In recent years, signal processing in the encrypted domain has attracted considerable research interest, especially embedding watermarking in encrypted image. In this work, a novel joint of image encryption and watermarking based on reversible integer wavelet transform is proposed. Firstly, the plain-image is encrypted by chaotic maps and reversible integer wavelet transform. Then the lossless watermarking is embedded in the encrypted image by reversible integer wavelet transform and histogram modification. Finally an encrypted image containing watermarking is obtained by the inverse integer wavelet transform. What is more, the original image and watermarking can be completely recovered by inverse process. Numerical experimental results and comparing with previous works show that the proposed scheme possesses higher security and embedding capacity than previous works. It is suitable for protecting the image information.
Along with significant improvements in information technology, information security is attracting a great deal of attention, especially image security. It can be mainly divided into two parts: one is image encryption [
In image encryption, chaotic maps are usually used to encrypt image, because they have the features of ergodicity, sensitivity to initial conditions and control parameters, and so forth. In [
As a natural idea, the technology which embeds watermarking in encrypted image is proposed. In [
However, these works have two main loopholes: without considering the permutation in encrypted stage and low embedding capacity in hiding data stage. Shannon suggested permutation and diffusion operations should be used in any cryptosystems [
In this paper, I propose a novel joint of image encryption and watermarking based on a reversible integer wavelet transform. In order to encrypt the image, a part of coefficient is diffused by the obits of chaotic maps. Then the inverse integer wavelet transform is used to obtain the encrypted image based on the diffused coefficient. In the stage of image watermarking, the encrypted image is processed by integer wavelet transform. Watermarking is embedded in another part of coefficient of integer wavelet transform by histogram modification. Finally an encrypted image containing watermarking is obtained by the inverse integer wavelet transform. Numerical experimental results and comparing with previous works show that the proposed scheme possesses higher security and embedding capacity than previous works. It is suitable for protecting the image information. In the part of the Discussions, another version of joint of image encryption and watermarking is presented. It can overcome the first loophole and improve visualized security of encrypted image.
The paper is organized as follows. In the next section, the related works are described in detail. In Section
In [
Flowchart of permutation-diffusion type of chaos-based image cryptosystems.
In this paper, logistic chaotic map is used to encrypt image. It can be denoted as follows:
In [
Recently, reversible integer wavelet transforms are widely used in image compression and image watermarking. A reversible integer wavelet transform is used in this paper. It can be denoted as follows:
The reversible integer transforms (
For the gray image, to prevent the overflow and underflow problems, it must restrict
In this paper, the technology of histogram modification, which is proposed in Ni [
Firstly, the watermarked image is scanned in the same sequential order as that used in the embedding procedure. If a pixel with its grayscale value, which is equivalent to pp + 1, is encountered, a bit “1” is extracted. If a pixel with its value, which is equivalent to pp, is encountered, a bit “0” is extracted. Then scanning the image again, for any pixel whose grayscale value is equivalent to the range of the histogram (zp, pp] the pixel value is subtracted by 1. If there is overhead bookkeeping information found in the extracted data, the original image can be recovered without any distortion.
According to the characteristic of logistic map, logistic map is chosen as the chaotic map. The different parameters and initial values for (
It is randomly generating the initial key and obtaining cipher key by relating to the plain-image.
It is evenly dividing cipher key into four parts as the parameters and initial values of logistic maps, iterating logistic maps for
It is processing the image by integer wavelet transform, namely, (
It is obtaining new coefficient
It is diffusing the coefficient
It is recovering image by inverse integer wavelet transform with the diffused coefficient
Output the encrypted image.
Where
Note that implementing Step 5 is convenient to deal with the overflow and underflow problems while calculating (
The detailed encryption is illustrated in Figure
The flowchart of encryption.
In order to encrypt image, the coefficient
It is processing the encrypted image by integer wavelet transform, namely, (
It is calculating the histogram of
It is embedding watermarking in
It is recovering encrypted image by inverse integer wavelet transform with the changed coefficient
It is obtaining the encrypted image which contains watermarking.
Note that, in order to prevent the overflow and underflow problems in embedding watermarking, index code is used in the stage. When the histogram is shifted, if the new values of
The extracting process is similar to that of embedding procedure in the reversed order. It can be briefly stated as follows.
It is implementing integer wavelet transform for the encrypted image which contains watermarking and obtaining the coefficient
It is calculating the histogram of
It is, according to the index code, zero point, and peak point, extracting the watermarking from peak point such as Ni’s method [
It is recovering the coefficient
It is obtaining the encrypted image without watermarking.
