Efficient visual secret sharing scheme for color images

A k-out-of-n visual secret sharing scheme (VSSS) resolves the visual variant of the k-out-of-n secret sharing problem where only k or more out of n participants can reveal the secret by human visual system without any cryptographic computation. The best pixel expansion of the general k-out-of-n VSSS for c-colored images was c×m by Yang and Laih [New colored visual secret sharing schemes, Des Codes Cryptogr. 24 (2000) 325-335] where m is the pixel expansion of an existing binary k-out-of-n VSSS. Regarding the c-colored n-out-of-n scheme, the best pixel expansion is (c-1)2^n-1-c+2 and c(c-1)2^n-2-c when n is odd and even, respectively, by Blundo et al. [Improved schemes for visual cryptography, Des Codes Cryptogr. 24 (2001) 255-278]. In this paper, we propose a new c-colored k-out-of-n VSSS by using a pixel expansion of that is more efficient than ever.     

Visual multiple-secret sharing for flexible general access structure by random grids

For visual secret sharing (VSS), general access structure (GAS), which can freely define the qualified set and the forbidden set, provides dealers the ability to share secret information with the qualified set but not the forbidden set. In previous studies, the proposed GAS schemes have focused on strong GAS, but it has retained restrictions and inconvenience in some secret-sharing scenarios. Recently, the random-grid-based VSS (RG-based VSS) technique has aimed to overcome the problem of pixel expansion from which the visual-cryptography-based VSS (VC-based VSS) techniques usually suffer. This paper presents a flexible GAS VSS scheme by RG that is appropriate for wide use and that serves special cases like (2, n), (n, n), and (k, n). The paper also outlines how the scheme can be extended for multiple secrets. The performance and the security of the scheme are theoretically analyzed.     

Probabilistic visual secret sharing schemes for grey-scale images and color images

Visual secret sharing (VSS) scheme is an encryption technique that utilizes the human visual system in recovering the secret image and does not require any cryptographic computation. Pixel expansion has been a major issue of VSS schemes. A number of probabilistic VSS schemes with minimum pixel expansion have been proposed for binary secret images. This paper presents a general probabilistic (k, n)-VSS scheme for grey-scale images and another scheme for color images. With our schemes, the pixel expansion can be set to a user-defined value. When this value is 1, there is no pixel expansion at all. The quality of reconstructed secret images, measured by average contrast (or average relative difference), is equivalent to the contrast of existing deterministic VSS schemes. Previous probabilistic VSS schemes for black-and-white images can be viewed as special cases in the schemes proposed here.     

Two secret sharing schemes based on Boolean operations

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.     

An enhanced threshold visual secret sharing based on random grids

Random grids (RG)-based visual secret sharing (VSS) scheme can easily avoid the pixel expansion problem as well as requires no codebook design. However, previous scheme still suffers from low visual quality. In this paper, a new threshold RG-based VSS scheme aiming at improving the visual quality of the previewed image is presented. Compared with previous schemes, our scheme can gain better visual quality in the reconstructed images as well as (k, n) threshold. In addition, the factor affecting the visual quality is analyzed and the differences between related approaches are discussed.     

Visibility bounds for visual secret sharing based on JND theory

Visual secret sharing (VSS) is a noteworthy variant of secret sharing. One special property of VSS is that the security of VSS is achieved by loosing the contrast and the resolution of the secret image. Generally, the reconstructed secrets of these schemes are considered to be visible if and only if the contrast is greater than 0. However, VSS is based on the human vision system (HVS), thus the visibility is not only dependent on the contract. In this paper, we discuss the limit of human vision for VSS (LHV-VSS), because HVS is actually complicated. We take several human vision parameters into consideration, and propose a profile to analyze the upper bound of n for k-out-of-n VSS schemes based on the just noticeable difference (JND) profile. We conclude some cases of VSS schemes are invisible practically according to the analyses. Finally, we give a definition for VSS, visibility condition.     

