# An Image Fragile Watermark Scheme Based on Chaotic Image Pattern

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```					An Image Fragile Watermark
Scheme Based on Chaotic Image
Pattern and Pixel-pairs

Source: Applied Mathematics and Computation, article
in press, 2006
Author: Shao-Hui Liu, Hong-Xun Yao, Wen Gao and Yong-
Liang Liu
Speaker: Yung-Chen Chou
Date: Nov. 16, 2006
Outline
   Introduction
   Two typical attacks
   The watermarking algorithm
   Experiments
   Conclusions

Yung-Chen Chou   2
Introduction
   Robust watermarking
   Anti general image processing
   Fragile watermarking
   Semi fragile  soft authentication
   Complete fragile  hard authentication

Yung-Chen Chou             3
Introduction (cont.)
   Walton’s method (1995)
4210=001010102

Check sum=1

H
001010112

   Yeung-Mintzer scheme (1997)
0    0
1    0
2    1
3    1
42                  :    :
1     ?
41
42    0     =
:
H                           :
255    1
LUT         W
Yung-Chen Chou             4
Two attacks
   Vector quantization attack (Wong and Memon, 2000)

Hw1

Hw2                    MSN                MSN

H                 HCF

Hwn
Yung-Chen Chou                   5
Two attacks (cont.)
   Oracle attack
…

SP
Hw           0
1
2

:

255          Oracle
…

SF

Yung-Chen Chou             6
The watermarking algorithm
   Chaotic image pattern
   Chaos theory (Edward Lorenz, 1963)

x(n  1)  g  ( x(n))    x(n)  (1  x(n))
g     x  (1  x)
 [1,4]

Yung-Chen Chou               7
The watermarking algorithm
(cont.) (Chaotic image pattern)
Example:
μ=3.89                                       μ=3.89
x(1) = 0.4567  104                          x(1) = 0.4568  104
x(2) = 3.89*0.4567*(1-0.4567)=0.9652 253    x(2) = 3.89*0.4568*(1-0.4568)=0.9652 253
x(3)=0.130637  8                            x(3)=0.130515  8
x(4)=0.441791  99                           x(4)=0.441441  99
x(5)=0.959319  251                          x(5)=0.95916  251             99.26% pixels have
x(6)=0.15181  14                            x(6)=0.152378  14                different values
x(7)=0.50089  117                           x(7)=0.502428  117
x(8)=0.972497  255                          x(8)=0.972477  255
x(9)=0.104045  0                            x(9)=0.104117  0
x(10)=0.362623  76                          x(10)=0.362848  76
x(11)=0.899086  233                         x(11)=0.899326  234
x(12)=0.352941  73                          x(12)=0.352195  73
x(13)=0.888373  230                         x(13)=0.887518  230
x(14)=0.385757  83                          x(14)=0.388337  83
x(15)=0.921729  240                         x(15)=0.923997  241
x(16)=0.280641  52                          x(16)=0.273181  50
x(17)=0.78532  200                          x(17)=0.772372  196
x(18)=0.655825  162                         x(18)=0.683914  170
x(19)=0.878045  227                         x(19)=0.840924  216
x(20)=0.41655  92                           x(20)=0.520369  122
…                                            …
Yung-Chen Chou                                        8
The watermarking algorithm
(cont.) (Embedding)
155    148    161    143    163                  163   180    145   178   161                            162    180     144     178     160
148    168    130    180    126                  143   130    158   145   161                            142    130     158     144     160
151    158    145    163    143                  168   151    148   148   155                            168    150     148     148     154
145    178    118    194    112                  194   112    112   143   194   Set LSB bitplane         194    112     112     142     194
HP=PT(H,K1)                                  of HP as 0
161    130    188    112    194                  188   126    163   118   130                            188    126     162     118     130

H                                               HP                                                        HPNLSB

104    253    8      99     251                 162   180    144   178   160
58      73     136     79      91
14     117    255    0      76                  142   130    158   144   160
128     13     97      144     84
233    73     230    83     240                 168   150    148   148   154
65      77     82      65      86
52     200    162    227    92                  194   112    112   142   194
142     88     50      85      102
45     76     56     160    104                 188   126    162   118   130
143     50     106     42      26

RCP                                           HPNLSB                                               D

Yung-Chen Chou                                                                9
The watermarking algorithm
(cont.) (Embedding)
58        73    136   79    91            0   1     0   1   1                0    1    1     1   0                 0    0    1     0     1

128       13    97    144   84            1   0     1   0   1                0    1    0     0   1                 1    1    1     0     0

65        77    82    65    86            1   1     1   1   1    ⊕           0    1    1     1   0                 1    0    0     0     1
142       88    50    85    102           0   1     0   1   1                0    1    0     0   1                 0    0    0     1     0
143       50    106   42    26            0   0     1   0   1                0    1    1     1   0                 0    1    0     1     1

D                             QD                                       WP

0        15    32         64                  128                                                          255                             Replace LSB
bitplane of HPNLSB
Set A  0
Set B  1                                                                                              162       180       144     178   160
155   148   160   143   162               162    180       145       178   161
142       130       158     144   160
148   169   131   180   127               143    131       159       144   160
168       150       148     148   154
150   159   145   162   143               169    150       148       148   155
194       112       112     142   194
144   178   119   192   112               194    112       112       143   194
188       126       162     118   130
161   131   188   112   194               188    127       162       119   131
HPNLSB
HW                                   Yung-Chen Chou                                                                 10
The watermarking algorithm
(cont.) (Extracting)
0   0     1    0    1

155   148   160       143   162                     162   180    145   178    161                1   1     1    0    0

148   169   131       180   127                     143   131    159   144    160                1   0     0    0    1

150   159   145       162   143                     169   150    148   148    155                0   0     0    1    0

194   112    112   143    194                0   1     0    1    1
144   178   119       192   112

161   131   188       112   194   HWP=PT(HW,K1)     188   127    162   119    131
162       180       144       178   160
HW                                                       HWP                       142       130       158       144   160
168       150       148       148   154
0   1     1    1    0
⊕                                              194       112       112       142   194
0   1     0    0    1                                                              188       126       162       118   130
58     73    136    79    91
0   1     1    1    0
128    13    97     144   84
0   1     0    0    1       0   1   0   1   1                                      104       253       8         99    251
65     77    82     65    86
0   1     1    1    0       1   0   1   0   1                                      14        117       255       0     76
142    88    50     85    102
WE                  1   1   1   1   1      143    50    106    42    26    233       73        230       83    240
0   1   0   1   1                                      52        200       162       227   92
0   0   1   0   1                                      45        76        56        160   104

RCP
Yung-Chen Chou                                                      11
Experiments

c         d

Yung-Chen Chou   12
Experiments (cont.)

Yung-Chen Chou   13
Conclusions
   Chaotic map and permutation transform
are used to improve the security.
   The method can exactly detect the
tampered areas on the watermarked
image.

Yung-Chen Chou        14

```
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