Polynomial-based Secret Image Sharing Research Articles

An efficient cheating-detectable secret image sharing scheme with smaller share sizes

As a new approach to image protection, polynomial-based secret image sharing (PSIS) has attracted a lot of attention from many researchers in recent decades. When SIS technology is applied in practice, it is inevitably subject to various types of attacks, with cheating being the most likely to occur. To deal with the cheating problem in the process of secret image reconstruction, several effective (k,n)-PSIS schemes have been proposed. However, most previous schemes need to sacrifice the size of the share to achieve cheating detection capability. To address this issue, an efficient cheating-detectable (k,n)-PSIS scheme with smaller share sizes is designed based on the singularity of square matrix in this paper. In comparison with previous schemes, the proposed one can not only detect the complicity of up to k−1 cheaters, but also reduce the size of shares to 1k times of the secret image. Moreover, the secret image can be recovered without loss, and it does not need to be scrambled before sharing, which could reduce the complexity of the scheme. Theoretical proofs and experiments show that the contrast and security conditions of the proposed scheme are satisfied, and the cheating detection capability is available as well.

Fake and Dishonest Participant Immune Secret Image Sharing

Secret image sharing (SIS) has received increased attention from the research community because of its usefulness in multiparty secure computing, access control, blockchain distributive storage and other security-oriented applications. Prevention of fake and dishonest participants is a key issue that has spurred interest in practical applications of SIS. Unfortunately, most previous SIS schemes failed to detect and locate fake or dishonest participants. In this article, an SIS for a ( k,n )-threshold without pixel expansion is presented, which can detect and locate both fake and dishonest participants. Using a screening operation, the proposed approach fuses the benefits of polynomial-based SIS, visual cryptographic scheme (VCS) , and hash functions to authenticate separate participants both with and without a dealer. In addition, the proposed approach achieves lossless rebuilding of the secret image. Analyses and experiments are conducted in this study to establish the effectiveness of the presented approach.

Boolean-based Two-in-One Secret Image Sharing by Adaptive Pixel Grouping

The two-in-one secret image sharing (TiOSIS) technique is a hybrid scheme that protects a secret image by combining visual cryptography (VCS) and polynomial-based secret image sharing (PSIS). There are two decoding methods available in TiOSIS: stacking-to-see decryption and lossless image recovery. However, the majority of current TiOSIS methods use Lagrange interpolation to precisely reconstruct the secret, which would result in intense computations. In this article, an efficient TiOSIS scheme using Boolean XOR operation for lossless image recovery is proposed. The proposed scheme consists of three building blocks: shared data generation, shadow construction, and image decryption. In shared data generation, the grayscale secret image is processed by a Boolean-based SIS to derive the shared bits. In shadow construction, an adaptive pixel grouping (APG) strategy is utilized to determine a grouping pattern. The halftone image adjustment algorithm is adopted to generate a suitable halftone image. With the grouping pattern and halftone image, we construct the shadows via the group-pixel embedding and sharing approach. In image decryption, we can reveal the secret image by stacking-to-see decoding or Boolean-based lossless image recovery. Extensive experiments and comparisons are illustrated to show the effectiveness and benefits of the proposed scheme.

Selective Medical Image Encryption Using Polynomial-Based Secret Image Sharing and Chaotic Map

The progressive development in telecommunication and networking technologies has led to the increased popularity of telemedicine usage, which involves the storage and transfer of medical images and related information. Recently, trust and privacy in the telemedicine system have attracted many researchers to investigate these topics. In medical image applications, selective image encryption plays an important role as it reduces computational cost and time. Therefore, a safe and efficient selective image encryption algorithm is designed in this work. In particular, the predetermined region of the original image data is encrypted to reduce the encryption/decryption time and the computational complexity of processing the huge image data. The image processing techniques are used to divide the image into a region of interest (ROI) and a region of non-interest (RONI), and then the more important component of the ROI is encrypted using a polynomial-based secret image sharing (SIS) and a chaotic map system. These techniques produce a test image cipher that has good confusion and diffusion properties. The experimental result shows that the Polynomial-based SIS and the chaotic image encryption are effectively performed for diffusion and confusion, which are crucial for concealment. According to the security research findings, sensitive encryption and decryption systems are extremely reliant on any improvement in the key. The encryption solution is sufficiently broad to withstand brute force attacks. Thus, protection may become an issue during the transmission of medical images via a network.