Meaningful visual secret sharing based on error diffusion and random grids

Random grid (RG) is an efficient method of eliminating the drawback of pixel expansion problem in visual secret sharing (VSS). Error diffusion (ED) technique is a brilliant method that improves the diffusion performance in an image by reducing the pattern noise and removing boundary and ’blackhole’ effects. In this paper, a novel meaningful RG-ED-based VSS, which encodes the (k, n) threshold into meaningful shadow images, is proposed at the price of not-clear recovered images. In addition, the novel scheme realizes the (k, n) threshold, avoids the design of complex codebook and averts the pixel expansion problem. Furthermore, the proposed RG-ED-based VSS inherits conventional benefits of VSS without the need of cryptographic efforts to decode the secret. Compared with other schemes reported in the literature, the present scheme has the benefits mentioned above, at the price of possible degrading of recovered images’ quality.     

Threshold visual secret sharing by random grids

A new visual secret sharing (VSS) approach by random grids (RG-based VSS), proposed by Kafri and Keren (1987), has drawn close attention recently. With almost all advantages of visual cryptography-based VSS, RG-based VSS benefits more from keeping the same size of secret images without the problem of pixel expansion from which VC-based VSS suffer. In this paper, a threshold RG-based VSS scheme aiming at providing the wide-use version is presented. This is the first effort to develop the technique. The experimental results and theoretically analysis in visual quality and security show that the proposed scheme performs well.     

Greyscale-images-oriented progressive secret sharing based on the linear congruence equation

Secret image sharing (SIS) can be applied to protect a secret image when the secret is transmitted in public channels. However, classic SIS schemes, e.g., visual secret sharing (VSS) and Shamir’s polynomial-based scheme, are not suitable for progressive encryption of greyscale images, because they will lead to many problems, such as “All-or-Nothing”, lossy recovery, complex computations and so on. Based on the linear congruence equation, three novel progressive secret sharing (PSS) schemes are proposed to overcome these problems: (k, k) threshold LCSS and (k, n) threshold LCPSS aim to achieve general threshold progressive secret sharing with simple computations. Furthermore, extended LCPSS (ELCPSS) is developed to generate meaningful shadow images, which enable simple management and misleading the enemy. Both theoretical proofs and experimental results are given to demonstrate the validity of the proposed scheme.     

A novel mapping-based lossless recovery algorithm for VSS

The disadvantages of the existing lossless recovery algorithms in visual secret sharing (VSS) are that n shadow images or complex computation operation (i.e., Lagrange interpolations) is required in the recovering phase. Inspired by this, a novel mapping-based lossless recovery algorithm (MbLRA) for VSS is proposed in this paper. MbLRA at least has two merits: (1) compared with the previous schemes, less number of shadow images (may be n or less than n) are required in the proceeding of lossless recovery. (2) Secret image can be reconstructed losslessly by using simple addition operation. The MbLRA proves that the condition of lossless recovery is \(\xi 0_n \cap \xi 1_n =\emptyset \) and \(t_r\) is the least number of the shadow images which can recover the secret losslessly by analyzing the Hamming weight of adding all n shadows. Experiments are conducted to evaluate the efficiency of the proposed scheme.     

Strong (n, t, n) verifiable secret sharing scheme

A (t, n) secret sharing divides a secret into n shares in such a way that any t or more than t shares can reconstruct the secret; but fewer than t shares cannot reconstruct the secret. In this paper, we extend the idea of a (t, n) secret sharing scheme and give a formal definition on the (n, t, n) secret sharing scheme based on Pedersen’s (t, n) secret sharing scheme. We will show that the (t, n) verifiable secret sharing (VSS) scheme proposed by Benaloh can only ensure that all shares are t-consistent (i.e. any subset of t shares defines the same secret); but shares may not satisfy the security requirements of a (t, n) secret sharing scheme. Then, we introduce new notions of strong t-consistency and strong VSS. A strong VSS can ensure that (a) all shares are t-consistent, and (b) all shares satisfy the security requirements of a secret sharing scheme. We propose a strong (n, t, n) VSS based on Benaloh’s VSS. We also prove that our proposed (n, t, n) VSS satisfies the definition of a strong VSS.     

