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Visual Cryptography Jiangyi Hu

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Jiangyi Hu, Zhiqian Hu2 Visual Cryptography Example Secret sharing Visual cryptography Model Extensions

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Jiangyi Hu, Zhiqian Hu3 Visual Cryptography Example What is visual cryptography?

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Jiangyi Hu, Zhiqian Hu4 Visual Cryptography Secret Sharing The General Idea All n parties can get together and recover secret s. Less than n parties cannot recover secret s.

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Jiangyi Hu, Zhiqian Hu5 Visual Cryptography Secret Sharing (Cont.) Suppose two parties are going to share a secret bit string 1011. A coin toss is used to generate the first bit of the first share. If the result of the coin toss is a head, then the bit is 0; otherwise, the bit is a 1. Now generate the first bit of the second share. If the first bit of the first share was 0, then copy the first bit of the secret. Otherwise, if the bit of the first share was 1, then flip the first bit of the secret and use that. Repeat this random process for each bit of the secret.

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Jiangyi Hu, Zhiqian Hu6 Visual Cryptography Secret Sharing (Cont.) Suppose the secret is 1011, toss the coin 4 times and get the sequence head, tail, tail, and head. Then the first share would simply be 0110. As a result, the bits of the second share would be 1101 (the XOR of 0110 and 1011). No information about the secret will be gained by looking at either the first share or the second share. Combine two share and can discover the secret: S1 XOR S2 = Secret. Secret: 1011 S1:0110 S2:1101

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Jiangyi Hu, Zhiqian Hu7 Visual Cryptography Visual cryptography was introduced by Naor and Shamir at EUROCRYPT '94. It is used to encrypt written material (printed text, handwritten notes, pictures, etc) in a perfectly secure way. The decoding is done by the human visual system directly.

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Jiangyi Hu, Zhiqian Hu8 Visual Cryptography Visual Cryptography (Cont.) For a set P of n participants, a secret image S is encoded into n shadow images called shares, where each participant in P receives one share. Certain qualified subset of participants can visually recover the secret image, but other, forbidden, sets of participants have no information on S.

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Jiangyi Hu, Zhiqian Hu9 Visual Cryptography Visual Cryptography (Cont.) A visual recovery for a set X of participants consists of copying the shares onto transparencies, then stacking them on a projector. The participants in a qualified set X will be able to see the secret image without any knowledge of cryptography and without performing any cryptographic computation.

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Jiangyi Hu, Zhiqian Hu10 Visual Cryptography Model Assume the message consists of a collection of black and white pixels and each pixel is handled separately. Each share is a collection of m black and white subpixels. Boolean matrix S=[s ij ] where s ij =1 iff the jth subpixel in the ith transparency is black. The grey level of the combined share is interpreted by the visual system as black if and as white if.

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Jiangyi Hu, Zhiqian Hu11 Visual Cryptography Model (Cont.) is some fixed threshold and is the relative difference. H(V) is the hamming weight of the vector. The visual effect of a black subpixel in one transparency can’t be undone by the color of that subpixel in other transparencies which are laid over it.

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Jiangyi Hu, Zhiqian Hu12 Visual Cryptography Model (Cont.)

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Jiangyi Hu, Zhiqian Hu13 Visual Cryptography 2 out of 2 visual cryptography

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Jiangyi Hu, Zhiqian Hu14 Visual Cryptography 2 out of 2 scheme (Cont.) A pixel P is split into two subpixels. If P is white, then a coin toss is used to randomly choose one of the first two rows in the figure above. If P is black, then a coin toss is used to randomly choose one of the last two rows in the figure above. The pixel P is encrypted as two subpixels in each of the two shares, as determined by the chosen row in the figure. Every pixel is encrypted using a new coin toss.

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Jiangyi Hu, Zhiqian Hu15 Visual Cryptography 2 out of 2 scheme (Cont.) For each pixel, neither the first share nor the second gives any clue as to whether the pixel is black or white. Since all the pixels in the secret image were encrypted using independent random coin flips, there is no information to be gained by looking at pixels on a share, either. This demonstrates the security of the scheme.

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Jiangyi Hu, Zhiqian Hu16 Visual Cryptography 2 out of 2 scheme (Cont.) When superimpose the two shares, consider one pixel P. If P is black, we get two black subpixels. If P is white, we get one black subpixel and one white subpixel. Thus, the reconstructed pixel (consisting of two subpixels) has a grey level of 1 if P is black, and a grey level of 1/2 if P is white. There will be a 50% loss of contrast in the reconstructed image, but it is still be visible.

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Jiangyi Hu, Zhiqian Hu17 Visual Cryptography 3 out of 3 visual cryptography 0011 11000101 1010 01101001 horizontal shares vertical shares diagonal shares

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Jiangyi Hu, Zhiqian Hu18 Visual Cryptography 3 out of 3 scheme (Cont.)

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Jiangyi Hu, Zhiqian Hu19 Visual Cryptography 3 out of 3 scheme (Cont.) Each matrix in either C 0 and C 1 contains one horizontal share, one vertical share and one diagonal share. The analysis of one or two shares makes it impossible to distinguish between C 0 and C 1. A stack of three transparencies from C 0 is only ¾ black, whereas a stack of transparencies from C 1 is completely black.

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Jiangyi Hu, Zhiqian Hu20 Visual Cryptography Extension and enhancement Each pixel in each one of the two transparencies is presented by a rotated half circle. Send innocent looking transparencies, e.g.. Send images a dog, a house, and get a spy message with no trace. Color visual cryptography

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Jiangyi Hu, Zhiqian Hu21 Visual Cryptography Color Visual Cryptography Verheul and van Tilborg ’ s method For a C-color image, we expand each pixel to C subpixels on two images. For each subpixel, we divide it to C regions. One fixed region for one color. If the subpixel is assigned color C 1, only the region belonged to C 1 will have the color.Other regions are left black.

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Jiangyi Hu, Zhiqian Hu22 Visual Cryptography Color Visual Cryptography (Cont.) Four subpixels Four regions Combined One pixel on four- color image

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Jiangyi Hu, Zhiqian Hu23 Visual Cryptography Color Visual Cryptography(cont.) Rijmen and Preneel ’ s method Each pixel is divided into 4 subpixels, with the color red, green, blue and white. In any order, we can get 24 different combination of colors.We average the combination to present the color. To encode, choose the closest combination, select a random order on the first share. According to the combination, we can get the second share.

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Jiangyi Hu, Zhiqian Hu24 Visual Cryptography Rijmen and Preneel ’ s method Pattern1 Pattern2 Combined Result

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Jiangyi Hu, Zhiqian Hu25 Visual Cryptography Some References Naor, M. and A. Shamir, Visual Cryptography, Eurocrypt ’94 Proceedings G.Ateniese, C. Blundo, A. De Santis and D.R. Stinson. Visual Cryptography for General Access Structures, Information and Computation, 1996 www.dia.unisa.it/VISUAL/ www.cacr.math.uwaterloo.ca/~dstinson/visual.html www.leemon.com/crypto/visualCrypto.html

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Jiangyi Hu, Zhiqian Hu26 Visual Cryptography Thank you !

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