2013 2nd National Conference on Information Assurance (NCIA)
A technique for digital watermarking in combined spatial and transform domains using chaotic maps Amir Anees
Adil Masood Siddiqui
Department of Electrical Engineering Military Collage of Signals, NUST, Rawalpindi Email:
[email protected]
Department of Electrical Engineering Military Collage of Signals, NUST, Rawalpindi Email:
[email protected]
Abstract—In this paper, the problems of robustness and quantity of embedded watermark of digital watermarking linked with independent spatial and frequency domains have been analysed. In attempt to overcome these problems to some extent, we have proposed a technique for watermarking in combined spatial and frequency domains based upon chaotic maps. By applying chaos effectively in secure communication, the strength (robustness) of overall anticipated algorithm has been increased to a significant level. In addition, few security statistical analyses such as correlation, entropy, energy, contrast, homogeneity, mean square error and peak signal to noise ratio have also been carried out and it is shown through confidence measure that it can survive against unintentional attacks such as addition of noise, compression and cropping.
I.
I NTRODUCTION
Today’s society is tightly surrounded by the sphere of the information era, which is classified by scholar assets and utilizable inside data being considered exceptionally precious. Furthermore, information is electronically processed and conveyed through public networks. This rapidly increasing usage of electronic commerce leads to the essential interest in content owners who owns digital representation of data like economic, official (documents), entertainment buisness, martial, and political. One of the suitable and legit tools developed for identification of owner, creator, source, distributor or authorized consumer of critical and important data is digital watermarking. It is the science that falls under the category of secure communications. Over the last millennium, digital watermarking has been used to indicate a particular ownership of copyright of information signals and has now current applications in covert communication, broadcast monitoring, proof of ownership, source authentication, copy control and locating content online. Watermarking can be interwoven with two other types of security systems, namely cryptography and steganography. The purpose of cryptography and steganography is same, i.e. to conceal the information message but the methodologies employed in these techniques are different. The methodology of watermarking and steganography is same but the purposes of these techniques are different. Watermarking deals with copyright protection of digital data while steganography concerns about the hiding of digital data. A digital watermarking method or watermarked data, WT is acheived by embedding a watermark, W (recognizable pattern) in digital data, C (whose ownweship has to be protected) through some secret key, ϕ. Mathematically, the concept is defined as: WT = ϕ(C, W ) 978-1-4799-1288-9/13/$31.00 ©2013 IEEE
(1)
The strength of any watermarking technique depends upon strength of ϕ. At the time of proving ownership, WT has to put in to inverse Watermark-function, ϕ−1 to retrieve its watermark, W 0 . If W 0 showes high correlation with the original watermark, W , it provens the ownership of owner. W 0 = ϕ−1 (WT )
(2)
Based on the characteristics of embedded watermarks and secret keys, watermarking can be classified into different techniques. Watermarks inserted in digital carrier as intended to visible to human visual system are called Visible or Perciptible watermarks, such as a logo inserted into a corner or centre of an image/video. In comparison, watermarks that could not be seen by naked human eye are known as Invisible or Imperceptible watermarks. Watermarking schemes can be classified based upon the extraction methods at the time of proving ownership as well. If it does not require original image, C with the watermark image, WT to extract watermark, W , then it is said to be Public or Blind watermarking technique, as one described in Eqs. (1)-(2) and if does require original image as well, then it is called Private or Nonblind, i.e. W 0 = ϕ−1 (WT , C)
(3)
The performance parameter, Robustness is one of the best tool to categorise watermarking scehmes. If a scheme can resist against intentional (alternation or removel of watermark) or unintentional (image processing operations) attacks, then it is termed as Robust watermarking scheme or otherwise Semifragile which resist against gentle and less modification or Fragile which simply fails to resist against these attacks. Watermarking techniques can also be identified based upon image domains, the watermark can be embedded and retrieve in spatial (time) domain or transform (frequency) domain. In literature, there are watermarking protocols proposed based upon different techniques and structures in combined spatial and frequency domains (A comprehensive survey on watermarking schemes can be seen in [1-3]) and still a lot of effort is being done to strengthen this area. As both the techniques have their own advantages and drawbacks, applying the combinational of these two techniques can result in various interesting properties and can coupe with the limitations faced independently. Watermark can be broken into two parts to be embedded in both domains, and further at random positions defined by some pseudo random number generator to specifically prevent it from cropping attack but none of 119
Fig. 1: Proposed chaotic watermarking algorithm.