Verifiable threshold quantum secret sharing with sequential communication

A (t, n) threshold quantum secret sharing (QSS) is proposed based on a single d-level quantum system. It enables the (t, n) threshold structure based on Shamir’s secret sharing and simply requires sequential communication in d-level quantum system to recover secret. Besides, the scheme provides a verification mechanism which employs an additional qudit to detect cheats and eavesdropping during secret reconstruction and allows a participant to use the share repeatedly. Analyses show that the proposed scheme is resistant to typical attacks. Moreover, the scheme is scalable in participant number and easier to realize compared to related schemes. More generally, our scheme also presents a generic method to construct new (t, n) threshold QSS schemes based on d-level quantum system from other classical threshold secret sharing.     

Space efficient secret sharing for implicit data security

This paper presents a k-threshold computational secret sharing technique that distributes a secret S into shares of size , where ∣S∣ denotes the secret size. This bound is close to the space optimal bound of if the secret is to be recovered from k shares. In other words, our technique can be looked upon as a new information dispersal scheme that provides near optimal space efficiency. The proposed scheme makes use of repeated polynomial interpolation and has potential applications in secure information dispersal on the Web and in sensor networks.     

A cheating prevention scheme for binary visual cryptography with homogeneous secret images

In 1995, Naor and Shamir proposed the k-out-of-n visual cryptography scheme such that only more than or equal to k participants can visually recover the secret through superimposing their transparencies. Visual cryptography schemes have been extensively investigated since their invention and extended to numerous applications such as visual authentication and identification, steganography, and image encryption. In 2006, Horng et al. proposed that cheating is possible where some participants can deceive the remaining participants by delivering forged transparencies. Meanwhile, Horng et al. also proposed two cheating prevention schemes. One scheme, however, requires extra verification transparencies and the other needs larger transparencies. In other words, compared to visual cryptography, both schemes burden each participant with an additional problem of transparency management. In this paper, a more secure scheme is given to solve the cheating problem without extra burdens by adopting multiple distinct secret images. Moreover, for sharing these secret images simultaneously, the share construction method of visual cryptography is redesigned and extended by generic algorithms. Finally, the results of the experiment and security analysis show that not only the proposed scheme is more secure in comparison with the two previous cheating prevention schemes in the literature, but extra burdens are also eliminated.     

On the security of a visual cryptography scheme for color images

Hou [Visual cryptography for color images, Pattern Recognition 36 (2003) 1619-1629] proposed a four-share visual cryptography scheme for color images. The scheme splits a dithered eight-color secret image into four shares: the black mask and other three shares. It was claimed that without knowing the black mask, no information about the secret image can be obtained even if all the other three shares are known. In this paper, we show that this may be true for a few specific two-color secret images only. In all other cases, however, security cannot be guaranteed. We show that an attacker can compromise a randomly chosen two-color secret image from any two of the other three shares with probability by completely recovering the shape and pattern of the secret image. The advantage will increase to if all the three shares are known. If the secret image has three or four colors, we show that the attacker can compromise it with probability and , respectively. Finally, we show that our technique can be extended to compromising secret images with more than four colors.     

Improved schemes for visual secret sharing based on random grids

Random grid (RG) is an alternative approach to realize a visual secret sharing (VSS) scheme. RG-based VSS has merits such as no pixel expansion and no tailor-made matrix requirement. Recently, many investigations on RG-based VSS are made. However, they need further improvements. In this paper, we obtain some improvements on RG-based VSS. Actually, two improved schemes are proposed, namely RG-based VSS for general access structure (GAS) with improved contrast and extended RG-based VSS with improved access structure. The first scheme can achieve better contrast than previous schemes. The second scheme reduces the chance of suspicion on secret image encryption by generating meaningful shares instead of noise-like shares in the first scheme, and improves the access structure from (k, k) to GAS while maintaining the property that the contrast of the recovered image is traded with that of share images by setting a certain parameter from small to large. Finally, theoretical analyses and experimental results are provided to demonstrate the effectiveness and advantages of the proposed schemes.

