data hiding in least significant bit (lsb) speaker: feng jen-bang ( 馮振邦 )

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

4

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

11


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

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


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

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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

data hiding in least significant bit (lsb) speaker: feng jen-bang ( 馮振邦 )

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