In Step 3, the whole image is scanned in a sequential order, say, column-by-column, from left to right. The whole pixels which are between zero and peak point are incremented by “1.” The values, which meet (
The decryption process is similar to that of encryption procedure in the reversed order. It can be briefly stated as follows.
It is iterating the logistic maps for
It is concurrently generating the chaotic orbits as encryption process.
It is obtaining
It is implementing integer wavelet transform and obtaining the coefficient
It is recovering
It is implementing inverse wavelet transform by the coefficient
It is outputting the plain-image.
In this chapter, performance analyses and simulation of proposed algorithm are described in detail. Firstly, the experimental results of image encryption are presented, such as the space of key and key sensitivity. Then the effect of image watermarking is provided, such as embedding capacity and peak signal-to-noise ratio (PSNR for short).
In a good image cryptosystem, the space of key should be large enough to make brute-force attack infeasible [
In this part, the key sensitivity will be performed as follows.
It is calculating the Imkey of the standard test
It is encrypting the test image by Ikey 987654321012345.
It is slightly changing the generated Ikey 987654321012346, and encrypt the same plain-image.
It is comparing the cipher-image which is encrypted by different key.
The results are as follows: the image encrypted by the key 987654321012345 has 99.32% of difference from the image encrypted by the key 987654321012346 in terms of pixel values, although there is only one-bit difference in the two keys. Figure
(a) Plain-image of Lena. (b) Encrypted image by key: 987654321012345. (c) Encrypted image by key: 987654321012346. (d) Difference image.
In image encryption, mutual information is usually used to make the quantitative analysis and evaluate the key sensitivity of two ciphered images [
In this proposed architecture, the standard Lena test image of size 512 × 512 is selected to test the property of resisting statistical analysis. The histograms of encrypted image are shown in Figure
(a) Plain-image of Lena. (b) Histogram of the plain-image. (c) Cipher-image. (d) Histogram of the cipher-image.
Figure
(a) The correlation of vertical adjacent two pixels for original image. (b) The correlation of vertical adjacent two pixels for cipher-image.
To test the property of resisting differential attack of the proposed architecture, two common quantitative criteria are employed: number of pixels’ change rate (NPCR) and unified average changing intensity (UACI). The NPCR and UACI are defined as follows [
In Table
Comparing results.
NPCR | UACI | |
---|---|---|
Proposed scheme | 99.96% | 29.74% |
Wang’s work | 44.27% | 14.874% |
Gupta’s work | 99.62% | 17.30% |
Teng’s work | 93.68% | 33.34% |
In the proposed scheme of image encryption, this scheme uses different parameters and values of chaotic maps which are used in the diffusion stage. At the same time, it makes the cipher key related to the plain-image. So the different control conditions, key streams, and nonidentical cipher-images will be generated by distinct plain-images. The attacker cannot obtain useful information by encrypting some special images since the resultant information is only related to those chosen-images. Therefore, the proposed algorithm can well resist the known-plaintext and the chosen-plaintext attacks.
The standard test 512 × 512 image Lena is firstly encrypted by above scheme. Then the encrypted image is employed to embed watermarking. The effects of embedding watermarking, extracting watermarking, and difference are shown in Figure
(a) Encrypted image of Lena. (b) Encrypted image with watermarking. (c) Encrypted image after extracting watermarking. (d) Difference image of (a) and (c).
Because Ni’s method is a reversible data hiding, the encrypted image and watermarking can be recovered in one piece. Watermarked image quality is evaluated by peak signal-to-noise ratio (PSNR), which is defined as
Figure
(a) Original image; (b) encrypted image; (c) after shifting operation; (d) after embedding watermarking.
In the third chapter, I briefly introduce index code in image watermarking. Index code will be described by example in this part. For Figure
The above method only uses diffusion operation in the stage of image encryption. As I describe in Section
Figure
(a) Encrypted image. (b) Histogram of the encrypted image. (c) Values of coefficient
To overcome the flaws of previous works, I propose a novel joint of image encryption and watermarking based on a reversible integer wavelet transform in this paper. In pursuit of high embedding capacity at the expense of security, diffusion operation is only used to encrypt image in the stage of image encryption, namely, diffusing the coefficient
The author declares that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (nos. 61370005, 61402066, and 61402067), and the project is sponsored by “Liaoning BaiQianWan Talents Program” (no. 2013921007) and the Basic Research Program of the Key Lab in Liaoning Province Educational Department (nos. LZ2014049 and LZ2015004); the project is supported by the Natural Science Foundation of Liaoning Province (no. 2014020132), Scientific Research Fund of Liaoning Provincial Education Department (no. L2014499), and the Program for Liaoning Key Lab of Intelligent Information Processing and Network Technology in University.