     

Reduce shadow size in aspect ratio invariant visual secret sharing schemes using a square block-wise operation

An aspect ratio invariant visual secret sharing (ARIVSS) scheme is a perfectly secure method for sharing secret images. Due to the nature of the VSS encryption, each secret pixel is expanded to m sub-pixels in each of the generated shares. The advantage of ARIVSS is that the aspect ratio of the recovered secret image is fixed and thus there is no loss of information when the shape of the secret image is our information. For example, a secret image of a circle is compromised to an ellipse if m does not have a square value. Two ARIVSS schemes based on processing one and four pixel blocks, respectively, were previously proposed. In this paper, we have generalized the square block-wise approach to further reduce pixel expansion.     

Secret image sharing based on cellular automata and steganography

Recently Lin and Tsai [Secret image sharing with steganography and authentication, The Journal of Systems and Software 73 (2004) 405-414] and Yang et al. [Improvements of image sharing with steganography and authentication, The Journal of Systems and Software 80 (2007) 1070-1076] proposed secret image sharing schemes combining steganography and authentication based on Shamir's polynomials. The schemes divide a secret image into some shadows which are then embedded in cover images in order to produce stego images for distributing among participants. To achieve better authentication ability Chang et al. [Sharing secrets in stego images with authentication, Pattern Recognition 41 (2008) 3130-3137] proposed in 2008 an improved scheme which enhances the visual quality of the stego images as well and the probability of successful verification for a fake stego block is 1/16.In this paper, we employ linear cellular automata, digital signatures, and hash functions to propose a novel (t,n)-threshold image sharing scheme with steganographic properties in which a double authentication mechanism is introduced which can detect tampering with probability 255/256. Employing cellular automata instead of Shamir's polynomials not only improves computational complexity from to O(n) but obviates the need to modify pixels of cover images unnecessarily. Compared to previous methods [C. Lin, W. Tsai, Secret image sharing with steganography and authentication, The Journal of Systems and Software 73 (2004) 405-414; C. Yang, T. Chen, K. Yu, C. Wang, Improvements of image sharing with steganography and authentication, The Journal of Systems and Software 80 (2007) 1070-1076; C. Chang, Y. Hsieh, C. Lin, Sharing secrets in stego images with authentication, Pattern Recognition 41 (2008) 3130-3137], we use fewer number of bits in each pixel of cover images for embedding data so that a better visual quality is guaranteed. We further present some experimental results.     

Visual Cryptography for General Access Structures

A visual cryptography scheme for a set ofnparticipants is a method of encoding a secret imageSIintonshadow images called shares, where each participant in receives one share. Certain qualified subsets of participants can “visually” recover the secret image, but other, forbidden, sets of participants have no information (in an information-theoretic sense) onSI. A “visual” recovery for a setX⊆ consists of xeroxing the shares given to the participants inXonto transparencies, and then stacking them. The participants in a qualified setXwill be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation. In this paper we propose two techniques for constructing visual cryptography schemes for general access structures. We analyze the structure of visual cryptography schemes and we prove bounds on the size of the shares distributed to the participants in the scheme. We provide a novel technique for realizingkout ofnthreshold visual cryptography schemes. Our construction forkout ofnvisual cryptography schemes is better with respect to pixel expansion than the one proposed by M. Naor and A. Shamir (Visual cryptography,in“Advances in Cryptology—Eurocrypt '94” CA. De Santis, Ed.), Lecture Notes in Computer Science, Vol. 950, pp. 1–12, Springer-Verlag, Berlin, 1995) and for the case of 2 out ofnis the best possible. Finally, we consider graph-based access structures, i.e., access structures in which any qualified set of participants contains at least an edge of a given graph whose vertices represent the participants of the scheme.