the previous techniques (to the best of author knowledge) employed chaos as a source of creating randomness. With the evolution of chaotic theory in recent decades, chaos has been applied extensively in secure communications. Chaotic dynamics are the impromptu behavior exhibited by some nonlinear dynamical system and can be used as a source of diffusion in security techniques [4]. It has been shown that chaotic security algorithms have commended several advantages such as high security, speed, reasonable computational overheads and computational power over the traditional algorithms. However, at the same time, this exponential growth in chaotic security algorithms leads to the rapid publication of those papers which are not secure enough and shows several flaws especially the early proposed analog chaotic security approaches. Recently published, number of papers represent statistical analysis of chaotic security systems showing the flaws in the strength of secure algorithms and can be easily broken in short computer times. Also, the performance analysis and security issues did not take due attention in proposing these techniques, which payoff as to be weak against differential attacks, while the safer ones can not be effectively implemented on the given hardware. In this paper, we have employed chaos to propose a watermarking technique for digital images in which watermark is embedded in both spatial and frequency domain. Watermark is broken into two parts, first part is embedded in spatial domain using chaotic map and second part is embedded in frequency domain using another chaotic map. The general layout of proposed algorithm is shown in Figure 1. The simulated results are calculated for original and watermark image, statistical analysis have been done and shown good results. The robustness of anticipated algorithm is checked by applying different image processing operations and then try to extract watermark which also exhibits good results. II.
P ROBLEM S TATEMENT AND P ROPOSED A LGORITHM
Data hiding in spatial domain by changing Least Significant Bits (LSBs) or some gray levels of digital image is a simple and straightforward technique that has also the advantage of embedding more information. According to a survey, digital image has the capability of hiding as much data as its 6.25% in spatial domain. But the problem with spatial techniques is the low robustness against statistical analysis and differential attacks. It cannot resist against image processing techniques because the watermark embedded is not distributed around the entire image and these operations can easily alter or destroy the watermark. In contrast, embedding the watermark into coefficients of transform image is more robust and can survive against differential attacks.
However, the problem with transform techniques is the quantity of embedded watermark, if we try to insert too much data in transform domain of digital image, the quality of image will be heavily degraded. So the overall problem is to embedd watermark in large quantity and at the same time, the watermark image must be able to confront intentional and unintentional attacks. One of possible solution to the existing problem is to embedd watermarks in combined spatial and transform domains as some of the techniques alreday proposed in literature [5]. The results of security statistical analysis of these techniques are based upon the random functions used to distribute watermark in the digital image and thus need to be futher improved. In our paper, we used two chaotic maps namely Logistic and Nonlinear Chaotic Algorithm (NCA) to distribute the watermark data in digital image, one chaotic map for distribution of watermark in spatial domain and the second one for transform domain. To justify the reason of using chaotic maps, it is important to discuss their influence in secure communication. Over the last two decades, it has been observed by many researchers that there exists the close relationship between chaos and secure communication; many properties of chaotic systems have their correspondings in traditional cryptosystems. Chaotic systems have several compelling features favorable to secure communications, such as sensitivity to initial condition, ergodicity, control parameters and random like behaviour, which can be correlated with some conventional cryptographic properties of good ciphers, such as confusion and diffusion proposed by shanon [6]. Let take the example of Logistic Chaotic Map: The logistic map is a model of population growth first proposed in [7]. It is derived from the continuous form of differential equation defined as: dx = rx(1 − x) (4) dt The discrete version in the form of difference equation is described as: xn+1 = r.xn .