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Universal Share for Multisecret Image Sharing Scheme Based on Boolean Operation
Abstract
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.
... Until now, color EVCS remains a challenging and open problem. Meghrajani and Mazumdar [8] also studied this design problem. They focused on providing threshold security. ...
... The color of each light ray reaching the receiver is the product of the colors of the intersection points in each layer. The color Fig. 3 The algorithm proposed by Meghrajani and Mazumdar [8] can produce VC with a unique general share. By superimposing the common share ( S c ) and other shares ( S 1 ,S 2 ), the user can see different secret images ( S S1 ,S S2 ) Fig. 4 Each layer of the object casts its shadow onto the receiver to form the target image [9] Page 5 of 31 Wu et al. ...
... Therefore, we think this may be a good direction for researchers in the future. Last, although designing decoding-related art is not a difficult task for graphics researchers, only a few works [6,8,22,65] exist. This may be because those artists rarely create this type of art, and researchers often follow the artists' designs. ...
Visual arts refer to art experienced primarily through vision. 3D visual optical art is one of them. Artists use their rich imagination and experience to combine light and objects to give viewers an unforgettable visual experience. However, the design process involves much trial and error; therefore, it is often very time-consuming. This has prompted many researchers to focus on proposing various algorithms to simplify the complicated design processes and help artists quickly realize the arts in their minds. To help computer graphics researchers interested in creating 3D visual optical art, we first classify and review relevant studies, then extract a general framework for solving 3D visual optical art design problems, and finally propose possible directions for future research.
... From theses computer based VSS schemes, multisecret image sharing (MSS) schemes have evolved. In these schemes, instead of single secret image, multiple secret images are to be distributed to the shareholders [3,4,6,20,21,24]. It is worth noting that two terms for the schemes, multi-secret sharing (MSS) and Multi-secret image sharing MSIS are being used synonymously in the state-of-the-art literature [6,21]. ...
... In these schemes, instead of single secret image, multiple secret images are to be distributed to the shareholders [3,4,6,20,21,24]. It is worth noting that two terms for the schemes, multi-secret sharing (MSS) and Multi-secret image sharing MSIS are being used synonymously in the state-of-the-art literature [6,21]. ...
... Several MSS schemes were proposed based upon conventional visual cryptographic system [20,24]. However, these schemes face the similar challenges as well [21]. Steganography based secret sharing schemes were also proposed [1,13], however high storage requirements for cover images is an issue for such approaches. ...
Multi-secret image sharing techniques (MSS) extend the secret image sharing schemes. The paper reports a novel MSS scheme designed to be collusion resistant. It starts with a brief introduction of the concept thereafter discussing the related works in the domain. Security is an implicit requirement for MSS techniques. There should be no possibility of collusion among the shareholders. No less than k shareholders for (k, n) MSS scheme should be having even a slight view of the secret from their shares, n being the total number of shareholders. The paper reviews and highlights the security issues like possibility of collusion, randomness issues or robustness against tampering attack in the state-of-the-art works. It proposes a new (n, n) MSS scheme in order to rectify the issues. The algorithm encrypts N different secret images to generate N noisy share images. It resolves the existing problems in a secure, and time efficient manner. A range of experiments specifically time complexity, noise, tampering, collusion and histogram analysis are performed for rigorous security analysis. The results, thus obtained indicated that the algorithm is efficient and preserves the security requirements in a much better way than the existing MSS schemes.
... Possessing a universal share, the company organizer with highest privilege can use this single universal share to attend secret reconstruction meetings for various tasks. In 2016, in order to develop an easy-to-manage approach, Meghrajani and Mazumdar [27] proposed a BMSIS scheme encoding n secret images into a universal share and n meaningless shares. ...
... Another challenge is that in the decoding phase of the above-mentioned n-out-of-n BMSIS schemes [22][23][24][25]27], the participants are asked to collect all share images to reconstruct all n secret images once. This shortcoming is called all-or-nothing. ...
