(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.     

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.     

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.     

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.     

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.     

Scalable secret image sharing

In this paper, we propose an innovative scheme, namely the scalable secret image sharing scheme, for sharing an image O among n participants such that the clarity of the reconstructed image (i.e., the amount of information therein) scales with proportion with the number of the participants. The proposed scheme encodes O into n shadow images that exhibit the following features: (a) each shadow image reveals no information about O, (b) each shadow image is only half the size of O, (c) any k (2⩽k⩽n) shadow images can be used to reconstruct O in a scalable manner such that the amount of information about O is proportional to k, and (d) O can be reconstructed perfectly when all of the n shadow images are available. The clarity of O can be measured in terms of several metrics. We define three modes, namely the multisecret, priority, and progressive modes, for sharing O in our scheme. The scalability and flexibility of the proposed schemes indicate the wide range of potential applications for secret image sharing.     

A Visual Secret Sharing Scheme for Progressively Restoring Secrets

Visual secret sharing has received more and more attention over the past years due to the fact that neither complex computation nor cryptographic knowledge is required to decrypt the secret image directly according to the characteristics of the human vision system. Considering the issue of sharing the secret image at multiple image resolutions with the meaningful shadows, in this paper, we present a friendly progressive visual secret sharing scheme without expanding the image size in the shadows and the reconstructed secret image based on applying a 22-sized block-wise operation to generate the shadows block by block. The proposed method can achieve these benefits: 1) the generated shadows are meaningful, and their sizes are not expanded, and 2) the secret image can be recovered at different resolutions by stacking different quantities of shadows together. The experimental results also show that the proposed method is superior to other compared schemes.     

多分存彩色图像秘密共享（2，n）方案

文献[2]中提出了一种基于异或（XOR）操作的彩色图像秘密共享（2,n）方案,简单易于实现,但恢复密图的效果较差。通过分析此方案,文章提出一个多分存的彩色图像秘密共享（2,n）方案,通过给用户增加分存图像的方法改善了恢复密图的质量。实验分析表明所提方案不仅取得了很好的恢复效果,而且保持了安全性和算法的简单性。     

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.     

Random grid-based visual secret sharing with abilities of OR and XOR decryptions

Random grid (RG) is a methodology to construct visual secret sharing (VSS) scheme without pixel expansion. In some reported RG-based VSS schemes, a secret image can be visually reconstructed only by stacking operation, even thought some light-weight computational devices are available. In this paper, a novel RG-based VSS is developed, where the secret image can be recovered in two situations: (1) when computational devices are not available, the secret image can be reconstructed by stacking the shares directly, and (2) when some light-weight computational devices are available, the secret image can be decrypted by XOR operation. Further, the decrypted secret image quality by stacking operation is approximately the same as that of conventional RG-based VSS. But better visual quality is obtained by XOR operation.     

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 verifiable secret sharing mechanism using theory of numbers and a method for sharing secrets

Verifiable secret sharing (VSS) has been extensively used as a cryptographic tool in many applications of information security in recent years. A VSS enables a dealer to divide a secret s into n shares and allows shareholders to verify whether their shares are generated by the dealer consistently without revealing the secrecy of both shares and the secret. More specifically, shareholders can verify that (i) the secret can be recovered by any t or more than t shares and (ii) the secret cannot be obtained by fewer than t shares. Many VSSs are based on polynomial, and only a few of them are based on the Chinese Remainder Theorem (CRT). Recently, Harn et al. proposed a CRT‐based VSS in which multiple verification secrets are used during the phase of verification. In this paper, we propose a VSS based on Asmuth‐Bloom's (t, n) SS scheme, which depends on the CRT. Our proposed VSS is simpler and more efficient than the scheme of Harn et al. Our proposed VSS is unconditionally secure. Copyright © 2014 John Wiley & Sons, Ltd.     

两种新的彩色图像(n, n)分存方案

提出了两种彩色图像的（n,n）．分存方案，解密过程仅需要执行XOR运算。这两种方案重构密图的复杂度与可视分存方案等价，更为重要的是该方案没有像素膨胀，并且重构密图的质量优于彩色可视分存方案。     

Multiple assignment scheme for sharing secret

In a secret sharing scheme, a datumd is broken into shadows which are shared by a set of trustees. The family {P′⊆P:P′ can reconstructd} is called the access structure of the scheme. A (k, n)-threshold scheme is a secret sharing scheme having the access structure {P′⊆P: |P′|≥k}. In this paper, by observing a simple set-theoretic property of an access structure, we propose its mathematical definition. Then we verify the definition by proving that every family satisfying the definition is realized by assigning two more shadows of a threshold scheme to trustees. This work was partly supported by the Telecommunications Advancement Foundation. Also the work of the second author was partly supported by the Grant in Aid for Scientific Research of the Ministry of Education, Science and Culture of Japan under Grant Number YSE (A) 62780017.     

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.     

Chaos-based color image block encryption scheme using S-box

A chaos-based color image encryption scheme using bijection is designed. The whole image is diffused by exclusive or (XOR) operation for random rounds, each color component is separated into blocks with the same size. A bijective function f: B → S between block set B and S-box set S, is built. The corresponding 8 × 8 S-box is dynamically generated by the Chen system with variable conditions. The ciphered image can be obtained after substituting each block with the paired S-box. Numerical simulation and security analysis demonstrate that the scheme is practical in image encryption.