Image Secret Sharing using IWT (Integer Wavelet Transform) Algorithm

Because of the importance of digital images and their extensive application to digital watermarking, block chain, access control, identity authentication, distributive storage in the cloud and so on ,image secret sharing(ISS) is attracting ever-increasing attention .Share authentication is an important issue in its practical application. However, most ISS schemes with share authentication ability require a dealer to participate in the authentication. To design an ISS for a(k ,n)-threshold with separate share authentication abilities of both dealer participatory authentication and dealer non participatory authentication .the advantage of polynomial-based ISS and visual secret sharing(VSS) are skilfully fused to achieve these two authentication abilities Without sending a share by using a screening operation. In addition, the designed scheme has the characteristics of low decryption (authentication) complexity, lossless decryption and no pixel expansion .Experiments and theoretical analyses are performed to show the effectiveness of the designed scheme.

Changing the Threshold in a Bivariate Polynomial Based Secret Image Sharing Scheme

Secret image sharing (SIS) is an important application of the traditional secret sharing scheme, which has become popular in recent years. In an SIS scheme, a confidential image is encrypted into a group of shadows. Any set of shadows that reaches the threshold can reconstruct the image; otherwise, nothing can be recovered at all. In most existing SIS schemes, the threshold on shadows for image reconstruction is fixed. However, in this work, we consider more complicated cases of SIS, such that the threshold is changeable according to the security environment. In this paper, we construct a (k↔h,n) threshold-changeable SIS (TCSIS) scheme using a bivariate polynomial, which provides h−k+1 possible thresholds, k,k+1,…,h. During image reconstruction, each participant can update their shadow according to the current threshold T based only on their initial shadow. Unlike previous TCSIS schemes, the proposed scheme achieves unconditional security and can overcome the information disclosure problem caused by homomorphism.

Applying Secret Image Sharing to Economics

Economics has some limitations, such as insecure multiple parties economical investment decision and leakage of business quotation. Secret image sharing (SIS) for (k, n)-threshold is such a technique that protects an image through splitting it into n shadows, a.k.a. shadow images or shares, assigned to n corresponding participants. The secret image can be disclosed by obtaining k or more shadows. Polynomial-based SIS and visual secret sharing (VSS) are the chief research branches. This paper first analyzes the insecure issues in economics and then introduces two methods to apply typical SIS schemes to improve economical security. Finally, experiments are realized to illustrate the efficiency of the methods.

Weighted Polynomial-Based Secret Image Sharing Scheme with Lossless Recovery

In some particular scenes, the shadows need to be given different weights to represent the participants’ status or importance. And during the reconstruction, participants with different weights obtain various quality reconstructed images. However, the existing schemes based on visual secret sharing (VSS) and the Chinese remainder theorem (CRT) have some disadvantages. In this paper, we propose a weighted polynomial-based SIS scheme in the field of GF (257). We use k , k threshold polynomial-based secret image sharing (SIS) to generate k shares and assign them corresponding weights. Then, the remaining n − k shares are randomly filled with invalid value 0 or 255. When the threshold is satisfied, the number and weight of share can affect the reconstructed image’s quality. Our proposed scheme has the property of lossless recovery. And the average light transmission of shares in our scheme is identical. Experiments and theoretical analysis show that the proposed scheme is practical and feasible. Besides, the quality of the reconstructed image is consistent with the theoretical derivation.

A Common General Access Structure Construction Approach in Secret Image Sharing

(k, n) threshold is a special case of the general access structure (GAS) in secret image sharing (SIS), therefore GAS is more extensive than (k, n) threshold. Most of conventional SIS, including visual secret sharing (VSS), polynomial-based SIS, linear congruence (LC)-based SIS, etc., were proposed with only (k, k) threshold or (k, n) threshold other than GAS. This article introduces a common GAS construction approach in SIS with on pixel expansion from existing (k, k) threshold or (k, n) threshold SIS. The authors input classic SIS methods to test the efficiency and feasibility of the proposed common GAS construction approach. Experiments are presented to indicate the efficiency of the approach by illustrations and analysis.

Secret Image Sharing with Dealer-Participatory and Non-Dealer-Participatory Mutual Shadow Authentication Capabilities

A ( k , n ) threshold secret image sharing (SIS) method is proposed to divide a secret image into n shadows. The beauty of this scheme is that one can only reconstruct a secret image with k or more than k shadows, but one cannot obtain any information about the secret from fewer than k shadows. In the ( k , n ) threshold SIS, shadow authentication means the detection and location of manipulated shadows. Traditional shadow authentication schemes require additional bits for authentication; need much information to be public; or need to put each shadow into a host image, utilizing the information hiding technique, which makes the generation, recovery and authentication complexity higher. Besides, most existing schemes work when a dealer participates in recovery. Our contribution is that we propose a SIS method for a ( k , n ) threshold with dealer-participatory and non-dealer-participatory mutual shadow authentication capabilities which integrates polynomial-based SIS and visual secret sharing (VSS) through using the result of VSS to “guide” the polynomial-based SIS by a screening operation. In our scheme, when an authentication image is public, all involved actors (participants and dealer) can mutually authenticate each other by exchange the lowest level plane instead of the whole shadow. Our scheme is suitable for the case with and without a dealer participate recovery. In addition, the proposed scheme has characteristics of low generation and authentication complexity, no pixel expansion, 100% detection rate and lossless recovery.