... Furthermore, with more than one special committees for given tasks or more than one departments in the company, the deputy as a proxy should attend all the meetings of the committees or departments. The design of GASlike BMSIS to meet this scenario should benefit the advantage of management from involving universal share [26,27] but not violates the basics of SIS. The potential solution is that the manager (resp. ...
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.
... Their scheme was able to share multiple secret images to the corresponding threshold access structures and reconstruct the secret images without distortion. Meghrajani et al. [30] used the concept of universal share to share multiple secret images. They encrypted n secret images into a general share and n unintelligible shares. ...
... The NPCR and UACI measure of share images of our secret images (Lena and Pepper) are shown in Table 5. The NPCR and UACI values for the shares generated by other reported works [22,24,30,44] are presented in Table 6 for comparative analysis. The data in Table 6 confirms that the proposed method has high NPCR and proper UACI values (close to 33.46), which indicates that the share images generated by our proposed scheme are robust against the differential attack. ...
... The traditional secret sharing schemes presented in [23,31,35,40,47] involving mathematical operations incurs a high computation cost of O(tlog 2 t) for a single image and O(ktlog 2 t) for k images. Khanzadi et al. [24] Meghrajani et al. [30] W a n ge ta l . [ 44] NPCR (%) Table 7 The comparative analysis of the proposed method with previous works Boolean Based [7,9,42] ...
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.
... Universal share-based system helps the chief-authority of an organization to improve the secrecy level because the authority holds universal share which is required while decryption of secrets. Meghrajani and Mazumdar [11] presented a universal share-based MSS scheme using Boolean operation. This scheme offers lossless reconstruction with less computational complexity. ...
... In our scheme, we offer a two-in-one decoding recovery for multi secret images. • Universal share-based scheme [11] offers a unique advantage of share management while sharing where the universal share is mandatory for the recovery. This scheme does not provide the two-in-one decoding whereas our proposed scheme has adopted the concept of universal share-based recovery and provides two-in-one decoding of multi secret images. ...
Multi-image secret sharing (MSS) scheme for two decoding options by employing universal share is discussed in this manuscript. One decoding option is piling of shares to get a secret image preview and the other option needs computation of shares to get a finer view of the secret image. In the past, universal share-based MSS schemes were presented using the common share. This paper presents a universal share-based MSS scheme which also offers two-in-one decoding. Boolean-based light-weight computation is utilized for lossless recovery of secret images. The proposed scheme encodes n secret images into a pie-shaped universal share and n noisy shares. Universal share is a common share for all n secrets; hence, it offers an efficient utilization of the available network bandwidth. Experimental results illustrate the effectiveness of the proposed scheme.
... The secret image sharing schemes proposed by researchers suffer from limitations such as more complex computations and lossy recovery [16,17], non-random shares [18] and threshold security [18,19]. Earlier schemes proposed by other researchers concentrated mainly on improvement in the pixel expansion value. ...
... The values of correlation, PSNR and MSSIM of reconstructed secret images by using proposed scheme are one, infinite and one respectively which indicates the lossless reconstruction of the secret images. A. Shamir [2] C.C. Thien and J.C. Lin [3] S.J. Shyu [4] Y. K. Meghrajani and H.S. Mazumdar [19] Table 4 shows the comparison of proposed (n, n) secret image sharing schemes with existing schemes. The proposed methods do not require any pixel expansion, code book design and basis matrices for generation of share images. ...
... The traditional VCS, which encrypts only a single image, has been extended to handle multiple secrets using two circle shares and different rotation angles [7]. Universal shares can decrypt multiple images using a unique share [8,9]. Among the various approaches, methods that employ universal shares [8,9] are most closely related to our proposed approach: our common share is a type of universal share. ...
... Universal shares can decrypt multiple images using a unique share [8,9]. Among the various approaches, methods that employ universal shares [8,9] are most closely related to our proposed approach: our common share is a type of universal share. A comprehensive review of VCSs can be found in the literature [10]. ...
