Wanmeng Ding

Progressive Visual Secret Sharing for General Access Structure with Multiple Decryptions

Visual secret sharing (VSS) for general access structure (GAS) owns wider applications than (k,n) threshold VSS. VSS with multiple decryptions realizes the functionalities of both OR-based VSS (OVSS) and XOR-based VSS (XVSS), which can broaden the applications compared to one recovery method-based VSS. In this paper, we propose a progressive VSS (PVSS) scheme for GAS with the features of both OR and XOR decryptions based on random grid (RG). The different regions of the secret image and corresponding genearted random bits are employed to gain progressive property as well as GAS with OR and XOR decryptions. For the qualified sets, we can reconstruct the secret by stacking. On the other hand, if a device with XOR operation is available, we can improve the visual quality of the recovered secret image as well as reconstruct the secret image losslessly when we collect all the n shares. In addition, our scheme has neither pixel expansion nor codebook design due to RG. The effectiveness of the proposed scheme is shown in terms of experimental results and analyses.

Exploiting the Homomorphic Property of Visual Cryptography

In this paper, homomorphic visual cryptographic scheme HVCS is proposed. The proposed HVCS inherits the good features of traditional VCS, such as, loss-tolerant e.g., k, n threshold and simply reconstructed method, where simply reconstructed method means that the decryption of the secret image is based on human visual system HVS without any cryptographic computation. In addition, the proposed HVCS can support signal processing in the encrypted domain SPED, e.g., homomorphic operations and authentication, which can protect the users privacy as well as improve the security in some applications, such as, cloud computing and so on. Both the theoretical analysis and simulation results demonstrate the effectiveness and security of the proposed HVCS.

Chinese Remainder Theorem-Based Secret Image Sharing for (k, n) Threshold

In comparison with Shamir’s original polynomial-based secret image sharing (SIS), Chinese remainder theorem-based SIS (CRTSIS) overall has the advantages of lossless recovery, low recovery computation complexity and no auxiliary encryption. Traditional CRTSIS methods generally suffer from no (k, n) threshold, lossy recovery, ignoring the image characteristics and auxiliary encryption. Based on the analysis of image characteristics and SIS, in this paper we propose a CRTSIS method for (k, n) threshold, through dividing the gray image pixel values into two intervals corresponding to two available mapping intervals. Our method realizes (k, n) threshold and lossless recovery for gray image without auxiliary encryption. Analysis and experiments are provided to indicate the effectiveness of the proposed method.

Polynomial-Based Secret Image Sharing Scheme with Fully Lossless Recovery

Losslessrecoveryisimportantforthetransmissionandstorageofimagedata.Inpolynomial-based secret image sharing, despite many previous researchers attempted to achieve lossless recovery, noneoftheproposedworkcansimultaneouslysatisfyanefficiencyexecutionandatnocostofsome storagecapacity.Thisarticleproposesasecretsharingschemewithfullylosslessrecoverybasedon polynomial-basedschemeandmodularalgebraicrecovery.Themajordifferencebetweentheproposed methodandpolynomial-basedschemeisthat,insteadofonlyusingthefirstcoefficientofsharing polynomial,thisarticleusesthefirsttwocoefficientsofsharingpolynomialtoembedthepixelsas wellasguaranteesecurity.Boththeoreticalproofandexperimentalresultsaregiventodemonstrate theeffectivenessoftheproposedscheme. KeywoRDS Lossless Recovery, Modulo Algebra, Polynomial-Based Secret Sharing, Secret Image Sharing

Security Analysis of Secret Image Sharing

Differently from pure data encryption, secret image sharing (SIS) mainly focuses on image protection through generating a secret image into n shadow images (shares) distributed to n associated participants. The secret image can be reconstructed by collecting sufficient shadow images. In recent years, many SIS schemes are proposed, among which Shamir’s polynomial-based SIS scheme and visual secret sharing (VSS) also called visual cryptography scheme (VCS) are the primary branches. However, as the basic research issues, the security analysis and security level classification of SIS are rarely discussed. In this paper, based on the study of image feature and typical SIS schemes, four security levels are classified as well as the security of typical SIS schemes are analyzed. Furthermore, experiments are conducted to evaluate the efficiency of our analysis by employing illustrations and evaluation metrics.

