VMVC: رمزنگاری بصری چند لحنی قابل بررسی VMVC: Verifiable multi-tone visual cryptography

1 Introduction Visual Cryptography (VC) is a category of secret sharing scheme, proposed by Naor et al. [17], that allows computation-less decoding of secret images. Mainly in a k-out-of-n visual secret sharing (VSS) scheme, a secret image is encoded into n noise-like shares and printed onto transparencies to distribute them among n participants. Secret image can be decoded by just stacking any k or more transparencies. In spite of using infinite computation power, k − 1 or fewer participants can not decode the secret image. Besides the secret sharing, visual cryptography can also be used for number of other purposes including access control, watermarking, copyright protection [5], identification [16] and visual authentication. To demonstrate the working of VSS, consider a 2-out-of-2 VSS (k = 2, n = 2) scheme shown in Fig. 1. Each pixel p of secret binary image is encoded into a pair of black and white subpixels for both shares. If p is white/black, one of the first/last two columns tabulated under the white/black pixel in Fig. 1 is selected randomly so that selection probability will be 50 %. Then, the first two subpixels in that column are alloted to share 1 and the following other two subpixels are alloted to share 2. Independent of whether p is black or white, pixel is encoded into two subpixels of black-white or white-black with equal probabilities. Thus an individual share has no idea about whether p is black or white. The last row of Fig. 1 shows the superimposition of the two shares, If the pixel p is black, the output of superimposition will be two black subpixels corresponding to a gray level 1. If p is white, then result of superimposition will be one white and one black subpixel, corresponding to a gray level 1/2. Hence by stacking two shares together, we can obtain the approximate visual information of the secret image. Figure 2 shows an example of the 2-out-of-2 VSS scheme. Figure 2a shows a secret binary image Isec to be encoded. According to the encoding scheme shown in Fig. 1, each pixel p of Isec is divided into two subpixels in each shares, as shown in Fig. 2b and c. Stacking the two shares leads to the output image shown in Fig. 2d. The decoded image is clearly revealed. There are some contrast loss and the width of the reconstructed image is just twice of the original secret image. The 2-out-of-2 VSS scheme shown above is a special case of the k-out-of-n VSS scheme. A more general model for VSS schemes based on general access structures has been designed by Ateniese et al. in [1]. An access structure is a specified set of all the qualified and forbidden subsets of the shares. The secret image can be decoded by the participants of a qualified subset only. The capabilities of VSS has also been enhanced by allowing gray scale images as secret rather than a binary image [15].