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 http://msn.iecs.fcu.edu.tw/~ccc

Outline Introduction Proposed scheme Experimental results Conclusions

Introduction (1/5) Information hiding Sender Receiver Compression code: 1000011010… Color palette image Reconstructed image Compression code 1000011010… Secret data: 011 Secret data: 011

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

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

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”

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?

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

The proposed scheme (2/6) Chinese remainder theorem (CRT) p=5, q=7 secret : (01011011)2 codeword pair (23, 28) Input: p, q, s, Ca , Cb Output: c, d p=5 (331)p s = 3 d = |Ca - Cb| = |23 - 28| = 5 c = 3 mod 5 c = 5 mod 7 0 ≤ d < q

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

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

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

The proposed scheme (6/6) Case-C: Otherwise (∵ d = |35 - 23| = 12 > q) Cb indicator : codeword ‘0’ and codeword ‘255’ Ca 35 23 (00)2 Ca’= ‘0’ || Ca Cb’ = ‘0’ || Cb (01)2 Ca’= ‘0’ || Ca Cb’ = ‘255’ || Cb (10)2 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 +

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%)

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