1. A Novel Reversible Data Embedding Scheme Using Chinese Remainder Theorem for Vector Quantizer Index
Chair Professor Chin-Chen Chang
Feng Chia University
National Chung Cheng University
National Tsing Hua University

2. Outline
Introduction
Proposed scheme
Experimental results
Conclusions

3. Introduction (1/5) Information hiding Sender Receiver
Compression code: …
Color palette image
Reconstructed image
Compression code …
Secret data: 011
Secret data: 011

4. Introduction (2/5) VQ Encoding Index table Original Image Codebook …
(120,155,…,80) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(90,135,…,120)
(100,125,…,150) …
Index table
Original Image
(49,117,…,25)
(50,42,…,98)
(20,65,…,110)
Codebook

5. Introduction (3/5) Principal component analysis (PCA) Ex: 2-dimension. X1 X2 D2 D1

6. Introduction (4/5) 鬼谷先生留下的一道算术题： “今有物，不知数，三三数之剩二，五五数之剩三，七七数之剩二，问物几何？”
明万历年间大商人程大位，以一首诗的形式对答此题：
“三人同行七十稀，五树梅花廿一枝，七子团圆整半月，除百零五便得知”

7. Introduction (5/5) Chinese remainder theorem (CRT) How to evaluate c?
Ex.
Let
be integers,
There exists an integer c, such that:
if gcd (mi, mj)=1, for all i ≠ j
How to evaluate c?

8. The proposed scheme (1/6)
VQ codebook
sorted codebook
codebook
reserved 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
(49,117,…,25)
(20,65,…,110) 1 2 3 4 5 6 7 8 9 10 11 12 13
(50,42,…,98)
(49,117,…,25)
(20,65,…,110)
(50,42,…,98)
indicator … …
(120,155,…,80)
(90,135,…,120)
(90,135,…,120)
(100,125,…,150)
(100,125,…,150)
(120,155,…,80)
reserved
PCA

9. The proposed scheme (2/6)
Chinese remainder theorem (CRT)
p=5, q=7
secret : ( )2
codeword pair (23, 28)
Input: p, q, s, Ca , Cb
Output: c, d
p=5
(331)p
s = 3
d = |Ca - Cb| = | | = 5
c = 3 mod 5
c = 5 mod 7
0 ≤ d < q

10. The proposed scheme (3/6)
codeword pair (Ca , Cb )
Case-A: ( Ca < Cb ) and ( Cb + c < 255 ) and ( d < q )
Case-B: (Cb < Ca ) and ( Ca + c < 255 ) and ( d < q )
Case-C: Otherwise

11. The proposed scheme (4/6)
How to convert (Ca, Cb) to (Ca’, Cb’) Cb Ca 23 28 28 28
d =5
s = 3
p = 5, q = 7
d = 5
Index table
+33 61
Cb’
c = 33
Ca’
Stego-index table

12. The proposed scheme (4/6)
How to convert (Ca’, Cb’) to (Ca, Cb)
Cb’
Ca’ 28 28 28 28 61
c = 33
p = 5, q = 7
c = 33
Stego-index table
d = c mod q
= 33 mod 7
= 5
s = c mod p
= 33 mod 5
= 3 Cb
d =5 , s = 3 Ca
Ca = Cb – d
= 28 – 5
= 23
Index table 23

13. The proposed scheme (6/6)
Case-C: Otherwise (∵ d = | | = 12 > q) Cb
indicator : codeword ‘0’ and codeword ‘255’ Ca 35 23
(00) Ca’= ‘0’ || Ca Cb’ = ‘0’ || Cb
(01) Ca’= ‘0’ || Ca Cb’ = ‘255’ || Cb
(10) Ca’= ‘255’ || Ca Cb’ = ‘0’ || Cb
(11)2 Ca’= ‘255’ || Ca Cb’ = ‘255’ || Cb
s =
Index table
Embed: s = 00
Cb’
Ca’= indicator + Ca
Cb’= indicator + Cb
Ca’= ‘0’ + 35
Cb’= ‘0’ + 23
Ca’
‘0’+35
‘0’+23
Extract : If ( indicator( Ca’ ) = ‘0’ ) or ( indicator( Ca’ ) = ‘255’ )
Extract and Restore
Ca = 35
Cb = 23
Stego-index table
s: 00 +

14. Number of index pairs judged as Case-A or Case-B
Experimental results
Total number of index pairs = 8192
Values of ( p, q )
Images
Number of index pairs judged as Case-A or Case-B
(5, 7)
Lena
4524 (>55%)
Baboon
4673 (>57%)
Pepper
4749 (>57%)
Toys
5102 (>62%)
(5, 11)
4865 (>59%)
4796 (>58%)
4870 (>58%)
5093 (>62%)

15. Conclusions
A new data embedding scheme with CRT is proposed for VQ index table
The proposed scheme achieves the goal of hiding secret bits into index value while reversible