Reversible hiding in DCT-based compressed images

Authors:Chin-Chen Chang, Chia-Chen Lin, Chun-Sen Tseng and Wei-Liang Tai

Adviser: Jui-Che Teng Speaker: Gung-Shian Lin

Date:2009/12/17

2

Outline

1. Introduction

2. Related works

3. Proposed scheme

4. Experimental results

5. Conclusions

3

Introduction

Lossless and reversible steganography scheme for hiding secret data in each block of quantized DCT coefficients in JPEG images.

4

Introduction

In 2001, Fridrich et al. proposed Invertible authentication watermark for JPEG images.

In 2004, Iwata et al. proposed Digital steganography utilizing features of JPEG images.

5

Related works

RGB transformation for JPEG

RGB Image

TransformationRGB→YCbCr

CompositionMCU

2-D DCT

QuantizationQuantization

Table

Runlength codingHuffman coding

HuffmanTable

JPEG Image

6

Proposed scheme

Embedding procedure

R5

R9

R8

R7

R6R1R2R4

R3

bi be the length of ceaseless zeros

zi,1 represents the zero value of the lowest frequency

7

Proposed scheme

2 0

3 3 4 0

2 0 2 2 0

1 0 2 0 0

1 0 0 0 0

0 1 0 1 0

0 0 0 0

0 0 0

R5

R4

R3

R2 R1

si be the secret bit we want to embed into set Ri

8

Proposed scheme

The embedding strategies and elimination measures for ambiguous conditions are as follows:

Case 1:If bi 2, we use the value of z≧ i,2 to indicate the hidden secret

bit in set Ri (1 i 9). We modify the value of z≦≦ i,2 to hide secret bit by using the Eq.

1, is when ,1or 1

0, is when ,0 2

i

ii,

s

sz

where 1 or -1 is randomly selected.

9

Proposed scheme

Ambiguous condition A and its remedial measure。

1

0

x

0

0

0

0R1

10

Proposed scheme

,0 when ,1

,0 when ,1'

11,

11,1,

i,j-ji

i,j-jiji

rr

rrr where 3 (j≦ － 1) k≦ i

3

0

0

0

1

0

0R2

11

Proposed scheme

Case 2: If bi < 2 and both zi,1 and zi,2 do not exist, none secret bits can be hidden in a set Ri.

Two ambiguous conditions may exist, and therefore two remedial measures for eliminating them are described below. Ambiguous condition B and its remedial measure

Ambiguous condition C and its remedial measure

,0 when ,1

,0 when ,1

11

111

i,i,

i,i,i,

r'r'

r'r'r'

,0' when ,1'

,0' when ,1''

2,2,

2,2,2,

ii

iii

rr

rrr

12

Proposed scheme

Example of embedding:assume four secret bits, 0, 0, 1 and 1

13

Proposed scheme Extracting procedure

Step 1. Obtain non-overlapping 8 * 8 blocks of quantized DCT coefficients of the Y components from a JPEG stego-image after Huffman decoding and runlength decoding.

Step 2. Scan each block according to a predetermined order.Step 3. For each set Ri in a block, let ri,j be the highest frequency non-zero component, where 1 i 9 and 1 j k≦≦ ≦≦ i.Step 4. Extract si from set Ri by using the following rules:Step 5. Repeat Steps 3 and 4 until all blocks are processed.Ri

ri,j ＝ 1 or -1 ri,j does not existri,j≠1 or -1

ri,j+1＝ 0 j 2≦ri,j-1＝ 0 and

ri,j-2＝ 0ri,j+1≠0

ri,j-1＝ 0 and ri,j-2＝ 0

j 2≦si=0

mark ri,j-2 as zi,2

si does not exist

si=0mark ri,1 as zi,2

si does not exist

si=0mark ri,j-2 as zi,2

si=1mark ri,j as zi,2

14

Proposed scheme

Restoring procedure Rule 1: If si exists and r’i,j+3＝ 0, where 4 (j≦ ＋ 3) k≦ i, then the origi

nal value of r’i,j+2 is restored by using Eq.

Rule 2:If si does not exist and the two highest coefficients (r’i,1， r’i,2) of set Ri equals (x, 0), where x≠0, then the original value of r’i,1 is restored by using Eq.

,0' when ,1'

,0' when ,1'

2,2,

2,2,2,

jiji

jijiji

rr

rrr where 3 (j≦ ＋ 2)＜ ki.

0r' when ,1'

0r' when ,1'

i,11,

i,11,1,

i

ii

r

rr

15

Proposed scheme

Rule 3: If si does not exist and the pair having the three highest coefficients (r’i,1, r’i,2, r’i,3) of set Ri equals (0,x,0), where x≠0, then the original value of r’i,2 is restored by using Eq.

,0' when ,1'

,0' when ,1'

2,2,

2,2,2,

ii

iii

rr

rrr

16

Proposed scheme

17

Proposed scheme Modifying quantization table for better image quality and

hiding capacity

16 11 10 16 24 40 51 61

12 12 14 19 26 58 60 55

14 13 16 24 40 57 69 56

14 17 22 29 51 87 80 62

18 22 37 56 68 109 103 77

24 35 55 64 64 104 113 92

49 64 78 87 103 121 120 101

72 92 95 98 112 100 103 99

16 11 10 16 24 40 51 61

12 12 14 19 26 41 60 55

14 13 16 17 28 40 48 56

14 17 22 20 36 61 56 43

18 22 26 39 48 76 72 54

24 25 39 56 57 73 79 64

49 64 55 61 72 85 84 71

72 92 95 69 78 70 72 70

18

Experimental results

19

Experimental results

20

Experimental results

21

Conclusions

The scheme provides stego-images with acceptable image quality and similar hiding capacity can be achieved with the Iwata et al. scheme。

The scheme can withstand visual and statistical attacks 。