Visual cryptography (VC) is an encryption technique for hiding a secret image in distributed and shared images (referred to as shares). VC schemes are employed to encrypt multiple images as meaningless, noisy patterns or meaningful images. However, decrypting multiple secret images using a unique share is difficult with traditional VC. We propose an approach to hide multiple images in meaningful shares. We can decrypt multiple images simultaneously using a common share, which we refer to as a magic sheet. The magic sheet decrypts multiple secret images depending on a given share. The shares are printed on transparencies, and decryption is performed by physically superimposing the transparencies. We evaluate the proposed method using binary, grayscale, and color images.
... A Collaborative VC scheme where two traditional schemes are merged or glued together is proposed [3] for binary images. A Boolean-based multi-secret sharing (MSS) scheme that encodes n secret images into a universal share and n meaningless shares, and reconstructs lossless secret image is proposed [4] for gray scale images. A multiple secret sharing of color images with no pixel expansion uses watermarking for the authenticity of secret images is discussed in [5]. ...
Security has become the foremost vital facet in today’s
banking system. As a result, banks are committed to give secured
banking services to their customers. Considering the case of a
joint bank locker operation, it needs a master key owned by the
bank to open the vaults along with the key the customers have. To
avoid using the manual operation of keys, a visual cryptographic
scheme is proposed to operate the vaults using shares. Visual
cryptography (VC) hides the details of the image used as a key by
generating shares. Image steganography embeds the shares with a
cover image, which ensures secure storage of the shares. A
completely secured smart joint bank locker operation using a
single share owned by the bank is introduced. The shares
generated by the bank for different customers are put together to
create a unique share to open all the vaults. The proposed
approach guarantees not only absolute security than the
traditional locker operation but also helps bank a simplified way
of maintaining lockers key.
... In 2019, Nag [43] proposed a multi secret sharing scheme with general access based on the Boolean operation; the shares are meaningless, and the concept of the public share is introduced, which come from the idea in [44]-the public share having high privilege participates in the recovery together with the owners' meaningless shares, which does not violate the basic principle of secret sharing. Meghrajani et al. [45] shared multi secret sharing using Boolean operation using the public share. In 2020, Chen [46] proposed a multi secret sharing scheme with the general access structure, which does not need to collect all the shares, and where the defined qualified participators can recover the secret images, and the shares are meaningless. ...
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.
... In the present scheme, a double encryption technique has been introduced. As proposed elsewhere, there are key based image encryption techniques (Ahmad et al. 2017;Meghrajani and Mazumdar 2016;Acharya et al. 2010;Yamuna et al. 2013;AbuTaha et al. 2011) and key based Shuffle encryption techniques (Naskar et al. 2014;Murugan and Gounder 2016). The first phase of image encryption uses Session key 1 based on a secret key, one byte invariant value which is extracted from secret image (Luo et al. 2015;Mishra and Sharma 2013) and size of the secret image. ...
Increased use of internet demands substantial protection for secret image file from any adversary, specifically during transmission. In the field of cryptography there are two role models: cryptographer and crypt-analyst/attacker. The cryptographer develops techniques to make sure certain safety and security for transmissions while the crypt-analyst attempts to undo the former’s work by cracking the same. The basic goal of our scheme is to design an image encryption model which is extra challenging against any attack. In our research article, we have introduced session key dependent image encryption technique wherein the session key is the function of an original secret key (known for a pair of sender and receiver one time forever at the beginning) and the present secret image to be encrypted. Additionally the scheme does not require extracting and remembering of session keys to construct the subsequent session keys although the keys change during each transmission. Besides, in our scheme a double encryption technique is required, which once again confirms that the technique we propose is more robust than the conventional image encryption techniques known till date and is capable of resisting cyber-attacks of such kinds.
