Information Hiding Based on Search Order Coding for

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 1

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

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. Host Image VQ SOC VQ indices Embed SOC indices Stego Image Secret Data 3

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

Vector Quantization(2/2) Block 18 45 43 72 Vector v = (18, 45, 43, 72) Compute the square of the Euclidean Distance 4 2 d(v, CWi) = ∥v - CWi∥ = Codebook = = ∑(v – CW ) j=1 j CW 1 32 57 49 36 CW 2 64 37 92 115 d(v, CW 1) d(v, CW 2) d(v, CW 3) d(v, CW 4) CW 3 82 47 96 55 Choice CW 4 into VQ indices. CW 4 49 36 50 67 2 ij 196 + 144 + 36 + 1296 = 1672 2116 + 64 + 2401 + 1849 = 6430 4096 + 4 + 2806 + 289 = 7195 961 + 81 + 49 + 25 = 1116 Min 5

Search-Order Coding(1/2) n n To increase the compression rate of the VQ indices of an image. There is usually a high correlation between the neighboring blocks. 18 21 31 30 30 31 29 30 32 6

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

The proposed scheme(1/3) n 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 01011101001001000 0 10 1 11010011 1 01001001 0 00 The secret data is 0110. n. The largest size of secret data can be the number of the blocks. 8

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

The proposed scheme(3/3) 1 1 2 3 18 21 31 (OIV) 30 30 31 (OIV) (SOC) 29 30 32 (OIV) (SOC) (OIV) A 3 · 3 index table for showing the original coding results of the SOC algorithm. 1 2 3 1 1 2 1 1 0 3 1 0 0 The hiding position of each bit of the secret bit string ‘‘ 111110100’’ in the raster scan order. n[(1, 1), 1] Status Secret Data OIV 1 1 00010010 Nothing to be changed 1 00010010 n[(2, 2), 1] 0 00 SOC 1 OIV instead of SOC 1 00011110 n[(2, 3), 0] 0 10 SOC 0 Nothing to be changed 0 10 n[(3, 3), 0] OIV 1 00100000 0 SOC instead of OIV 0 11 00100000 10

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 0 n log 2 Nc – n 0 Table 2 Bit rate for embedding different sized secret binary image ‘‘Lena’’ into six host images The size of secret data (bits) 1024 2048 3072 4096 Airplane Boat Girl Lena Peppers Toys 0. 3976 0. 4367 0. 4707 0. 4962 0. 4162 0. 4484 0. 4730 0. 5025 0. 4571 0. 4821 0. 5158 0. 5418 0. 4509 0. 4817 0. 5144 0. 5418 0. 4468 0. 4721 0. 4972 0. 5196 0. 3733 0. 4134 0. 4520 0. 4789 11

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 SOC (Hsieh and Tsai, 1996) OIV represents to hide ‘‘ 1’’ OIV represents to hide ‘‘ 0’’ Images Airplane Boat Girl Lena Peppers Toys 0. 3602 0. 3980 0. 3983 0. 3814 0. 4227 0. 4197 0. 4319 0. 4558 0. 4561 0. 4206 0. 4525 0. 4514 0. 4168 0. 4471 0. 4419 0. 3316 0. 3749 0. 3740 Table 4 Bit rates of the SOC scheme and our information hiding method with secret binary image ‘‘Lena’’ of 1024 bits Methods SOC (Hsieh and Tsai, 1996) OIV represents to hide ‘‘ 1’’ OIV represents to hide ‘‘ 0’’ Images Airplane Boat Girl Lena Peppers Toys 0. 3602 0. 3976 0. 3987 0. 3814 0. 4162 0. 4262 0. 4319 0. 4571 0. 4548 0. 4206 0. 4509 0. 4531 0. 4168 0. 4422 0. 3316 0. 3733 0. 3756 12

Conclusions n n n 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 13 time.

Comments n Find a function f such that f( indicators ) = secret data Ex. n 18 21 31 (OIV) 30 30 31 (OIV) (SOC) 29 30 32 (OIV) (SOC) (OIV) indicators 111100101 secret data 111110100 f(111100101) = 111110100 Increase distortion, and increase compression rate. 14