(1 − xn ) (5) where the initial parameters are: r ∈ (0, 4) x0 ∈ (0, 1) The parameter r is the rate of population growth, or in physical term, defines the rate of heating in a convection equation or may be velocity of fluid in a mechanical rotating circle of convection. The characteristic of logistic equation is 120
or xn (0, 1] α (1.5, 1.57] β [3, 15]
Fig. 2: Bifurcation diagram of logistic map, that is, graph plotted for logistic sequence against each value of parameter r for r = 1 to 4 with spacing of 0.0005 with initial condition of x0 = 0.5 and r = 3.7
heavily dependent upon parameter r. Robert May [8] deeply analyzed the conduct of logistic equation based upon r. After plotting the performance of logistic iterative parameter xn as a function of r, it was noticed that when r is low, the map settles on a steady state after some iterations. When r is high, the stable state break into bifurcation-into two state periodic form, this bifurcation is further divided into four state periodic form and then into eight. On added value of r, the map sequence enter into an chaotic behavior region. Figure 2 shows the graph of logistic sequence, xn verses r. It assembles all the information of xn against r for r = 1 to 4 in one figure. The values of parameter r are presented on horizontal axis from left to right and values of logistic sequence against each value of r with spacing of 0.0005 are plotted on vertical axes. The sequences are plotted after 40 iterations to see the long term behavior for each value of r. Nonlinear Chaotic Algorithm (NCA) map was proposed especially for image encryption [9] and stated as:
xn+1 = (1−β
−4
) cot
α 1+β
α 1+β
β
tan(αxn )(1−xn )β (6)
The detailed flowchart of proposed algorithm is depicted in Figure 3. The host image, H in spatial domain taken, of size 512 × 512 is rehape into one vector. Watermark, W (a digital image as well) in parallel of size 100×100 (5% of host image) is first reshape into one vector, then break into two parts, W1 contains 70% of W has to embedd in spatial domain and W2 contains 30% of W has to embedd in frequency domain. The reason of giving less percentage to W2 is the low tolerance of embedding watermark of frequency components. At first stage of watermark embedding, W1 is embedded at random positions of H defined by logistic chaotic map. The resulted image is reshape into original size and stated as first version of watermark image, WT 1 in spatial domain. WT 1 is then transformed into frequency domain using discrete cosine transform (DCT), reshape into one vector and let it be called WT 1f . At second stage of watermark embedding, first largest values of WT 1f equal to 30% of W are seperated then W2 is embedded at random positions of these values defined by NCA map. The resulted image is reshape into original size and stated as second version of watermark image, WT 2 in frequency domain. Finally, the completed watermark image, WT is acheived by applying inverse dct on WT 2 . III.
S IMULATED R ESULTS AND S TATISTICAL A NALYSIS
The proposed algorithm is applied on 512 × 512 images of lena, baboon and pepper with 100 × 100 watermark image. The original image of baboon is depicted in Figure 4 (a), first version of watermarked image (spatial domain) in Figure 4 (b), complete version of watermarked image (spatial plus frequency domain) in Figure 4 (c), watermark image before and after extraction in Figure 4 (d) and Figure 4 (e) respectively. Some of the statistical security analyses such as correlation, entropy, energy, contrast, homogeneity, mean square error and peak signal to noise ratio have been done on the proposed algorithm for original and watermarked images to show the strength of it. The results for first five analyses for lena, baboon and pepper images are listed in Table I. The values for MSE and PSNR as comparison of original and watermarked images are listed in Table II.
