INTRODUCTION

In recent years, the security of data storage and transmission has drawn much attention among researchers (Ruan et al., 2010). Block Truncation Coding (BTC) (Amarunnishad et al., 2008; Guo et al., 2009) is a popular lousy image compression method due to low computational complexity and storage demands. It never requires any auxiliary information during the encoding and decoding procedures. However, transmission security is also a problem must be considered in more and more situations. Besides traditional data encryption algorithms (e.g., DES), secret sharing (Ahlswede and Csiszar, 1993; Luo et al., 2010; Zhao et al., 2010) and data hiding (Pan et al., 2007) are another two powerful complementary techniques and also play important roles in information security.

The block truncation coding compression is based on a block-wise thresholding operation. Hence, the task of block truncation coding compressed image transmission is reduced to transmitting binary matrices and thresholds of image blocks. The compression ratio is determined by the partitioned block size. That is, a larger block size partition results to fewer binary matrices and thresholds to be transmitted. However, the compressed image quality is worse than that obtained by a smaller block size partition. Consequently, a good tradeoff is usually achieved between the compression ratio and the reconstructed image quality.

In this study, we aim to develop a secure transmission system for block truncation coding compressed images. The application scenario can be described as follows. Given a gray-level or color image, we need to compress and transmit it over two independent but not secure channels. Besides transmission security, the following three factors must be considered in the system design. (1) The reconstruction image quality should be preserved, i.e., nearly the same as that in block truncation coding compression. (2) Low complexity encoding and decoding, thus the real-time performance of block truncation coding compression is maintained. (3) Small size of shares. This is essential to save transmission time and channel resources. In fact, in most available secret sharing methods, the sizes of shares are expanded compared to the original secret data.

In particular, these three advantages are achieved in the proposed system with secret sharing and data hiding well synthesized. The compressed image can be reconstructed as long as both shares are collected. Otherwise, no meaningful information is decrypted. Besides, the encoding/decoding procedures are quite simple and the reconstructed image quality is nearly the same as that in block truncation coding compression. Furthermore, each share is half size of the compressed image and thus no extra burden is laid on transmission channels.

The standard BTC compression technique is reviewed below. Suppose the original image I is a gray-level image. In the encoding stage, I is first partitioned into a set of non-overlapping kxk blocks and the mean value p_m of each block is calculated as:

(1)

where, p(x, y) denotes the pixel value in the position (x, y). Next, the block pixels are thresholded as:

(2)

resulting in a binary bitmap M, where b(x, y) is the pixel value in the position (x, y) of M. Third, two quantization levels p_h and p_l are computed for each block, i.e., the mean values of those pixels with p(x, y)>p_m and p(x, y) = p_m respectively. Thus, each block is represented by a pair of integers p_h, p_l in the range of (0, 255) and a kxk bitmap. The encoding procedure is completed and the compressed content is transmitted.

In the decoding stage, each block can be approximately recovered with p_h, p_l and M as:

(3)

where, p'(x, y) is the reconstructed pixel value in the position (x, y) of the current decoded block. In this way, the decoded image can be reconstructed by collecting all the reconstructed blocks. In our context, p_m, p_h and p_l are rounded to their nearest integers.

PROPOSED SCHEME

Our scheme is conducted as a part of the project work on satellite image transmission from Feb, 2009. The design and test duration is completed till Sep., 2010.

Joint data encryption and data hiding model: We start from presenting the joint data encryption and data hiding model. Suppose the secret data is composed by two binary sequences u = (u₁,u₂,…u_K) and v = (v₁,v₂,…v_K-1). The main idea of our model is to encrypt u and meanwhile v is also hidden in two shares m=(m₁,m₂,…m_K) and n=(n₁,n₂,…n_K). The encryption strategy of this model is shown in Fig. 1.

The encoding procedures are described below:

Step 1: Encrypt u₁ in m₁ and n₁. Randomly select a “1” or “0” and assign it to m₁ and then n₁ is determined by m₁ and u₁ as:

(4)

Step 2: Hide v₁ in n₁ and m₂. That is, n₁ and v₁ as determine m₂:

(5)

Step 3: Encrypt u₂ in m₂ and n₂. That is, m₂ and u₂ as determine n₂:

(6)

Step 4: Repeat the above operations until v_j-1 is hidden in n_j-1 and m_j as indicated with the dash arrow and u_j is encrypted in m_j and n_j as indicated with the solid arrow.

