^{1}

^{1}

^{1}

^{1}

^{1}

^{*}

Generally speaking, being an efficient information hiding scheme, what we want to achieve is high embedding capacity of the cover image and high visual quality of the stego image, high visual quality is also called embedding efficiency. This paper mainly studies on the information hiding technology based on gray-scale digital images and especially considers the improvement of embedding capacity and embedding efficiency. For the purpose of that, two algorithms for information hiding were proposed, one is called high capacity of information hiding algorithm (HCIH for short), which achieves high embedding rate, and the other is called high quality of information hiding algorithm (HQIH for short), which realizes high embedding efficiency. The simulation experiments show that our proposed algorithms achieve better performance.

The protection of digital data, especially for confidential data, becomes more and more important. As a kind of data security technique, digital steganography has been developed rapidly and attracts a great deal of attention from both the industrial and academic communities [1-15].

Digital steganography based on images is a way of hiding the existence of secret message under the cover of a carrier signal in such a way that no one apart from the sender and intended recipient even realizes there is a hidden message. An original image, used to carry secret message as a carrier signal, is called the cover image. And an image which has carried secret message is called the stego image. By virtue of generating stego images that are perceptually identical to the cover images with small embedding distortion, the secret messages are embedded into cover images.

The desires of good steganographic schemes are high embedding efficiency and security as well as large embedding payload. A steganographic scheme with low image distortion is more secure than that with high distortion because it does not raise any suspicion of adversaries. A steganographic scheme with high payload is expected because more secret messages can be transmitted. A steganographic scheme with high security can be powerful to resist the attacks by the steganalysis. However, the three factors are irreconcilable conflict. Therefore, we often make a compromise among them depending on different application requirements. A commonly used method, called the LSB (i.e. least significant bits) replacement method, is a simple hiding method by modifying the LSB of cover pixels to embed secret data [3-6]. However, it is easy to be detected. To improve the embedding efficiency, the (7,4) Hamming Code method is introduced into the steganographic schemes [1,11,13- 15]. The WPC (i.e. wet paper codes) schemes [7,13,14], not only achieving high embedding efficiency but also providing a non-shared selection channel, are also proposed. On the contrary, some other hiding methods are utilized to the steganographic schemes so as to achieve large embedding payload [2,10-12,15-18]. Specifically, the embedding payload of the scheme proposed in [

For the current information hiding schemes, the improvement of the embedding capacity and the embedding efficiency is still the goal that we pursuit and the starting point that we consider as to improve the algorithms. Considering the advantages and disadvantages of the previous methods, the paper proposed two algorithms for information hiding, one is high capacity of information hiding algorithm (HCIH algorithm), and the other is high quality of information hiding algorithm (HQIH algorithm).

On the one hand, considering the performance standard of embedding capacity, we present a high capacity of information hiding algorithm (HCIH algorithm), based on the (7,4) Hamming Code and the LSB replacement method, and inspiring from the “Hamming + 1” method. The HCIH algorithm can be used to embed an email address as the secret message into an 8-bit gray-scale image, and achieves to embed twelve secret bits of the binary string of the secret message, which is converted from an email address, into a block of cover pixels of a cover image sized each time. Then we evaluate the validity of HCIH algorithm through experimental simulation. The experimental results show that our proposed HCIH algorithm achieves high embedding capacity (i.e. 0.75 bpp) and acceptable visual quality of the stego image, and can be used for the applications about large payload secret message transmission.

On the other hand, considering the performance standard of embedding efficiency, we present a high quality of information hiding algorithm (HQIH algorithm), by introducing wet paper codes technology, for the purpose of improving the embedding efficiency. Considering that the embedding capacity may be lower because of introducing wet paper codes technology, when the embedding operation fails first time, the HQIH algorithm may try the second embedding operation to embed again by (7,4) Hamming Code oriented wet paper codes, to assure the embedding capacity. Meanwhile, the double operation also achieves higher security. Then, we evaluate the validity of HCIH algorithm through experimental simulation. The simulation experiments show that the HQIH algorithm achieves high embedding efficiency, that is the value of PSNR [19,20] is more than 52 dB, and large embedding payload, that is the value of ER is between 0.5499 bpp and 0.8291 bpp, which can be used for different applications. Specially, our HQIH algorithm gives some degree of security by considering twofold safeguards.