An Image Secret Sharing Method Based on Matrix Theory

Most of today’s secret image sharing technologies are based on the polynomial-based secret sharing scheme proposed by shamir. At present, researchers mostly focus on the development of properties such as small shadow size and lossless recovery, instead of the principle of Shamir’s polynomial-based SS scheme. In this paper, matrix theory is used to analyze Shamir’s polynomial-based scheme, and a general (k, n) threshold secret image sharing scheme based on matrix theory is proposed. The effectiveness of the proposed scheme is proved by theoretical and experimental results. Moreover, it has been proved that the Shamir’s polynomial-based SS scheme is a special case of our proposed scheme.

Secret Image Sharing for (k, k) Threshold Based on Chinese Remainder Theorem and Image Characteristics

Secret image sharing (SIS) based on Chinese remainder theorem (CRTSIS) has lower recovery computation complexity than Shamir’s polynomial-based SIS. Most of existing CRTSIS schemes generally have the limitations of auxiliary encryption and lossy recovery, which are caused by that their ideas are borrowed from secret data sharing. According to image characteristics and CRT, in this paper we propose a CRTSIS method for (k, k) threshold, based on enlarging the grayscale image pixel values. Our method owns the advantages of no auxiliary encryption and lossless recovery for grayscale image. We perform experiments and analysis to illustrate our effectiveness.

Partial Secret Image Sharing for (n, n) Threshold Based on Image Inpainting

Shamir’s polynomial-based secret image sharing (SIS) scheme and visual secret sharing (VSS) also called visual cryptography scheme (VCS), are the primary branches in SIS. In traditional (k, n) threshold secret sharing, a secret image is fully (entirely) generated into n shadow images (shares) distributed to n associated participants. The secret image can be recovered by collecting any k or more shadow images. The previous SIS schemes dealt with the full secret image neglecting the possible situation that only part of the secret image needs protection. However, in some applications, only target part of the secret image may need to be protected while other parts may be not in a full image. In this paper, we consider the partial secret image sharing (PSIS) issue as well as propose a PSIS scheme for (n, n) threshold based on image inpainting and linear congruence (LC). First the target part is manually selected or marked in the color secret image. Second, the target part is automatically removed from the original secret image to obtain the same input cover images (unpainted shadow images). Third, the target secret part is generated into the pixels corresponding to shadow images by LC in the processing of shadow images texture synthesis (inpainting), so as to obtain the shadow images in a visually plausible way. As a result, the full secret image including the target secret part and other parts will be recovered losslessly by adding all the inpainted meaningful shadow images. Experiments are conducted to evaluate the efficiency of the proposed scheme.

A General (k, n) Threshold Secret Image Sharing Construction Based on Matrix Theory

Shamir proposed a classic polynomial-based secret sharing (SS) scheme, which is also widely applied in secret image sharing (SIS). However, the following researchers paid more attention to the development of properties, such as lossless recovery, rather than the principle of Shamir’s polynomial-based SS scheme. In this paper, we introduce matrix theory to analyze Shamir’s polynomial-based scheme as well as propose a general (k, n) threshold SIS construction based on matrix theory. Besides, it is proved that Shamir’s polynomial-based SS scheme is a special case of our construction method. Both experimental results and analyses are given to demonstrate the effectiveness of the proposed construction method.

A Novel Progressive Secret Image Sharing Method with Better Robustness

Secret image sharing (SIS) can be utilized to protect a secret image during transmit in the public channels. However, classic SIS schemes, e.g., visual secret sharing (VSS) and polynomial-based scheme, are not suitable for progressive encryption of greyscale images in noisy environment, since they will result in different problems, such as lossy recovery, pixel expansion, complex computation, “All-or-Nothing” and robustness. In this paper, a novel progressive secret sharing (PSS) method based on the linear congruence equation, namely LCPSS, is proposed to solve these problems. LCPSS is simple designed and easy to realize, but naturally has many great properties, e.g., (k, n) threshold, progressive recovery, lossless recovery, lack of robustness and simple computation. Experimental results are given to demonstrate the validity of LCPSS.