Application of random elements in ISS

The ( k , n ) -threshold image secret sharing (ISS) encodes a secret image into n shares. When k or more shares are obtained, the secret image can be decoded; however, less than k shares could decode none of the secret image. ISS primarily includes polynomial-based ISS and visual secret sharing (VSS). In this study, the authors find that the random elements in ISS can be used not only to hide information but also to obtain more features such as multiple decryptions and comprehensible share. They have established an application model of random elements that is suitable for both polynomial-based ISS and VSS. On the basis of the model, they have extended three algorithms to achieve information hiding, multiple decryptions and comprehensible share. Experiments indicate the effectiveness of these algorithms.

A compressed secret image sharing method with shadow image verification capability.

Secret image sharing (SIS) is an important research direction in information hiding and data security transmission. Since the generated shadow images (shares) are always noise-like, it is difficult to distinguish the fake share from the unauthorized participant before recovery. Even more serious is that an attacker with a fake share can easily collect shares of other honest participants. As a result, it is significant to verify the shares, before being taken out for recovery. Based on two mainstream methods of SIS, such as polynomial-based SIS and visual secret sharing(VSS), this paper proposed a novel compressed SIS with the ability of shadow image verification. Considering that the randomness of the sharing phase of polynomial-based SIS can be utilized, one out of shares of (2, 2)-threshold random-grid VSS is embedded into all shares of polynomial-based SIS by a XOR operation as the verification information, while the other binary share is private for verification. Before recovery, each participant must extract the binary share from the grayscale share to perform XOR operation with the private share, and the original binary image can be recovered only with the true share. The proposed scheme also has the characteristics of shadow image verification, pixel compression, loss tolerance and lossless recovery. Through experiments and comparative analysis of related research results, the effectiveness and advantages of the method are verified.

Image inpainting-based behavior image secret sharing.

The polynomial-based image secret sharing (ISS) scheme encodes a secret image into n shadows assigned to n participants. The secret image with high resolution is decoded by Lagrange interpolation when collecting any k or more shadows. Thus, ISS is used in applications such as distributive storage in the cloud, digital watermarking, block chain, and access control. Meaningful shadows are significant in ISS because meaningful shadows decrease the suspicion of image encryption and increase the efficiency of shadow management. Generally, previously meaningful ISS schemes were achieved through embedding the shadows into cover images using information hiding techniques and suffer from large pixel expansion and complex decoding procedure. Digital image processing, such as inpainting (texture synthesis), is a standard technique in multimedia applications. It will be highly significant if ISS can be performed in the processing of a normal digital image processing technique. Generally, the encoding method of an ISS scheme entails the use of a mathematical function that is sensitive to any slight change in the ISS output; therefore, the development of a method for performing the ISS procedure and simultaneously achieving image processing behavior is a key challenge. In this paper, we exploit the behavior ISS (BISS) and realize an image inpainting-based BISS scheme for the (k, n) threshold. Using screening operations, a secret image is encoded into the pixels of cover images by polynomial-based ISS in the processing of inpainting shadows to obtain meaningful shadows similar to the input cover images. In addition, the secret image can be losslessly decoded by Lagrange interpolation when collecting any k or more shadows. Experiments are given to confirm the efficiency of the scheme.

Secret image sharing with separate shadow authentication ability

Secret image sharing (SIS) is attracting increasing attention due to its wide application to the distributed storage of digital images in a cloud and the importance of digital images. Shadow authentication plays an important role in the practical application of SIS. However, most SIS schemes with shadow authentication ability embed each shadow into a cover image using an existing information hiding technique, which leads to high generation and recovery (authentication) complexity and pixel expansion. In this paper, we propose an SIS scheme for a (k,n) threshold with a separate shadow authentication ability based on SIS itself rather than information hiding through applying visual secret sharing (VSS) to polynomial-based SIS by using a screening operation. The proposed scheme has low generation and recovery (authentication) complexity and no pixel expansion with a separate shadow authentication ability. In addition, it achieves lossless recovery without auxiliary encryption. We validate the proposed scheme by means of illustrations, theoretical analyses and comparisons.