In short, considering the improvement of the embedding capacity and the embedding efficiency, this paper mainly studies on the information hiding technology based on gray-scale digital images and proposes two algorithms with detailed procedures and effective simulation experiments.

On this part, considering the performance standard of embedding capacity, we present a high capacity of information hiding algorithm (HCIH algorithm), based on the (7,4) Hamming Code and the LSB replacement method, and inspiring from the “Hamming + 1” method. The HCIH algorithm can be used to embed an email address as the secret message into an 8-bit gray-scale image, and achieves to embed twelve secret bits of the binary string of the secret message, which is converted from an email address, into a block of 4 × 4 cover pixels of a cover image sized 512 × 512 each time. The date embedding phase and data extracting phase are described in the following sections 2.1 and 2.2 respectively.

Step 1: Give a cover image I sized 512 × 512 pixels as the carrier and an email address as the secret message needed to be embedded.

Step 2: Convert the email address into binary string S of l bits by the ASCII code, denoted as, where. And then divide it into non-overlapping partitions of twelve secret bits, denoted as , where and Ns is the total number of the partitions.

Step 3: Segment the cover image I into 128 × 128 blocks of 4 × 4 cover pixels, denoted as

where

Step 4: Embed the first three bits of s_{i} into the first seven cover pixels of block P_{i} by the (7,4) Hamming code and the LSB replacement method. And generate the first seven stego pixels of the stego block Q^{i}.

Step 5: Embed the secret bits sh into the cover pixel, where by taking the operation in (1).

where e_{j} is the 2^{nd}-rightmost LSB of p_{j}_{ } , where and is the 1^{st}-rightmost LSB of, where. If (1) holds, embed S_{h} with unchanged; If (1) does not hold, modify the value of by taking the opposite of the 1^{st}-rightmost LSB, to make (1) hold. At last, we embed sh and obtain the stego pixel of the stego block Q^{i}.

Step 6: Repeat Step 4 to Step 5 until all the secret bits are embedded and generate the stego image.

The receiver can extract the secret message S from the received stego image. The detailed steps are as follows:

Step 1: Segment the stego image into 128 × 128 blocks of 4 × 4 stego pixels, denoted as

where

.

Step 2: Extract the first three bits of s^{i} from the first seven stego pixels of block by (7,4) Hamming code and the LSB replacement method.

Step 3: Extract s_{h} from the stego pixel by taking the operation in (2).

f_{j} is the 2^{nd}-rightmost LSB of and f_{h+}_{4} is the 1^{st}-rightmost LSB of,.

Step 4: Repeat Steps 2 and 3 until all the secret bits of the secret binary string are extracted.

Step 5: Convert the secret binary string into its original email address by the ASCII code.

On this part, considering the performance standard of

embedding efficiency, we present a high quality of information hiding algorithm (HQIH algorithm), by introducing wet paper codes technology, for the purpose of improving the embedding efficiency. Considering that the embedding capacity may be lower because of introducing wet paper codes technology, when the embedding operation fails first time, the HQIH algorithm may try the second embedding operation to embed again by (7,4) Hamming Code oriented wet paper codes, to assure the embedding capacity. Meanwhile, the double operation also achieves higher security.

The main idea of the HQIH algorithm is as follows: Firstly, give an 8-bit gray-scale image as the cover image and the binary secret message need to be embedded. Secondly, segment the given cover image into non-overlapping pixel-groups, each pixel-group contains seven pixels, among which there may be some wet pixels (i.e. unchangeable pixels). Thirdly, after weighing the methods described above, we try to embed the first seven secret bits into the first pixel-group of seven pixels. If none of the wet pixels of the first pixel-group are modified during the embedding, the embedding operation is successful and the instruction array we have set flag. If not, we try to embed the first three secret bits into the first pixel-group of seven pixels, if none of the wet pixels are altered this time, the embedding operation is successful and flag, if not, flag, that isthe operation of embedding secret bits into the first pixelgroup fails. So we try to embed the secret bits into the next pixel-group in the same way. Until all the secret bits are embedded, we can get the stego image I' and the instruction array flag at last.

The date embedding phase and the data extracting phase are described in the following sections 3.1 and 3.2 respectively.

A cover image I sized pixels is given as the carrier and the binary secret message need to be embedded.

