Secret image sharing (SIS) with small-sized shadow images has many benefits, such as saving storage space, improving transmission time, and achieving information hiding. When adjacent pixel values in an image are similar to each other, the secret image will be leaked when all random factors of an SIS scheme are utilized for achieving small sizes of shadow images. Most of the studies in this area suffer from an inevitable problem: auxiliary encryption is crucial in ensuring the security of those schemes. In this paper, an SIS scheme with small-sized shadow images based on the Chinese remainder theorem (CRT) is proposed. The size of shadow images can be reduced to nearly 1 / k of the original secret image. By adding random bits to binary representations of the random factors in the CRT, auxiliary encryption is not necessary for this scheme. Additionally, reasonable modifications of the random factors make it possible to incorporate all advantages of the CRT as well, including a ( k , n ) threshold, lossless recovery, and low computation complexity. Analyses and experiments are provided to demonstrate the effectiveness of the proposed scheme.
In general, in a secret image sharing (SIS) scheme with a (k, n) threshold, the participants have equal weights, and their shares have the same average light transmission. No share can reveal any information about the secret. Only when the number of participants involved in restoration is greater than or equal to k can the secret image be revealed. However, on some occasions, the participants' weights need to be set differently, and their shares have different effects on the restoration of the secret image. Therefore, there are many studies of weighted SIS, including schemes based on visual secret sharing using random grids (VSSRG). However, they can only share binary images, not grayscale images. Therefore, we propose a scheme based on the Chinese remainder theorem (CRT) for sharing grayscale images. The shares are generated with different weights. When the threshold is reached and shares with higher weights are involved in restoration, the quality of the restored image is higher. As the number of participating shares increases, the quality of the recovered secret image increases, and if all the shares are involved, lossless restoration can be achieved.INDEX TERMS (k, n) threshold, secret image sharing, the Chinese remainder theorem, weighted secret image sharing.
A typical Chinese remainder theorem (CRT)-based secret sharing (SS) scheme has been proposed by Asmuth and Bloom for several decades, with lower computation complexity compared to Shamir's original polynomial-based SS. But when applied to images, CRT-based image secret sharing (CRTISS) shows many problems, such as lossy recovery, auxiliary encryption, and extra parameters requirement. We analyze the characteristics of images and ISS and propose a (k, n)-threshold CRTISS based on the Asmuth and Bloom's scheme by sharing the high 7 bits of a grayscale secret pixel and embedding the least significant bit (LSB) into the random integer. The pixel values of a grayscale image are divided into two parts, which make it possible to share all the secret pixels with no expansion. Our method has the advantages of (k, n) threshold, lossless recovery, and no auxiliary encryption. The parameters requirement is the same as that in the Asmuth and Bloom's original method. Analysis and experiments are provided to validate the effectiveness of the proposed method. INDEX TERMS Image secret sharing, Chinese remainder theorem, lossless recovery, (k, n) threshold.
Quick response (QR) codes are becoming increasingly popular in various areas of life due to the advantages of the error correction capacity, the ability to be scanned quickly and the capacity to contain meaningful content. The distribution of dark and light modules of a QR code looks random, but the content of a code can be decoded by a standard QR reader. Thus, a QR code is often used in combination with visual secret sharing (VSS) to generate meaningful shadows. There may be some losses in the process of distribution and preservation of the shadows. To recover secret images with high quality, it is necessary to consider the scheme's robustness. However, few studies examine robustness of VSS combined with QR codes. In this paper, we propose a robust (k, n)-threshold XOR-ed VSS (XVSS) scheme based on a QR code with the error correction ability. Compared with OR-ed VSS (OVSS), XVSS can recover the secret image losslessly, and the amount of computation needed is low. Since the standard QR encoder does not check if the padding codewords are correct during the encoding phase, we replace padding codewords by initial shadows shared from the secret image using XVSS to generate QR code shadows. As a result, the shadows can be decoded normally, and their error correction abilities are preserved. Once all the shadows have been collected, the secret image can be recovered losslessly. More importantly, if some conventional image attacks, including rotation, JPEG compression, Gaussian noise, salt-and-pepper noise, cropping, resizing, and even the addition of camera and screen noises are performed on the shadows, the secret image can still be recovered. The experimental results and comparisons demonstrate the effectiveness of our scheme.
Different color patterns of quick response (QR) codes, such as RGB, grayscale, and binary QR codes, are widely used in applications. In this paper, we propose a novel XOR-based visual secret sharing (VSS) scheme using grayscale QR codes as cover images and binary QR code as secret image. First, all the codewords of the secret QR code image are encoded into n temporary binary QR code images, which are substituted for the second significant bit planes of the grayscale QR code cover images to generate n shares. Each share is a grayscale QR code image, which can be decoded by a standard QR code decoder, so that it may not attract the attention of potential attackers when distributed in the public channel. The secret image can be recovered by XORing the codewords regions of QR codes which are extracted from the second significant bit planes of the grayscale shares. More importantly, the proposed scheme is robust to JPEG compression, addition of different noises, rotation, resizing, and cropping, which is useful in practice. The effectiveness and robustness of our scheme are shown by the experimental results. The application of QR code is suitable for wireless multimedia data security.
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