Information Hiding Based on Search Order Coding for VQ Indices

1. Information Hiding Based on Search Order Coding for VQ Indices Source: Pattern Recognition Letters, Vol.25, 2004, pp.1253–1261 Authors: Chin-Chen Chang, Guei-Mei Chen, and Min-Hui Lin Speaker: Chiuan-Bo Yeh (葉權柏) Date: 2004/09/15

2. Outline • Introduction • Vector Quantization (VQ) • Search-Order Coding (SOC) • The proposed scheme • Experimental results • Conclusions • Comments

3. Introduction 1.Compress host image by VQ, and generate VQ indices. 2.Compress VQ indices by SOC, and generate SOC indices. 3.Use the proposed scheme to embed the secret data into SOC indices, and generate stego image. VQ SOC Embed Host Image VQ indices SOC indices Stego Image Secret Data

4. Vector Quantization(1/2) Divided into blocks of the same size Record the VQ index 0 1 … i … i Encoded by the closest codeword in the codebook

5. Vector Quantization(2/2) Block Vector v = (18,45,43,72) Compute the square of the Euclidean Distance 4 d(v,CWi) = ∥v - CWi∥2= ∑(vj – CWij)2 j=1 d(v,CW1) = 196 + 144 + 36 + 1296 = 1672 d(v,CW2) = 2116 + 64 + 2401 + 1849 = 6430 d(v,CW3) = 4096 + 4 + 2806 + 289 = 7195 d(v,CW4) = 961 + 81 + 49 + 25 = 1116 Min Choice CW4 into VQ indices. Codebook CW1 CW2 CW3 CW4

6. Search-Order Coding(1/2) • To increase the compression rate of the VQ indices of an image. • There is usually a high correlation between the neighboring blocks.

7. Search-Order Coding(2/2) Defineindicator 0 search order codes (SOC) 1 original index values (OIV) If one of the SPs matches 0 11 indicator SOC If none of the SPs matches 1 01010001 indicator OIV

8. The proposed scheme(1/3) • Receiver determines that each bit of secret data is ‘‘0’’ or ‘‘1’’ according to whether the received compression code is SOC or OIV. • Ex. Receive 010111010011101001001000 • 0 10 1 11010011 1 01001001 0 00 • The secret data is 0110. • The largest size of secret data can be the number of the blocks.

9. The proposed scheme(2/3) In the hiding process, there are four categories taken into consideration. Indicator Secret data 1 1 There is nothing needing to be changed. 0 1 Preserve the OIV compression code instead of the SOC one. The compression rate will decrease. 0 0 There is nothing needing to be changed. 1 0 A translation technique of translating OIV into SOC is performed. The compression rate will decrease.

10. The proposed scheme(3/3) 1 2 3 Secret Data Status 1 • [(1,1),1] OIV 1 Nothing to be changed 1 000100101 00010010 • [(2,2),1] SOC 1 OIV instead of SOC 0001 00011110 • [(2,3),0] SOC 0 Nothing to be changed • 010010 • [(3,3),0] OIV 0 SOC instead of OIV • 1 00100000 011 00100000 2 3 A 3 · 3 index table for showing the original coding results of the SOC algorithm. 1 2 3 1 2 3 The hiding position of each bit of the secret bit string ‘‘111110100’’ in the raster scan order.

11. Experimental results(1/2) Table 1 The amount of increasing bits for hiding data in the compression codes Code category in the results of the original SOC coding method Code category in the results of our information hiding OIV SOC OIV 0 n SOC log2Nc– n 0 Table 2 Bit rate for embedding different sized secret binary image ‘‘Lena’’ into six host images The size of secret Airplane Boat Girl Lena Peppers Toys data (bits) 1024 0.3976 0.4162 0.4571 0.4509 0.4468 0.3733 2048 0.4367 0.4484 0.4821 0.4817 0.4721 0.4134 3072 0.4707 0.4730 0.5158 0.5144 0.4972 0.4520 4096 0.4962 0.5025 0.5418 0.5418 0.5196 0.4789

12. Experimental results(2/2) Table 3 Bit rates of the SOC scheme and our information hiding method with secret binary image ‘‘Barbara’’ of 1024 bits Methods Images Airplane Boat Girl Lena Peppers Toys SOC (Hsieh and Tsai, 1996) 0.3602 0.3814 0.4319 0.4206 0.4168 0.3316 OIV represents to hide ‘‘1’’ 0.3980 0.4227 0.4558 0.4525 0.4471 0.3749 OIV represents to hide ‘‘0’’ 0.3983 0.4197 0.4561 0.4514 0.4419 0.3740 Table 4 Bit rates of the SOC scheme and our information hiding method with secret binary image ‘‘Lena’’ of 1024 bits Methods Images Airplane Boat Girl Lena Peppers Toys SOC (Hsieh and Tsai, 1996) 0.3602 0.3814 0.4319 0.4206 0.4168 0.3316 OIV represents to hide ‘‘1’’ 0.3976 0.4162 0.4571 0.4509 0.4468 0.3733 OIV represents to hide ‘‘0’’ 0.3987 0.4262 0.4548 0.4531 0.4422 0.3756

13. Conclusions • The first scheme that embeds the secret data into the compression codes of the VQ indices directly. • Embedding the secret data will not incur any distortion. • Receive both the compressed image and the embedded data almost at the same time.

14. Comments • Find a function f such that f( indicators ) = secret data Ex. • Increase distortion, and increase compression rate. indicators 111100101 secret data 111110100 f(111100101) = 111110100