User-friendly secret image sharing scheme with verification ability based on block truncation coding and error diffusion

Conventional secret image sharing schemes, which are constructed based on Shamir’s method, often suffer from random-liked shares, lossy reconstruction and high computation complexity. In addition, their generated shares are generally in original image format which may lead to more storage and suspicion from invaders. In this paper, we propose a user-friendly secret image sharing scheme based on block truncation coding (BTC) and error diffusion, where meaningful shares can be directly generated without any extra process. The meaningful shares by the proposed scheme are in BTC-compressed format which can reduce the capacity of transfer and storage. In the reconstructing phase, the secret image can be losslessly reconstructed by performing XOR operations on bit planes of sufficient BTC-compressed shares. Further, the proposed scheme provides extra verification ability to identify cheaters and check false shares. Theoretical analysis and simulation results demonstrate the feasibility of the proposed scheme.     

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.     

基于Shamir秘密共享的密钥分发与恢复算法

在经典的Shamir秘密共享方案中,秘密分发者把秘密 分为 个影子秘密并分发给持有者;其中任意不少于t个影子秘密均能恢复秘密s,少于t个影子秘密则得不到秘密 的任何信息。现实的秘密恢复过程中可能存在超过t个参与者的情形,因此,在Shamir的秘密共享方案基础上讨论此种情形下秘密共享问题,通过引入影子秘密的线性组合——拉格朗日因子来恢复秘密,并进一步将其扩展为一个多秘密共享方案。理论分析与仿真实验表明：改进算法在同样复杂度条件下既保证影子秘密的安全,又能阻止欺骗者得到秘密,提高了整体安全性。     

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.     

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.     

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。     

Implementation of TiOISSS with meaningful shadows and with an additional authentication image

Visual Cryptography Scheme (VCS) is a cryptographic technique for protecting secret images. The advantage of using VCS is that decoding can be done without use of any computations. Nevertheless, the reconstructed image has poor visual quality. Therefore, Two in One Image Secret Sharing Scheme (TiOISSS) was proposed which takes the advantage of VCS and provides good quality decoded images. However, the existing TiOISSS has security limitations as it is implemented only for noisy shadows. Hence, in this paper, modified TiOISSS is proposed and implemented for meaningful shadows. To enhance the security of the shares and prevent fake shares that may be introduced by hackers, an authentication image is shared along with the secret image. The quality of the reconstructed image is improved by using adaptive halftoning technique. Experimental results demonstrate the improved security and quality by the proposed scheme.     

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.     

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.     

一种可验证的基于超混沌系统的灰度图像多密钥共享算法

提出一种可验证的图像多密钥共享方案。算法中,灰度图像首先被置乱,而后划分为多个图像子块,利用图像子块的哈希值作为超混沌系统的初始值,生成多个随机网格(RG),最后利用RG和图像子块的异或生成共享的多个子密钥。提出的算法具有共享密钥空间小、能够无损恢复秘密图像,同时能够验证密钥的持有者是否对密钥进行了恶意篡改,能应用于重要领域如医学以及军事图像的保护。实验结果和对算法的比较分析,验证了算法的有效性。     

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.     

一种安全的门限多秘密共享方案

提出了一种可认证的门限多秘密共享的新方案,通过成员提供的子密钥的一个影子来恢复秘密,由影子难以得到子密钥本身,因此可以复用,也即通过同一组子密钥共享多个秘密.该方案可以对分发者发布的信息和参与者提供的子密钥影子进行认证,从而可以抵御分发者欺骗和参与者欺骗.方案的安全性基于RSA密码系统和Shamir的(k,n)门限秘密共享方案.另外,本文还提出两种对这类门限多秘密共享方案的欺骗方法,能不同程度的破坏几个已有方案的安全性,但本文所提出的方案对这些欺骗有免疫能力.该方案是计算安全的,并且性能较现有诸方案更好.     

(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.     

