Abstract
Visual cryptography is a potentially important technique for optical information security. However, the limitations of carrier materials and the high precision requirements of the reconstruction process limit the application scope of visual cryptography. Herein, we propose a novel visual cryptography technique based on ghost imaging. The spatial information on one visual key image is encoded into time-varying factors in ghost imaging and loaded onto Hadamard illumination patterns. The secret image can be recovered when the illumination patterns are projected onto another visual key image. This method utilizes light-intensity superposition to overlap visual key image pixels. Simulation and experimental results substantiate the feasibility and security of the proposed technique. This method incorporates the unique advantages of ghost imaging and visual cryptography and is not limited by carrier materials and precision. Hence, it has high scalability and broad application scenarios in ghost imaging broadcasting systems and information authentication, among others.
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Acknowledgements
The authors are indebted to the anonymous referees for their instructive comments and suggestions.
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This research was funded by the National Natural Science Foundation of China (Grant No. 62205207).
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Appendix
Appendix
Two visual cryptography schemes are described in this paper. One extends secret images into two meaningless images while in the other, secret images can be composed of two meaningful images. These two coding methods are described as follows.
1.1 A. The (2,2) visual cryptographic coding scheme
In this scheme, a secret image is extended into two meaningless images. Any image cannot get information about the secret image. The secret image can be obtained only if the two images are superimposed together. The operation of encryption and decryption is shown in Fig.
Process schematic diagram of encryption and decryption of visual cryptographic
14.
We first process the secret image in pixels, and each pixel is divided into two shared blocks. The separation rule is shown in Table
2.
When a pixel in the secret image is a white pixel, we can randomly select a combination mode of white pixels as presented in Table 1. The two shared blocks contain two subpixels, one black and one white, and the results are also black and white when two shared blocks are superimposed. When a pixel is black, we randomly choose the combination mode but the superposition result is black. Thus, the secret image is extended into two shared images. Because of the random selection, each black or white pixel in the secret image is encrypted into two subpixels (one black and one white) in the shared image, so it is not possible to obtain any information on the secret image from the shared image. The information on the secret image can only be obtained in the case of overlapping of the two shared images.
In this rule, one pixel in the secret image is expanded into two subpixels, so the shared image is twice as large as the secret image. For instance, when the size of the secret image is \(128 \times 128\) pixels, the size of the shared image is \(128 \times 256\) pixels. One pixel can also be expanded into 4, 8, or 16 subpixels according to this rule. In this study, one pixel is expanded into 4 subpixels.
1.2 B. An enhanced visual-cryptographic coding scheme
In this coding scheme, multiple shared images are generated based on the secret image and mask images, and the shared image is a halftone image generated after encoding the mask image. When multiple shared images overlap, the secret image can be recovered.
We encode the image as a halftone image and the grayscale value of each pixel in the image determines the number of black and white pixels in the halftone image’s subpixels. We divide the grayscale values of the image into different levels. Herein, they are divided into 16 levels (the grayscale value of 0~15 is the 1 level and 16~31 is the 2 level). A pixel in the original image is expanded into a \(4 \times 4\) subpixel. For example, if the grayscale value of a pixel is 100, then its grayscale level is 7, so there are seven white pixels in a \(4 \times 4\) grid. After processing, the size of the original \(128 \times 128\) pixel image will become \(512 \times 512\), as shown in Fig.
a Original image. b Halftone image
15.
The order of the black and white pixels in the subpixels will not affect the visual effect but will give the overlay result different grayscale levels. As shown in Fig.
Examples of subpixel arrangements. Arranging two subpixels with \(a = 6/16\) and \(b = 9/16\) as the examples make \(c = 9/16,\;c = 15/16,\;c = 10/16\)
16, the two subpixels’ grayscale levels are 6 and 9, respectively. If their black and white pixels are located at different positions then the grayscale level of their superimposed results also differs.
According to the rules, the secret and shared images are encoded into halftone images. The order of the black and white pixels in the two shared images’ subpixels is adjusted according to the grayscale level of the secret image. If necessary, we can slightly change the grayscale level of the shared images’ subpixels. The coded shared image can be superimposed to obtain the expected grayscale level and the secret image can be reproduced. Figure
Specific example of the enhanced visual-cryptographic coding scheme. a Shared image 1. b Shared image 2. c Reconstructed secret image
17 shows a specific example.
Using this scheme, the secret image can be composed of meaningful images which significantly increases the information capacity and reduces the possibility of being suspected.
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Kang, Y., Zhang, L., Ye, H. et al. Visual cryptography based on ghost imaging and Hadamard transform. Quantum Inf Process 22, 116 (2023). https://doi.org/10.1007/s11128-022-03821-1
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DOI: https://doi.org/10.1007/s11128-022-03821-1