Initialization: Set an index i = 0, to indicate the secret bit; Set an instruction array flag, to indicate the embedding.

Step 1: Segment the given cover image I sized H×W into x non-overlapping pixel-groups, denoted as Q^{k}. Each pixel-group contains seven pixels, among which there may be some wet pixels by any possibility, denoted as

is one of the subsets of .

Step 2: From i, read the first seven bits of the binary secret message S, denoted as.

Step 3: Read one pixel-group Q^{k }of seven pixels, and calculate the LSB of Q^{k}, denoted as .

Step 4: Calculate the decimal value a of bits and the decimal value b of bits. If, where ⊕ is the bitwise exclusive-or operation, and, where, we replace C^{k }with, and then go to Step 2; if, where, then go to Step 5.

Step 5: Calculate the decimal value u of the first three bits and compare the values between and C^{k} from v = 0 to 15 in group. If, where ⊕ is the bitwise exclusive-or operation, and, where, we replace C^{k} with, and, then go to Step 2; if, where, , that is, the embedding operation fails. Go to Step 3 to try the next pixel-group.

At last, we can obtain the stego image I' when all the secret bits are embedded.

The receiver can extract the secret message S from the received stego image I' with the help of the pre-shared instruction array flag between the sender and the receiver. The detailed steps are narrated as follows.

Step 1: Segment the received stego image I' sized H × W pixels into x non-overlapping pixel-groups, denoted as. Each pixel-group contains seven pixels.

Step 2: Read the next pixel-group of seven pixels:

If, no secret bits are embedded into, go to Step 2;

If, calculate the LSB of, denoted as, compute

and reconstruct S bywhere || denotes the concatenation operation, then go to Step 2;

If, calculate the LSB of, denoted as, compute

, and extract the next partition s of seven secret bits. Reconstruct S by, where || denotes the concatenation operation, then go to Step 2.

At last, we can extract all the secret bits and the block diagrams of the data extracting phase are shown in

As is well-known, high embedding efficiency and high

embedding payload are the primary goal of a good steganographic scheme. So, correspondingly, there are two important evaluation criterions to measure the performance of a steganographic scheme, one is the embedding efficiency of the stego image, and the other is the embedding payload of the cover image.

For embedding efficiency, also called embedding quality or visual quality of the stego image, in order to avoid a subjective evaluation by the human naked eyes, a wellknown measurement, namely peak-signal-to-noise-r-ate (PSNR for short), is used to evaluate the degree of similarity between a stego image and its original image. PSNR is defined as following equation in (3).

Here, MSE, being short for the mean square error, represents the difference between the stego image and its original image sized H × W pixels. The MSE is defined as in (4).

According to the visual quality evaluation, a high value of PSNR means that a stego image is very similar to its original image and the embedding efficiency of the steganographic scheme is high. In contrast, a low value of PSNR means that a stego image has visible and sensible distortion with its original image and the embedding efficiency is low. Generally speaking, if the value of PSNR is higher than 30 dB, it is hard to distinguish the distortion by human eyes.

For embedding payload, also called embedding capacity, we use ER, being short for embedding rate, to represent the percentage of the embedded secret bits in the whole pixels of the cover image. The ER is defined as in (5).

Here, N is the total number of the embedded secret bits and H × W is the size of the carrier. According to the embedding payload evaluation, a large value of ER represents that the steganographic scheme has better performance in terms of the embedding payload, that is, a cover pixel in the cover image can carry more secret bits. On the contrary, a small value of ER represents a worse performance.

In order to evaluate the performance of HCIH algorithm, nine commonly-used gray-scale images sized 512 × 512 pixels were used to simulate the experiments as shown in

By using MATLAB 7.0 software, we simulated the procedure of the HCIH algorithm.

From the

By using MATLAB 7.0 software, we simulated the procedure of the HQIH algorithm. In our simulation experiments, we chose 4 different wet rates (i.e. the values of WR is from 0.1 to 0.4) for each test image, in order to assure high accuracy of the experimental results. Meanwhile, we randomly generated 10 different wet maps for each WR, each map had different distribution of the wet pixels, and also generated 10 different binary strings of the same size as the different secret data. Based on the experimental data mentioned above, cyclic-cross tests were adopted. Ultimately, the average of all the values except for the maximum and the minimum was considered as the experimental results.