一种改进的图像秘密共享方案

秘密共享是一种将秘密信息的片段共享给多个合法参与者的保密技术,可以有效预防对秘密信息的破译、截取、恶意破坏。图像秘密共享是近年来一个具有实用价值研究分支,目前已经衍生出很多种共享算法。L.Bai的投影矩阵方案是一种面向图像秘密共享的方案,可对该方案进行改进,对残差矩阵进行保护,可以避免残差矩阵因通信丢失而导致图像无法重构的问题,提高了该方案的安全性和可用性。     

Efficient multi-secret image sharing based on Boolean operations

(n,n) visual secret sharing (VSS), first proposed by Naor and Shamir (1995) [4], is used to encode (encrypt) a secret image into n meaningless share images to be superimposed later to decode (decrypt) the original secret by human visual system after collecting all n secret images. In recent years, VSS-based image sharing (encryption) and image hiding schemes, two of a variety of applications based on VSS, have drawn much attention. In this paper, an efficient (n+1,n+1) multi-secret image sharing scheme based on Boolean-based VSS is proposed to not only keep the secret images confidential but also increase the capacity of sharing multiple secrets. The Boolean-based VSS technology, used to encode the secret images, generates n random matrices; then the n secret images are subsequently encoded into the n+1 meaningless share images. It is worthwhile to note that n secret images can be hidden by means of sharing only n+1 share images in the proposed scheme instead of 2n share images. Thus, the present scheme thus benefits from (1) reducing the demand of image transmission bandwidth, (2) easing the management overhead of meaningless share images, and (3) involving neither significant extra computational cost nor distortion for reconstructed secret images. The experimental results show the performance in terms of feasibility and image sharing capacity. Applied into image hiding schemes, the proposed scheme can enhance the hiding capacity.     

基于随机网格的视觉多秘密共享方案

为了提高视觉秘密共享(VSS)的恢复效果,该文提出一种基于随机网格的视觉多秘密共享方案.通过使用一种基于圆柱面的随机网格阈值多秘密图像共享方案,使得用户一次可以共享多个秘密图像;部分份额图像受到篡改仍然可以恢复秘密图像,具有较好的鲁棒性;同时份额的数量和最后恢复图像的视觉质量成正相关.仿真结果表明所提出的多秘密视觉共享...     

多版本备份和限制性双重认证主密钥(t,s,k,n)图像分存

传统影子图像连接的（t,s,k,n）分存易导致分发影子图像大小不等,基于伯克霍夫插值的（t,s,k,n）分存不能高效恢复;而双认证自修复图像分存对密图和备份图恢复能力十分有限.针对以上问题,采用随机参与值通过（k,s）和（k-t,n-s）分存来构造主密钥（t,s,k,n）分存并通过第3方公信方存储的MD5值以防止作弊.所提策略由主密钥对密图LL子带置乱来形成对显著比特多备份、对非显著比特少备份和经主密钥不同程度置乱的多版本备份图;引入限制性双重认证在保持认证精度的同时,将尽可能多的备份比特通过GF（2^8）域（k,n）分存嵌入来形成嵌密掩体.理论和实验表明,主密钥（t,s,k,n）分存可高效求解;随机参与值可避免参与者编号泄露,分发信息的篡改和认证比特的揣测;多版本备份可对备份图高置信度地恢复;而限制性双重认证在认证能力上不低于双认证自修复图像分存.     

一种安全有效的（t,n）多秘密共享认证方案

基于双子密钥的思想给出了一种安全有效的(t,n)多秘密共享认证方案,其优点是每个成员可以多次使用自己的子密钥来恢复庄家任意给定的用于共享的多个密钥,重构一个密钥只需公开3个参数,为抵抗成员的欺骗无须执行零知识证明协议.所给的方案与已有的方案相比在计算量和通信量方面有明显的优越性.     

AN EFFICIENT AND SECURE （t, n） THRESHOLD SECRET SHARING SCHEME

Based on Shamir＇s threshold secret sharing scheme and the discrete logarithm problem, a new （t, n） threshold secret sharing scheme is proposed in this paper. In this scheme, each participant＇s secret shadow is selected by the participant himself, and even the secret dealer cannot gain anything about his secret shadow. All the shadows are as short as the shared secret. Each participant can share many secrets with other participants by holding only one shadow. Without extra equations and information designed for verification, each participant is able to check whether another participant provides the true information or not in the recovery phase. Unlike most of the existing schemes, it is unnecessary to maintain a secure channel between each participant and the dealer. Therefore, this scheme is very attractive, especially under the circumstances that there is no secure channel between the dealer and each participant at all. The security of this scheme is based on that of Shamir＇s threshold scheme and the difficulty in solving the discrete logarithm problem. Analyses show that this scheme is a computationally secure and efficient 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.