data hiding in least significant bit (lsb)
DESCRIPTION
Data hiding in Least Significant Bit (LSB). Speaker: Feng Jen-Bang ( 馮振邦 ). Outline. Data Hiding by LSB Simple LSB LSB with Permutation Find Optimal Solution Use Genetic Algorithm Use Dynamic Algorithm Use Modulus Function Comparisons Comments. Data Hiding by LSB. - PowerPoint PPT PresentationTRANSCRIPT
Data hiding inLeast Significant Bit (LSB)
Speaker: Feng Jen-Bang ( 馮振邦 )
2
Outline Data Hiding by LSB Simple LSB LSB with Permutation Find Optimal Solution
Use Genetic Algorithm Use Dynamic Algorithm
Use Modulus Function Comparisons Comments
3
Data Hiding by LSB Extract does not need cover image Capacity is 1/8 – 1/2 PSNR is about 51 - 31
Embedded by LSB
Secret message
Cover image
Stego image
Secret message
Extract
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Simple LSB
0(0000 0000)2
128(1000 0000)2
129(1000 0001)2
135(1000 0111)2
155(10011011)2
Embedded with 6 (110)2
158(10011011)2
Usually hidden in 1 to 4 bits
00101101
00101001
00101100
00101001
k = 3 101 001
100 001
(1010 0110 0001)2
= (A 6 1)16
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LSB with Permutation Cover pixels: c0, c1, …, cn
Secret pieces: s0, s1, …, sn
k bits each Exchange values
(0, 1, …, 2k-1) (v0, v1, …, v2k-1) Exchange positions
Permutation keys: k0, k1
k1 is relatively prime to n
nikki mod ' 10
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LSB with Permutation
00101101
00101001
00101100
00101001
Cover image
Secret message(C 2)16 = (1100 0010)2
k = 2n = 4
Value permutation(0, 1, 2, 3) (2, 0, 1, 3)
k0 = 1k1 = 3
(1100 0010)2
(11 00 00 10)2
value permu (11 10 10 01)2
pos. permu (10 11 01 10)2
nikki mod ' 10
i ’ = (1, 0, 3, 2)
00101110
00101011
00101101
00101010
Stego image
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Finding Optimal Solution Find the optimal solution of value permutation.
k0 and k1 are keys Too much computation of exhausted method
2k! possible permutations
00101101
00101001
00101100
00101001
Cover image
00101110
00101011
00101101
00101010
Stego image
Value permutation(0, 1, 2, 3) (2, 0, 1, 3)
00101111
00101000
00101100
00101010
Cover image
Simple LSB
Sum of square error22+12+02+12= 6
Sum of square error12+22+12+12= 7
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Image Hiding by Optimal LSB Substitution and Genetic Algorithm Ran-Zan Wang, Chi-Fang Lin, and Ja-Chen Lin Pattern Recognition, Vol. 34, 2001, pp. 671-683 Use genetic algorithm to find nearly optimal soluti
on of value permutations
10 random permus.
Crossover
Mutation
Fitnessfunction
10 pairs
Reproduction
P=0.1Nearly optimal
Solution
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Image Hiding by Optimal LSB Substitution and Genetic Algorithm
Crossover 0 1 2 3 4 5 6 7 0 2 4 6 1 3 5 7
0 1 2 3 1 3 5 7
0 1 2 3 4 6 5 7 0 2 4 6 1 5 3 7
0 2 4 6 4 5 6 7
0 1 2 3 4 5 6 7
0 5 2 3 4 1 6 7
Mutation Fitness function is the sum of square errors.
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Finding Optimal Least Significant Bit Substitution in Image Hiding by Dynamic Programming Strategy
Chin-Chen Chang, Ju-Yuan Hsiao, and Chi-Shiang Chan
Pattern Recognition, Vol. 36, 2003, pp. 1583-1595
Reduce complexity Find real optimal solution
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Finding Optimal Least Significant Bit Substitution in Image Hiding by Dynamic Programming Strategy
20010
0111
02
13
S
20000
1011
00
23
R
0149
9410
1014
9410
44M
mi,j = sum of square errors that change j to i
0,4 Cost
9,4]0][3[0,3 CostmCost
4,4]1][3[1,3 CostmCost
1,4]2][3[2,3 CostmCost
0,4]3][3[3,3 CostmCost
4
91
40min
0,3]1][2[
1,3]0][2[min1,0,2
Costm
CostmCost
1
94
10min
0,3]2][2[
2,3]0][2[min2,0,2
Costm
CostmCost
0
99
00min
0,3]3][2[
3,3]0][2[min3,0,2
Costm
CostmCost
2
44
11min
1,3]2][2[
2,3]1][2[min2,1,2
Costm
CostmCost
12
Finding Optimal Least Significant Bit Substitution in Image Hiding by Dynamic Programming Strategy
1
49
01min
1,3]3][2[
3,3]1][2[min3,1,2
Costm
CostmCost
4
19
04min
2,3]3][2[
3,3]2][2[min3,2,2
Costm
CostmCost
2
40
11
24
min
1,0,2]2][1[
2,0,2]1][1[
2,1,2]0][1[
min2,1,0,1
Costm
Costm
Costm
Cost
1
41
01
14
min
1,0,2]3][1[
3,0,2]1][1[
3,1,2]0][1[
min3,1,0,1
Costm
Costm
Costm
Cost
0
14
00
44
min
2,0,2]3][1[
3,0,2]2][1[
3,2,2]0][1[
min3,2,0,1
Costm
Costm
Costm
Cost
1
21
10
41
min
2,1,2]3][1[
3,1,2]2][1[
3,2,2]1][1[
min3,2,1,1
Costm
Costm
Costm
Cost
1
29
14
01
10
min
2,1,0,1]3][0[
3,1,0,1]2][0[
3,2,0,1]1][0[
3,2,1,1]0][0[
min3,2,1,0,0
Costm
Costm
Costm
Costm
Cost
0149
9410
1014
9410
44M
Optimal permutation
(0, 2, 1, 3)
02
13S
00
23R
01
23'S
13
Use Modulus Functions
A Simple and High-Hiding Capacity Method for Hiding Digit-by-Digit Data in Images Based on Modulus Function Chih-Ching Thien, Ja-Chen Lin. Pattern Recognition, Vol. 36, 2003, pp. 2875-2881
Hiding Data in Images by Simple LSB Substitution Chi-Kwong Chan, L.M. Cheng Pattern Recognition, Vol. 37, 2004, pp. 469-474
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Use Modulus Functions
Cover pixel(1100 1001)2
Secret piece(110)2
(1100 1110)2
Square error = 52 = 25
Consider(1100 1000)2 + (110)2 - (1000)2
= (1100 0110)2
Square error = 32 = 9
K = 3
If (r – s) > 2k-1
c = c + 2k
If (r – s) < 2k-1
c = c – 2k
rc
s
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Comparisons
Schemesk
Simple LSB
Genetic Dynamic
Modulus
1 51 51 51 51
2 44 45 45 46
3 37 * 40 40
4 31 33 33 34
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Comments
The most simple and easy way
A blind method
Almost largest capacity
Applied wildly