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A Combined Approach to Integrity Protection and Verification of Palette Images Using

Fragile Watermarks and Digital Signatures

Source: IEICE TRANS. On FUNDAMENTALS, vol.

E87-A, no. 6, pp. 1612- 1619, Jun. 2004

Author: Chih-Hsuan Tzeng and Wen-Hsiang Tsai

Speaker: Na-I Wu ( 吳男益 )

Data: 2004/09/16

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Outline

• Introduction

• The proposed method

(1) Fragile watermarking embedding

(2) Generate “digital signatures”

• Experimental results

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Introduction An indexed image consists of data matrix, X, and a colormap matrix, map.

Size: 129 x 126

Ex: 256 色Indices:

form 1 to 256

File Size: Color map: 129 x 126 x 8 Indices: 256 x 3 x 8

6.19k bytes

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Introduction

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The proposed method Fragile watermarking embedding

To classify pixels into embeddable and non-embeddable

ones.

Embed

authentication

signals

Generate

Digital

signature

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Fragile watermarking embedding

• Raster Scanning Manner : to find “embeddable”, and “non-embeddable”

256 256 256 200 154 123 200 154

256 256 256 200 155 132 200 155

256 256 256 200 156 133 200 156

200 200 200 200 163 50 200 163

256 256 256 200 154 123 200 154

256 256 256 200 155 132 200 155

256 256 256 200 156 133 200 156

200 200 200 200 163 50 200 163

8x8

• Raster Scanning Manner : to find “embeddable”, and “non-embeddable”

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• Raster Scanning Manner : to find “embeddable”, and “non-embeddable”

P1(i-1, j-1) P2(i, j-1) P3(I+1, j-1)

P4(i-1, j) X(i,j)

Raster Scanning

Fragile watermarking embedding

α: the number of distinct colors of pixels in Prec(X)

β: The maximum color distance dmax(X, Prec(X))

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• How to compute α, β values

12 12 12

12 60 α = 1

12 12 16

10 10 α = 3

Fragile watermarking embedding

12(50, 60, 70) 轉成 L, a, b 顏色模式 (69, 10, 5)10(90, 10, 60) 轉成 L, a, b 顏色模式 (10, 7, 6)兩者的距離 =[(69-10)2+(10-7)2+(5-6)2]1/2

L: luminancea: green to red B: blue to yellow

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Fragile watermarking embedding

The values of Tc and Td be set by user

EX1: Tc =2, Td =10

12 12 12

12 12α = 0, β = 0

12 12 12

12 60α = 1, β = 48

“non-embeddable”

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The values of Tc and Td be selected by user

EX2: Tc =2, Td =10

“embeddable”

12 12 16

10 10α = 3, β = 6

12 16 17

10 18α = 4, β = 8

Fragile watermarking embedding

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Palette Mapping Function M

Fragile watermarking embedding

1 (120,50,30)

2 (111,51,21)

3 (112,52,32)

4 (123,13,33)

5 (134,4,34)

6 (25,55,35)

Color palette

重排列

f(u)=216xr +28xg +b

換算權重值 1 7877150

2 7287573

3 7353376

4 8064289

5 8782882

6 1652515

5 8782882

4 8064289

1 7877150

3 7353376

2 7287573

6 1652515

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Palette Mapping Function M

Fragile watermarking embedding

58782882

48064289

17877150

37353376

27287573

6 1652515

K: secret key

Generate a random bit stream

1 1 0 0 1 1 若為 n 色，則產生 n bits.

51

41

10

30

21

6 1

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Fragile watermarking embedding

Palette Mapping Function M

1 (120,50,30)1

2 (111,51,21)1

3 (112,52,32)0

4 (123,13,33)0

5 (134,4,34)1

6 (25,55,35)1

attack

1 (120,50,30)1

3 (112,52,32)1

2 (111,51,21)0

4 (123,13,33)0

5 (134,4,34)1

6 (25,55,35)1

將 pixel 值 2 變 3 ， 3 變2

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EX2: Tc =2, Td =10 ， and want to hide “0”

12 12 16

10 10α = 3, β = 6

Fragile watermarking embedding

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

1 0 1 1 0 1 0 1

0 0 1 0 1 0 1 1

K: secret key

No modify

Authentication Data: 010101011

K: secret key

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EX2: Tc =2, Td =10 ， and want to hide “1”

12 12 16

10 10α = 3, β = 6

Fragile watermarking embedding

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

1 0 1 1 0 1 0 1

0 0 1 0 1 0 1 1

K: secret key

(1) 去找週遭 4 個的 Lab 顏色 模式，其差最小的那一個and (2) M(i)==secret data修改完之必需符合

“Embeddable pixels” 的規定 α > Tc and Td < β

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The proposed method Generate “digital signatures”

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

1 0 1 1 0 1 0 1

0 0 1 0 1 0 1 1

EX1: Tc =2, Td =10

12 12 12

12 12α = 0, β = 0

“non-embeddable”

0

Authentication Data: 010101011

K: secret key

XOR operator

0Generate “digital signatures”

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The proposed method

每個 8x8 區塊的 “ digital signatures ” 的長度不一樣， 故每個 簽章的前面先放 ceil(nxn) bits ，用來 記錄每個 小區塊的 簽章的長度。

將每個小區塊的簽章的長度，合併起來來， 最後放在檔頭。

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The Authentication ProcessThe Authentication ProcessEX2: Tc =2, Td =10

12 12 16

10 10α = 3, β = 416

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

1 0 1 1 0 1 0 1

0 0 1 0 1 0 1 1

K: secret key

K: Authentication Data

secret data “1”

temper

12 12 16

10 10α = 3, β = 412

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The Authentication ProcessThe Authentication ProcessEX1: Tc =2, Td =10

12 12 12

12 12α = 0, β = 0

“non-embeddable”

1 2 3 4 5 6 7 8

9 10 11 12 13 14 15 16

K: secret key

K: Authentication Data

010101011

“digital signatures” 0

1 0 1 1 0 1 0 1

0 0 1 0 1 0 1 1

XOR operator

temper

12 12 12

10 13α = 1, β = 1

1

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Experimental Results

1

1( , ' )

N

i ii

ADEPB d c cN

Block size = 8 × 8 Tc= 2, Td= 15

Size: 560 × 504

256 palette colors

Digital signatures:

7938bytes

The degrees of average distortion in the embeddable pixels of a block:

1

1( , ' )

N

i ii

ADEPB d c cN

ADEPB(max):8.25

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Experimental Results

Size: 488 × 672

64 palette colores

Digital signatures: 11907bytes

ADEPB(max):9.76