... Meghrajani et al. [92] used universal share to share multiple secrets. Recently, they have overcome the computational complexity issues present in the conventional secret sharing schemes. ...
With the speedy progress of network technology and internet applications, protection of digitized data against unauthorized access and modification has become a paramount issue. In order to face this challenge, numerous secret image sharing schemes have been introduced. Secret image sharing scheme is a method used for safeguarding the sensitive digitized image against illegal copying and tempering. The secret image is divided into many random shares in such a way that each share does not reveal any information to the intruders. In this paper, we present a comprehensive survey from over 100 papers which explains the new approaches and challenges. This paper also provides a comparative analysis of different methods based on different properties.
... First intermediate images generated using additive modulo and by applying bit reverse on each intermediate image n public images are generated. Y. K. Meghrajani and H. S. Mazumdar [9] proposed universal share-based MSIS scheme. An arbitrary integer matrix generated and used as universal share image which dimensions are same as secret images. ...
Since the beginning of time, humans have had secrets, and individuals have always been curious to learn about them. People transmit digital data to convey secret information in a variety of methods, such as text messages, secret images, and email conversations as internet technology advances. A concrete instance of a cryptography technique is visual cryptography, which allows secret images to be encrypted and decrypted by the human vision without making use of computers. Many researchers have surveyed the secret sharing schemes with factors like pixel expansion, computational complexity, threshold security, contrast and quantity of secret images. This chapter presents a survey on review and performance evaluation of several visual secret sharing schemes. Moreover, the basic overview of methods which adopt the concept of quantum cryptography with secret sharing schemes are presented with comparative study of recent research trends.
Nowadays, the requirements for image data sharing among participant nodes of the Internet of Things (IoT) are constantly emerging. And thanks to the popularity of digital cameras and the development of digital photography technologies, the processes of data sharing commonly concern substantial amounts of data that may contain critical or private information. So, how to design a secure and efficient secret image sharing (SIS) method suitable for IoT apparatuses is attracting ever-increasing attention. With the aim of simultaneously realizing secret image sharing, image data compression and critical information or privacy protection, this paper proposes a multi-group secret image sharing method based on the model of compressed sensing (CS) and the chaos theory. In the proposed method, participants of SIS are classified into two groups with different authorization levels. Solely members of full-authorized groups could reconstruct secret images with visible critical sectors. Members of restricted-authorized groups, however, could merely obtain reconstruction results with critical sectors concealed. The CS model is introduced to the proposed method to accomplish image data compression and applications of the chaos theory contribute to the secure data transmission. Experimental simulations and theoretical analyses are performed to discuss the feasibility, flexibility and security of the proposed method.
In this article, we propose a key secret-sharing technology based on generative adversarial networks (GANs) to address three major problems in the blockchain: 1) low security; 2) hard recovery of lost keys; and 3) low communication efficiency. In our scheme, the proposed network plays the role of a dealer and treats the secret-sharing process as a classification issue. The key idea is to view the secret as an image during the secret-sharing process. If the user's private key is text, we can covert the key text into an image called the original image. Specifically, we first divide the original image into original subimages by the image segmentation. Next, we encode each original subimage by DNA coding. Finally, we train the proposed network to find the key secret-sharing results. Our proposed scheme is not only a significant extension of the GANs but also a new direction for the key secret-sharing technology. The simulation results show that the scheme is secure, and both flexible and efficient in communication.
In a (n, n)-secret image sharing scheme, a secret image is distributed among n parties in such a way that cooperation of all the shares is needed for reconstruction of the original secret image. Moreover, in these schemes, we have the security requirement which states that fewer than n shares should not reveal any information about the secret. Recently, three efficient (n, n)-multi-secret image sharing schemes based on Boolean operations are proposed. The goal of this paper is to prove that these schemes don’t satisfy the threshold security, i.e., with knowledge of (n-1) or fewer shares, considerable information about the secret image can be obtained using efficient computations. We further propose an improvement which successfully overcomes the reported security flaw. We show that the improved scheme generates pseudo-random shares and outperforms the recent secure Boolean-based schemes in computational cost.
