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 Tsaiab,Tzung-her Chenc and Gwoboa Hornga

aDepartment of Computer Science, National Chung Hsing UniversitybDepartment of Information Management, Hsiuping institue of Technology

cDepartment of Computer Science and Information Engineering, National Chiayi University報告人：張淯閎

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

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Abstract Naor and Shamir proposed the (k,n) Visual Cr

yptography(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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Visual Cryptography The nm subpixels is described as an n×m boolean matrix S=[S

ij] such that Sij = 1 if and only if the jth subpixel of the ith share is black. A solution to the (k,n) VC scheme consists of two collections of n×m boolean matrices C0(For white) and C1(For black).

The solution is considered valid if the following three conditions are met：1.H(V) ≦ d-α*m in C0

2.H(V) ≧ d in C1 3.For any subset {i1,i2,…,iq} of {1,2,…,n} with q < k, the two collections of q×m matrices Dt for tε{0,1} obtained by restricting each n×m matrix in Ct (where t=0,1) to rows i1,i2,…,iq are indistinguishable in the sense that they contain the same matrices with the same frequencies.

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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 an

d 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.

Figure 1.: the cheating process

Pixel in

Secret

Image

Share pixel in Share SA

Share pixel in Share SB

Share pixel in Share SC

Pixel in

Cheating

Image

Share pixel in

Share SA’

Share pixel in

Share SB’

Case1 white [1 0 0] [1 0 0] [1 0 0] white [1 0 0] [1 0 0]

Case2 white [1 0 0] [1 0 0] [1 0 0] black [0 1 0] [0 0 1]

Case3 black [1 0 0] [0 1 0] [0 0 1] white [0 0 1] [0 0 1]

Case4 black [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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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.

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nC

Figure 2. The sketch of proposed scheme

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VC Cheating Protection Scheme(2)Individual 1Individual 2Individual 3

...

Fitness Function

Transmutation stop yes or no?

Reproduction Crossover Mutation

Population

Simulation environment

MatingPool

New generation

Figure 3.GA Process

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VC Cheating Protection Scheme(3)

Figure 4. The chromosomes

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VC Cheating Protection Scheme(4)IF H(V j) = EV THEN

ρ j= 1 ELSEρ j = 0, where j = 1,2,…,n

IF H(g(i1 ,i2 ) ) satisfy SV (i1 ,i2 ) THEN

ψ(i1 ,i2 ) = 1 else ψ(i1 ,i2 ) = 0, where i 1 < i 2 < n

fitness value =

2

1*

),( 21

njii

Fitness function algorithm

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Simulated Results(1)

Figure 5. Decoded images in the (2, 4) cheating prevention scheme

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Simulated Results(2)

Figure 7: Results of simulated cheating attack.

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Conclusion The proposed scheme does against the

cheating attack in VC. The GA based share construction method

provides another direction for creating shares.