. To our best knowledge, no work has been published for MPLS multicast security. We have implemented our model and measured its time complexity on variable packets size.     

The Size of a Share Must Be Large

A secret sharing scheme permits a secret to be shared among participants of an n-element group in such a way that only qualified subsets of participants can recover the secret. If any nonqualified subset has absolutely no information on the secret, then the scheme is called perfect. The share in a scheme is the information that a participant must remember. In [3] it was proved that for a certain access structure any perfect secret sharing scheme must give some participant a share which is at least 50\percent larger than the secret size. We prove that for each n there exists an access structure on n participants so that any perfect sharing scheme must give some participant a share which is at least about times the secret size.^1 We also show that the best possible result achievable by the information-theoretic method used here is n times the secret size. ^1 All logarithms in this paper are of base 2. Received 24 November 1993 and revised 15 September 1995     

Sharing more information in gray visual cryptography scheme

Visual cryptography scheme (VCS) shares a binary secret image into several binary shadows, and the secret image can be visually revealed by stacking qualified shadows without computation. From the point of view of sharing secret information, VCS is not efficiency because of the large size expansion and low visual quality. In this paper, we introduce a general gray visual cryptography scheme, which can share more information, called Sharing More Information Gray Visual Cryptography Scheme (SMIGVCS). All the shadow pixels of VCS embed additional information to generate gray shadows of SMIGVCS, and the embedded information comes from the shadows of a polynomial-based secret sharing scheme (PSSS). In the revealing process, a vague secret image is visually decoded by stacking qualified shadows, and more information is revealed by computation. Compared with the two-in-one image secret sharing scheme (TiOISSS), our SMIGVCS can achieve smaller shadow size with acceptable visual quality.     

Constructions and Properties of General (k,n) Block‐Based Progressive Visual Cryptography

Recently, Hou and others introduced a (2, n) block‐based progressive visual cryptographic scheme (BPVCS) in which image blocks can be gradually recovered step by step. In Hou and others’ (2, n)‐BPVCS, a secret image is subdivided into n non‐overlapping image blocks. When participants stack their shadow images, all the image blocks associated with these t participants will be recovered. However, Hou and others’ scheme is only a simple 2‐out‐of‐n case. In this paper, we discuss a general (k, n)‐BPVCS for any k and n. Our main contribution is to give two constructions (Construction 1 and Construction 2) of this general (k, n)‐BPVCS. Also, we theoretically prove that both constructions satisfy a threshold property and progressive recovery of the proposed (k, n)‐BPVCS. For , Construction 1 is reduced to Hou and others’ (2, n)‐BPVCS.]