Visual cryptography scheme (VCS) is an encryption technique that utilizes
human visual system in recovering secret image and it does not require any
complex calculation. However, the contrast of the reconstructed image could be
quite low. A number of reversing-based VCSs (or VCSs with reversing) (RVCS)
have been proposed for binary secret images, allowing participants to perform a
reversing operation on shares (or shadows). This reversing operation can be
easily implemented by current copy machines. Some existing traditional VCS
schemes without reversing (nRVCS) can be extended to RVCS with the same pixel
expansion for binary image, and the RVCS can achieve ideal contrast,
significantly higher than that of the corresponding nRVCS. In the application
of greyscale VCS, the contrast is much lower than that of the binary cases.
Therefore, it is more desirable to improve the contrast in the greyscale image
reconstruction. However, when greyscale images are involved, one cannot take
advantage of this reversing operation so easily. Many existing greyscale nRVCS
cannot be directly extended to RVCS. In this paper, we first give a new
greyscale nRVCS with minimum pixel expansion and propose an optimal-contrast
greyscale RVCS (GRVCS) by using basis matrices of perfect black nRVCS. Also, we
propose an optimal GRVCS even though the basis matrices are not perfect black.
Finally, we design an optimal-contrast GRVCS with minimum number of shares held
by each participant. The proposed schemes can satisfy different user
requirement, previous RVCSs for binary images can be viewed as special cases in
the schemes proposed here.
To share numerous grey-valued images (or numerous color-valued images), this study presents a system with a universal share. A company organizer can use this universal share to attend the recovery meeting of any shared image. No storage space is wasted; i.e. for each shared image, the total storage space occupied by all generated shares (including the universal share) is identical to the image size.
Color visual cryptography (VC) encrypts a color secret message into color halftone image shares. Previous methods in the literature show good results for black and white or gray scale VC schemes, however, they are not sufficient to be applied directly to color shares due to different color structures. Some methods for color visual cryptography are not satisfactory in terms of producing either meaningless shares or meaningful shares with low visual quality, leading to suspicion of encryption. This paper introduces the concept of visual information pixel (VIP) synchronization and error diffusion to attain a color visual cryptography encryption method that produces meaningful color shares with high visual quality. VIP synchronization retains the positions of pixels carrying visual information of original images throughout the color channels and error diffusion generates shares pleasant to human eyes. Comparisons with previous approaches show the superior performance of the new method.
This paper presents two layered security for data hiding by combining steganography and visual cryptography (VC). Classically, VC encrypts a secret image into noise like images called as shares and decrypts secret message by stacking of shares, whereas steganography hides secret into another image called as cover image, where only intended receiver decodes the message. Steganography often encodes secret message using secret key before hiding into another image. In this paper, cover message and encrypted secret message are encoded into noise-like shares using (2, 2) VC where concept of digital invisible ink of steganography is incorporated with VC (DIIVC) to hide secret message. Unlike typical steganography, shares are modified to conceal secret message instead of cover image. At receiver, decryption of shares using conventional VC results poor contrast cover image. Apparently, this result appears as sole secret disclosed using VC whereas only intended receiver has knowledge of secret message. Further, intended receiver retrieves encrypted secret message by applying proposed DIIVC algorithm on resultant cover image. Finally, original secret message is revealed using secret key.
This paper presents a novel highly efficient secret image sharing scheme that is symmetric, Boolean-based, secure, and enables multi-secret image sharing. The proposed (n, n) scheme involves sharing n secret images among n shared images and recovers all n secret images from n shared images, and losing any shared image prevents recovering any secret image. We propose a novel symmetric sharing-recovery function (SSRF) for performing sharing and recovery. The scheme is based on Boolean operations to attain low computational complexity and is more secure than previous Boolean-based schemes; it exhibits more randomness in each shared image, more randomness between two or more shared images, and higher shared image sensitivity. The experimental results showed that a similar CPU computation time is required for both generating shared images from secret images, and recovering secret images from shared images. Furthermore, the computation time of the SSRF is proportional to the number of secret images.