A combination of color-black-and-white visual cryptography and polynomial based secret image sharing

A new (k,n) threshold secret image sharing scheme with two decoding options is introduced in this paper. The proposed scheme combines color-black-and-white visual cryptography scheme (CBW-VCS) and polynomial based secret image sharing (PSIS) together, to offer stacking-to-see decryption and lossless image reconstruction. To construct the color shares, a general (k,n) threshold CBW-VCS is firstly given. A grayscale secret image is converted to a p-radix image and a binary image. The p-radix image is encrypted by the (k,n) PSIS under mod p operation, and n p-radix shadows are obtained. Then, a color share generation algorithm with data embedding is proposed to construct n color shares. Theoretical analysis and sufficient experiments are provided to show the effectiveness and advantages of the proposed scheme.

Efficient and Lossless Polynomial-Based Secret Image Sharing for Color Images

In today's era of developed network, it is particularly important to ensure the security of information. Secret image sharing is a kind of secret information protection technology with loss tolerance by sharing a secret image to a number of shadow images. Most of the researches on secret image sharing focus on grayscale images, but the images we use in our daily life are mostly in color, so the research on the secret image sharing for color image is very meaningful and has great application value. The traditional color image sharing scheme is to share and recover R, G, and B color planes separately, which cause that the time of sharing and recovering one color image is at least triple that of sharing and recovering one grayscale image with the same size as the color image. In this paper, we propose an efficient and lossless secret image sharing scheme for color images. We concatenate the R, G, and B values of every color pixel into a long integer and share it by the polynomial-based secret image sharing, thus the sharing efficiency of color images is greatly improved by reducing the number of sharing operations to 1/3 of the traditional scheme. And we achieve lossless recovery by taking GF(16777259) as the finite field of polynomial operations. 16777259 is the smallest prime number greater than 2 24 - 1, so we intend to screen the random numbers to drop the invalid share values. Theoretical analyses and experiments are used to prove the effectiveness of the proposed scheme.

A general progressive secret image sharing construction method

Classic secret image sharing (SIS) including polynomial-based SIS, visual secret sharing (VSS), linear congruence (LC)-based SIS and so on, generally has the shortcoming of “all-or-nothing”, which is mainly caused by that most of their ideas are borrowed from secret data sharing designed for data rather than image. Progressive secret image sharing (PSIS) has the feature that the more shadows the better recovered secret image quality. In this paper, we introduce a general PSIS construction method with no pixel expansion from classic “all-or-nothing” SIS. Based on our PSIS construction method, three PSIS algorithms with selective progressive thresholds are extended from classic SIS schemes, respectively. Experiments are provided to demonstrate the efficiency of our method in terms of illustrations and analyses.

Lossless and Efficient Polynomial-Based Secret Image Sharing with Reduced Shadow Size

Thien-and-Lin’s polynomial-based secret image sharing (PSIS) is utilized as the basic method to achieve PSISs with better performances, such as meaningful shares, two-in-one property and shares with different priorities. However, this (k,n) threshold PSIS cannot achieve lossless recovery for pixel values more than 250. Furthermore, current solutions to lossless recovery for PSIS have several natural drawbacks, such as large computational costs and random pixel expansion. In this paper, a lossless and efficient (k,n) threshold PSIS scheme with reduced shadow size is presented. For lossless recovery and efficiency, two adjacent pixels are specified as a secret value, the prime in the sharing polynomial is replaced with 65,537, and then the additional screening operation can ensure each shared value in the range [0,65,535]. To reduce shadows size and improve security, only the first k−1 coefficients are embedded with secret values and the last coefficient is assigned randomly. To prevent the leakage of secrets, generalized Arnold permutation with special key generating strategy is performed on the secret image prior to sharing process without key distribution. Both theoretical analyses and experiments are conducted to demonstrate the effectiveness of the proposed scheme.

Polynomial-Based Secret Image Sharing Scheme with Fully Lossless Recovery

Lossless recovery is important for the transmission and storage of image data. In polynomial-based secret image sharing, despite many previous researchers attempted to achieve lossless recovery, none of the proposed work can simultaneously satisfy an efficiency execution and at no cost of some storage capacity. This article proposes a secret sharing scheme with fully lossless recovery based on polynomial-based scheme and modular algebraic recovery. The major difference between the proposed method and polynomial-based scheme is that, instead of only using the first coefficient of sharing polynomial, this article uses the first two coefficients of sharing polynomial to embed the pixels as well as guarantee security. Both theoretical proof and experimental results are given to demonstrate the effectiveness of the proposed scheme.

Optimizing Information Rate in Polynomial Based Image Secret Sharing Scheme Using Huffman Coding

Optimizing Information Rate in Polynomial Based Image Secret Sharing Scheme Using Huffman Coding