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A New Cheating Prevention Scheme For Visual Cryptography 第十六屆全國資訊安全會議 Jun 8 2006 Du-Shiau Tsai ab,Tzung-her Chen c and Gwoboa Horng a a Department of Computer Science, National Chung Hsing University b Department of Information Management, Hsiuping institue of Technology c Department of Computer Science and Information Engineering, National Chiayi University 報告人：張淯閎

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2 Conspectus Abstract Visual Cryptography Cheating in Visual Cryptography VC Cheating Protection Scheme Simulated Results Conclusion

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3 Abstract Naor and Shamir proposed the (k,n) Visual Cryptography(VC for short) scheme in 1995, and has been used in numerous applications. In 2006, Horng et al. proposed that cheating is possible in VC. In this study, a new scheme used Generic Algorithms(GA for short) is proposed to solve the cheating problem.

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4 Visual Cryptography The nm subpixels is described as an n×m boolean matrix S=[S ij ] such that S ij = 1 if and only if the j th subpixel of the i th share is black. A solution to the (k,n) VC scheme consists of two collections of n×m boolean matrices C 0 (For white) and C 1 (For black). The solution is considered valid if the following three conditions are met ： 1.H(V) ≦ d-α*m in C 0 2.H(V) ≧ d in C 1 3.For any subset {i 1,i 2, …,i q } of {1,2, …,n} with q < k, the two collections of q×m matrices D t for t ε {0,1} obtained by restricting each n×m matrix in C t (where t=0,1) to rows i 1,i 2, …,i q are indistinguishable in the sense that they contain the same matrices with the same frequencies.

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5 Cheating in Visual Cryptography Horng et al. proposed that cheating is possible in (k,n) VC when k is smaller than n. The key point of cheating is how to predict and rearrange the positions of black and white subpixels in the victim ’ s and cheater ’ s share. Figure 1. shows the whole cheating process and Table 1. shows the cheaters create to change the decoded image.

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Figure 1.: the cheating process

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Pixel in Secret Image Share pixel in Share S A Share pixel in Share S B Share pixel in Share S C Pixel in Cheating Image Share pixel in Share S A ’ Share pixel in Share S B ’ Case1white[1 0 0] white[1 0 0] Case2white[1 0 0] black[0 1 0][0 0 1] Case3black[1 0 0][0 1 0][0 0 1]white[0 0 1] Case4black[1 0 0][0 1 0][0 0 1]black[1 0 0][0 1 0] Table 1.: The concept of cheating in VC

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8 VC Cheating Protection Scheme(1) Figure 2. shows the process to proposed scheme. ● First, The rotation process turns SI with different degrees of angle to generate SI. ● Second, used GA to proposed scheme. Figure 2. The sketch of proposed scheme

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9 VC Cheating Protection Scheme(2) Individual 1 Individual 2 Individual 3... Fitness Function Transmutation stop yes or no? ReproductionCrossoverMutation Population Simulation environment MatingPool New generation Figure 3.GA Process

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10 VC Cheating Protection Scheme(3) Figure 4. The chromosomes

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11 VC Cheating Protection Scheme(4) IF H(V j ) = E V THEN ρ j = 1 ELSEρ j = 0, where j = 1,2, …,n IF H(g (i1,i2 ) ) satisfy S V (i1,i2 ) THEN ψ (i1,i2 ) = 1 else ψ (i1,i2 ) = 0, where i 1 < i 2 < n fitness value = Fitness function algorithm

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12 Simulated Results(1) Figure 5. Decoded images in the (2, 4) cheating prevention scheme

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13 Simulated Results(2) Figure 7: Results of simulated cheating attack.

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14 Conclusion The proposed scheme does against the cheating attack in VC. The GA based share construction method provides another direction for creating shares.

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