Recently, Chen and Wu propose a (n, n) multi secret image sharing (MSIS) scheme that shares n secret images into n shared images. These n shared images can be together used for reconstructing n secret images by Boolean operations. However, there is an inaccuracy in Chen and Wu's (n, n)-MSIS scheme that one can recover some secret images (partial secret information) from (n−1) or fewer shared images. This compromises the threshold security in (n, n)-MSIS scheme. In this paper, we overcome this inaccuracy and propose a strong threshold (n, n)-MSIS scheme without leaking partial secret information from (n−1) or fewer shared images. Moreover, by an inherent property of image that a permutated image with a chaotic reallocation of pixels without effect on their intensity levels, we propose a modified strong (n, n)-MSIS scheme to further enhance the randomness of shared images.
As one of the most efficient multi-secret visual cryptography (MVC) schemes, the tagged visual cryptography (TVC) [1] is capable of hiding tag images into randomly selected shares. However, the encoding processes of TVC and other MVC schemes bring distortion to shares, which definitely lowers the visual quality of the decoded secret image. This letter proposes an extended TVC scheme, named as lossless TVC (LTVC). Specifically, “lossless” means that the proposed LTVC scheme encodes the tag image without affecting the rebuilt secret image, i.e., the decoded secret image of LTVC has the same visual quality with that of the conventional VC scheme [2]. Moreover, we propose the probabilistic LTVC (P-LTVC) to solve the potential security problem of LTVC. Finally, the superiority of the proposed scheme is experimentally verified.
An (n, n) multi-secret image sharing scheme shares n secret images among n shared images. In this type of schemes, n shared images can be used to recover all n secret images, but the loss of any shared image prevents the recovery of any secret image. Among existing image sharing techniques, Boolean-based secret schemes have good performance because they only require XOR calculation. This study presents a secure Boolean-based secret image sharing scheme that uses a random image generating function to generate a random image from secret images or shared images. The proposed function efficiently increases the sharing capacity on free of sharing the random image. The use of a bit shift subfunction in the random image generating function produces a random image to meet the random requirement. Experimental results show that the proposed scheme requires minimal CPU computation time to share or recover secret images. The time required to share n secret images is nearly the time as that required to recover n secret images. The bit shift subfunction takes more computation load than the XOR subfunction needs.
Visual secret sharing (VSS) can encode a secret image into several share images where the original secret can be reconstructed and recognized by sight by stacking all share images. There are two categories of VSS schemes: visual cryptography (VC) and random grids (RG). VC has three main drawbacks: the large size, the need for the codebook to be redesigned for specific applications, and the ability to encode only one secret image at a time. RG removes the first two drawbacks. This paper proposes a novel RG-based VSS scheme that encodes multiple secret images at a time. The scheme encrypts multiple secret images into two circular cipher-grids and decrypts the images by stacking two circular cipher-grids to obtain the first secret and gradually rotating one circular cipher-grid at a fixed degree (based on the quantity of the secret images encrypted) to disclose other secrets. Compared with conventional VC-based VSS, the proposed scheme has no pixel expansion, a higher capacity for secret sharing, and no need for a complex VC codebook to be redesigned. Theoretical analysis of visual quality and security is demonstrated.
A region incrementing visual cryptography scheme (RIVCS) deals with the sharing of an image consisting of multiple regions with different secrecy levels, which can be incrementally revealed as the number of shares increases. The encoding basis matrices of RIVCS for an image containing three to five regions have been reported in the literature, but no construction method has ever been studied. We develop a novel and efficient construction for RIVCS using linear programming in this paper. The proposed integer linear program aims at the minimization of the pixel expansion under the constraints for being a RIVCS. Experimental results demonstrate the feasibility, applicability, and flexibility of our construction. The pixel expansions and contrasts derived from our scheme are also better than the previous results.
