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視覺密碼學視覺密碼學

Chair Professor Chin-Chen Chang ( 張真誠 )

National Tsing Hua University ( 清華大學 ) National Chung Cheng University ( 中正大學 ) Feng Chia University ( 逢甲大學 ) http://msn.iecs.fcu.edu.tw/~ccc

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Outlines Concept of Secret Sharing Concept of visual cryptography Visual cryptography for binary images Visual cryptography for grayscale images

Meaningful visual cryptography for grayscale images

Meaningful and progressive visual cryptography Visual cryptography for color images Authenticatable VSS Scheme

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shadows

secret message

Traditional (t, n)-secret sharing (Shamir’s Method 1979)

secret retrieval

(2, 3)-secret sharing

Alice KenBob

ShamirShamir, A. (1979): How to Share a Secret, CACM, Vol. 22, Nov. 1979, pp. 612-613., A. (1979): How to Share a Secret, CACM, Vol. 22, Nov. 1979, pp. 612-613.

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Ex: (2, 3)-threshold Scheme (The secret k=7)

7mod112xf(x)

3 shadows: (1, 9), (2, 0), (3, 2)

x

y

7)0( f

(1, 9)

(2, 0)

(3, 2)

How to Share a Secret (t, n)-threshold Scheme

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Ex: (3, 5)-threshold Scheme (t=3, n=5, k=13, p=17)

8)1( f

13mod1710x2xf(x) 2

Alice KenBob Jesse Eva

ID1=1 ID2=2 ID3=3 ID4=4 ID5=5

7)2( f 10)3( f 0)4( f 11)5( f

(1, 8)

(3, 10)

(5, 11)

13mod1710x2xf(x) 2

Lagrange Interpolation

)35)(15(

)3)(1(11

)53)(13(

)5)(1(10

)51)(31(

)5)(3(8)(

xxxxxx

xf

k

How to Share a Secret (t, n)-threshold Scheme

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Concept of Visual Cryptography

Cryptography Traditional Cryptography Symmetric: DES, AES Asymmetric: RSA

The encryption and decryption processes need high computation costs

Need secret key for decoding Visual Cryptography

low computation Fast decoding Without the secret key

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Hidden in Hidden in

The Basis Image: Mickey The Counterfeit Image: Minnie

The Secret Image: Airplane

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The Basis Image: Mickey The Counterfeit Image: Minnie

The Expanded Basis Image: Mickey-3X3

The Expanded Counterfeit Image: Minnie-3X3

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Airplane

Mickey-3X3 Minnie-3X3

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Naor and Shamir (1994) proposed a (k, k)–VSS scheme Extend a secret pixel into a block of 22 s

ub-pixels Contain two white pixels and two black p

ixels for each block White pixel: transparent Black pixel: black

Visual Cryptography for Binary Image

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Secret pixel

stacked result

Secret image

Share 1

Share 2

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Transfer the grayscale image to the halftone image

Utilize the density of black dots to simulate the content of grayscale image White area: low density of black dots Black area: high density of black dots

Visual Cryptography for Grayscale Image

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Share 1 Share 2

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shadow 1 shadow 2

camouflage

cover image

stego image1 stego image2

secret image

Meaningful Visual Cryptography for Grayscale Image

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0 1

1 0

152

167

140

137

cover image

shadow1

140

transparent

stego image1

0 1

1 0

170

97

150

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0 1

1 0

1 0

0 1

140

167 170

83

shadow2

stego image2

167 97

150

shadow1

shadow2

17

140

167

83

170

140 150

167 97

stego image1

stego image2

stacked result

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Experimental Resultsshadow1 cover image1 stego image1

shadow2 cover image2 stego image2

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stego image1

stego image2

stacked result

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shadow1 cover image1 stego image1

shadow2 cover image2 stego image2

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stego image1

stego image2

stacked result

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Meaningful and Progressive Visual Cryptography

Meaningful shares: friendly content Progressive visual cryptography

Improve the stacked result progressively

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Progressive Visual Cryptography (t, 6)

(2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

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Meaningful shares: friendly content

Progressive & Meaningful Visual Cryptography

shadow 1 shadow n

camouflage

cover image

stego image1 stego image n

…

…

secret image

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secret image

cover image

secret image cover image shadow imageextended secret image

shadow image 1 shadow image 2 shadow image 3 shadow image 4

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secret image

cover image

t =2 t = 3

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(2, 6) (3, 6) (4, 6) (5, 6) (6, 6)

Experimental Results

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RGB: TV’s and Monitors CMY: Color Printing Press

Visual Cryptography for Color Image

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shadow image 1 shadow image 2 stacked image 2

Experimental Results

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Participant 1

Participant 2

Share 1

Share 2

Stack

Recovered secret image

Hacker

Authentication

Original secret image

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Share 1

Share 2

Correct stacking result

Share 1 Share 2

Correct stacking result

Legal extra confidential image

Legal revealed secret image

Authentication

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Tampered share 1

Share 2

Tampered share 1

Share 2

Tampered secret imageTampered secret image

NothingTampered revealed secret image

Authentication

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Grayscale image Lena Grayscale image Baboon Binary main secret

Halftone image of Lena Halftone image of Baboon Binary extra confidential image

Authenticatable VSS Scheme for Binary Secret

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Share image A Share image B

Stacking result Revealed extra confidential image

Authenticatable VSS Scheme for Binary Secret

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Color image Lena

Color image Baboon

Color main secret

Color halftone image of Lena

Color halftone image of Baboon Color halftone extra confidential image

Authenticatable VSS Scheme for Color Secret

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Share image A Share image B

Stacking result Revealed extra confidential image

Authenticatable VSS Scheme for Color Secret

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Visual cryptography (Cont.)

Share 1 Share 2

Secret 1 “VISUAL” Secret 2 “SECRET”

Stacking Stacking

Rotating 40o

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Steganography (Cont.) Text 壞的毛病 壞毛病 山東的蘋果 山東蘋果 我的媽媽 我媽媽 主要的問題 主要問題 另外的一件事 另外一件事 其他的問題 其他問題 北京的大學 北京大學 Video Sound

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Conclusions An alternative for hiding visual secret Less secret Low computation cost

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