In this way, the sequence u is encrypted and v is hidden in two produced shares m and n.

In decoding, the sequences u and v can be recovered as:

(7)

(8)

where denotes the exclusive-OR operation.

Joint block truncation coding and secret sharing: In the joint BTC and secret sharing scheme, the standard BTC compression and the joint data encryption and data hiding model are applied. In our case, the original image is partitioned into 4x4 blocks.

Fig. 1:	Encryption strategy of the joint data encryption and data hiding model

In the encoding stage, operations are given below:

(9)

Considering in natural images, pixel values change gradually in a 4x4 block, the difference d is small for most natural image blocks. Therefore, it is reasonable to regard d as an integer belongs to (0, 127), otherwise we set d = 127.

The corresponding operations in the decoding stage are described as follows:

(10)

(11)

EXPERIMENTAL RESULTS

The 512x512 gray-level Lena image is selected as the test image and the related experimental results are shown in Fig. 2. Obviously, the two 128x256 share images produced in our scheme look like random noises, thus transmission security of the compressed image can be guaranteed.

Fig. 2:	Experimental results on Lena image, (a) the original image, (b) the constructed image by our scheme, (c) the share image S1, (d) the share image S2

Fig. 3:	Experimental results on the received shares suffering transmission errors, (a) the corrupted S1, (b) the corrupted S2 (c) the reconstructed image

Furthermore, the total amount of the transmission content is the same as that in the standard BTC compression, i.e., the compression ratio is kept as 4.Many transmission scenarios, especially wireless transmissions usually suffer some abrupt errors such as packet loss (Lee et al., 2007). As our scheme is based on a block-wise processing mechanism, these transmission errors of share images only corrupt the associated decrypted blocks. In other words, errors are not diffused to other reconstructed blocks, as illustrated in another experiment shown in Fig. 3. Figure 3a and b are the corrupted versions of Fig. 2c and d respectively. From Fig. 3c, it is easy to find that only the corresponding blocks are corrupted, while others still reconstructed correctly.

It is necessary to note that, compared with the reconstructed image based on the standard block truncation coding; there is a slight quality degradation of the reconstructed image with the two intact shares. This is due to the computed p_h for image reconstruction in our scheme is not exactly equal to that directly transmitted in the standard BTC. Namely, error is introduced in Eq. 9-11 when a floating-point number is rounded to its nearest integer. A large quantity of experimental results shows that this image quality degradation is acceptable. For example, the PSNR of the reconstructed Lena using the standard BTC is 34.00 dB, while 33.96 dB obtained in our scheme.

As mentioned earlier d is set as 127 when it is larger than 127 such that it can be translated into 7-bit sequence. Thus truncation errors may be produced for the range of d is (0, 255) theoretically. Fortunately, as high correlation exists among pixels in natural image blocks, d is small in most cases. Ten 512x512 gray-level images (Lena, Baboon, Barbara, Bridge, Boat, F16, Peppers, Elaine, Aerial, Truck) are selected to investigate the statistics of d values. Each image is partitioned into 4x4 blocks, thus totally 163840 blocks, i.e., 163840 d values are obtained and examined. The 256-bin histogram of d values is shown in Fig. 4. The bins at the high end (bins from 150-255) are empty and hence only a part (150 out of 256) of the histogram is shown. In this experiment, only 44 d values are larger than 127. In addition, these large d values are in the range of (128, 150). That is, the percentage of the special case is merely about 0.027% and thus the possible errors are acceptable in practical.

In addition, there is another special case in our scheme, i.e., all the pixels in an original image block are of the same value. Suppose this value is denoted by ps. In this case, p_m= p_s, p_l = p_s, d = 0 and all bits in the bitmap M are 0. Obviously, Eq. 11 cannot be applied any longer for both its denominator and numerator equal 0.

Fig. 4:	Statistical histogram of values

Thus we set p_h= p_s and remain all the other operations unchanged.

Actually, our scheme is also suitable for BTC-compressed color image transmission. Specifically, the original color image is decomposed into red, green and blue channels and each channel is encoded as a gray-level image. Finally all encoded channels are recomposed into color noise-like shares.