The visual secret sharing for multiple secrets (VSSM) allows for the encryption of a greater number of secret images into a given image area. Previous researches on VSSM schemes incur a very serious pixel expansion that will damage capable of increasing the capacity of secret image encryption. Moreover, the most of VSSM schemes will decrease the contrast of recover images while the amount of secret image encryption increases. These drawbacks limit applicability of the existing VSSM schemes. In this paper, we propose a highly efficient encryption algorithm to cope with this problem. The proposed algorithm adopts a novel hybrid encryption approach that includes a VC-based encryption and a camouflaging process. The experimental results demonstrate that the proposed approach not only can increase the capacity efficient for VSSM schemes, but also maintains an excellent level of contrast in the recovered secret images.
This letter presents a novel visual cryptography scheme, called region incrementing visual cryptography (RIVC), for sharing visual secrets with multiple secrecy levels in a single image. In the proposed n-level RIVC scheme, the content of an image S is designated to multiple regions associated with n secret levels, and encoded to n+1 shares with the following features: (a) each share cannot obtain any of the secrets in S, (b) any t (2lestlesn+1) shares can be used to reveal t-1 levels of secrets, (c) the number and locations of not-yet-revealed secrets are unknown to users, (d) all secrets in S can be disclosed when all of the n+1 shares are available, and (e) the secrets are recognized by visually inspecting correctly stacked shares without computation. The basis matrices for constructing the proposed n-level RIVC with small values of n=2, 3, 4 are introduced, and the results from two experiments are presented.
Secret sharing is to send shares of a secret to several participants, and the hidden secret can be decrypted only by gathering the distributed shares. This paper proposes an efficient secret sharing scheme using Largrange’s interpolation for generalized access structures. Furthermore, the generated shared data for each qualified set is 1/(r − 1) smaller than the original secret image if the corresponding qualified set has r participants. In our sharing process, a sharing circle is constructed first and the shared data is generated from the secret images according to this sharing circle. The properties of the sharing circle not only reduce the size of generated data between two qualified sets but also maintain the security. Thus the actual ratio of the shared data to the original secret images is reduced further. The proposed scheme offers a more efficient and effective way to share multiple secrets.
In this paper, we propose a method such that a secret image is shared by n shadow images, and any r shadow images (r⩽n) of them can be used to restore the whole secret image. The size of each shadow image is smaller than the secret image in our method. This property gives the benefit in further process of the shadow images, such as storage, transmission, or image hiding.
A practical specific (r, n) threshold scheme for secret digital images is proposed in this paper. By this scheme, we divide a secret digital image into n pieces and distribute them to n participants. The secret digital image can be reconstructed when and only when r or more participants cooperate for it. The time complexity of this proposed scheme is independent of the size of the secret image. In this scheme, the setup phase is bounded by i × j × ⌊r − 1/2⌊ + 2 module multiplications plus i × j × (r − 1) module additions, where i × j is the size of the codebook, except the time needed for generating the codebook. The reconstructing phase is bounded by O(r log2r). This scheme also achieves perfect secrecy.
Visual cryptography (VC), proposed by Naor and Shamir, has numerous applications, including visual authentication and identification, steganography, and image encryption. In 2006, Horng showed that cheating is possible in VC, where some participants can deceive the remaining participants by forged transparencies. Since then, designing cheating-prevention visual secret-sharing (CPVSS) schemes has been studied by many researchers. In this paper, we cryptanalyze the Hu-Tzeng CPVSS scheme and show that it is not cheating immune. We also outline an improvement that helps to overcome the problem.
Traditional secret sharing schemes involve complex computation. A visual secret sharing (VSS) scheme decodes the secret without computation, but each shadow is m times as big as the original. Probabilistic VSS solved the computation complexity and space complexity problems at once. In this paper we propose a probabilistic (2,n) scheme for binary images and a deterministic (n,n) scheme for grayscale images. Both use simple Boolean operations and both have no pixel expansion. The (2,n) scheme provides a better contrast and significantly smaller recognized areas than other methods. The (n,n) scheme gives an exact reconstruction.
The basic (k, n)-threshold visual cryptography (VC) scheme is to share a secret image with n participants. The secret image can be recovered while stacking k or more shares obtained; but we will get nothing if there are less than k pieces of shares being overlapped. On the contrary, progressive VC can be utilized to recover the secret image gradually by superimposing more and more shares. If we only have a few pieces of shares, we could get an outline of the secret image; by increasing the number of the shares being stacked, the details of the hidden information can be revealed progressively. Previous research, such as Jin in 2005, and Fang and Lin in 2006, were all based upon pixel-expansion, which not only causes the waste of storage space and transmission time but also gets a poor visual quality on the stacked image. Furthermore, Fang and Lin's research had a severe security problem that will disclose the secret information on each share. In this letter, we proposed a brand new sharing scheme of progressive VC to produce pixel-unexpanded shares. In our research, the possibility for either black or white pixels of the secret image to appear as black pixels on the shares is the same, which approximates to 1/n. Therefore, no one can obtain any hidden information from a single share, hence ensures the security. When superimposing k (sheets of share), the possibility for the white pixels being stacked into black pixels remains 1/n, while the possibility rises to k/n for the black pixels, which sharpens the contrast of the stacked image and the hidden information, therefore, become more and more obvious. After superimposing all of the shares, the contrast rises to (n-1)/n which is apparently better than the traditional ways that can only obtain 50% of contrast, consequently, a clearer recovered image can be achieved.
(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.
The optimal pixel expansion of an visual cryp- tographic scheme (VCS) was proven as in 1995; and that of a -VCS was proposed in 2002. Yet, most existing best pixel expansions of -VCSs for have not been improved since 1996. Whether they are already optimal, and if not how to find the optimums have never been explored. In this paper, we modeltheminimizationofthepixelexpansionina -VCSinto an integer linear program to acquire the optimum solution. Com- putational results demonstrate that our integer linear program is simple, effective to obtain the optimum solution and flexible for coping with various types of -VCSs.
This letter presents a method for implementing visual cryptography (VC) in which an additional tag is attached to each generated share. The proposed (t, n), 2 ≤ t ≤ n tagged visual cryptography (TVC) scheme works like a traditional VC scheme does, where the original image is encoded in n shares in such a way that the secret can be revealed by superimposing any t or more shares, but knowledge of less than t shares gets no secret information. A notable characteristic of TVC is that an extra tag can be revealed by folding up each share, which provides users with supplementary information such as augmented message or distinguishable patterns to identify the shares. The tagging property can easily be applied to any reported VC scheme to endow the generated shares with more capabilities. Construction methods and simulation results of the proposed (t , n) TVC based on conventional matrix-based VC and probabilistic-VC are illustrated in the letter.
In this paper we consider a new type of cryptographic scheme, which can decode concealed images without any cryptographic computations. The scheme is perfectly secure and very easy to implement. We extend it into a visual variant of the k out of n secret sharing problem, in which a dealer provides a transparency to each one of the n users; any k of them can see the image by stacking their transparencies, but any k Gamma 1 of them gain no information about it. A preliminary version of this paper appeared in Eurocrypt 94. y Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. E-mail: naor@wisdom.weizmann.ac.il. Research supported by an Alon Fellowship and a grant from the Israel Science Foundation administered by the Israeli Academy of Sciences. z Dept. of Applied Mathematics and Computer Science, Weizmann Institute of Science, Rehovot 76100, Israel. E-mail: shamir@wisdom.weizmann.ac.il. 1 Introduction In this paper we conside...