where the seed parameters can be A. Correlation xn (0, 1] α (0, 1.4] β [5, 43] or
The most fundamental method used in determining the similarity between two images is the correlation analysis. The correlation of an image is given as: X (i − µi)(j − µj)p(i, j) Corr = (7) σi σj where
xn (0, 1] α (1.4, 1.5] β [9, 38]
i, j corresponds to image pixels positions p(i, j) is pixel value at ith row and jth column of digital image µ is the variance σ is the standard deviation 121
TABLE I: Statistical Security Analysis of Original and Watermarked images of lena, baboon and pepper. Statistical Analysis Correlation Entropy Homogenity Contrast Energy
Baboon Original 0.8398 7.1872 0.8423 0.3540 0.1387
Baboon Watermark 0.8380 7.1012 0.8427 0.3531 0.1395
(a)
Lena Original 0.8991 7.4677 0.8727 0.3778 0.1311
Lena Watermark 0.8933 7.2512 0.8687 0.3857 0.1288
(b)
Pepper Original 0.9295 7.6003 0.8917 0.3181 0.1233
Pepper Watermark 0.9307 7.4115 0.8916 0.3188 0.1220
(c)
(d)
(e)
Fig. 4: Simulated results of proposed algorithm, (a) original baboon image, (b) watermarked image in only spatial domain, (c) fully watermarked image in both spatial and freqency domains, (d) watermark image before extraction, (e) watermark image after extraction.
B. Entropy Entropy is a magnitude of the uncertainty of a random variable to come in a random process and can be use to show the randomness of the digital image as well. Entropy is defined as: X H=− p(xi ) log2 p(xi ) (8) where p(xi ) is the probability of random variable x at ith index. C. Contrast The contrast analysis of the image enables the viewer to vividly identify the objects in texture of an image. The contrast values for chaotic algorithm give bigger and thus
better values. The contrast of an image is given as: X C= |i − j|2 p(i, j)
(9)
D. Homogeneity The homogeneity analysis processes the closeness of the distribution in the gray level cooccurrence matrix (GLCM) to GLCM diagonal. The GLCM shows the measurements of combinations of pixel brightness values or gray levels in tabular form. The frequency of the patterns of gray levels can be inferred from the GLCM table. The homogeneity can be determined as: X p(i, j) (10) Hom = 1 + |i − j| 122
G. Peak Signal to Noise Ratio Pick Signal to Noise Ratio (PSNR) has the same function as MSE, but it takes the signal strength and divided it by noise strength or the difference between the images (MSE), thus gives the better compartive statisitical analysis. It is given as: P SN R = 10 log10 IV.
M AXi2 M SE
(13)
ROBUSTNESS T EST BASED ON I MAGE P ROCESSING O PERATIONS
If the watermarked image goes through different image processing operations and at the time of extracting watermark, if the extracted watermark shows high correlation with original watermark, it proves the robustness of watermarking algorithm. To check the similarity between the extracted and original watermark, Cox et. al. [10] provide the quantity of confidence measure which returns numerical value of similarity between the watermarks, the higher the value, the more correlation will be between them. The quantity is given as: P ti .si Sim = p P 2 P 2 ( ti . si )
(14)
where ti corresponds to ith element of extracted watermark si corresponds to ith element of original watermark
Fig. 3: Flowchart of proposed watermarking algorithm.
TABLE II: Statistical Security Analysis of MSE and PSNR. Image
MSE
PSNR
Baboon Lena Pepper
4.8888 10.5424 15.7225
91.4501 86.2247 81.9784
In our simulated results, if the extracted watermark matches exactly with the original watermark, it gives the numerical value of 98.21 for confidence measure showing the perfect correlation between them. Now we have to apply image processing operations on watermarked image then try to extract watermark and see how much similarity we can acheive. Few of the important image processing operations are: A. Noise Attack The watermark image can go through noise attack by adding different types of noises such as gaussian, poisson, salt & pepper, and speckle. In our testing bench, we add salt & pepper noise.
E. Energy The energy of the image gives the sum of squared values of gray pixels of a digital image defined as: X E= p(i, j)2 (11)
F. Mean Squared Error Mean Squared Error (MSE) is used to measure the difference between two digital images. It can be defined as: 1X M SE = (Xi − Xi∗ )2 (12) n
B. Compression Attack One of the well known compression attack can be launched by JPEG (Joint Photographic Experts Group) coding distortion. C. Cropping Attack If some part of extracted image is damaged or taken away, it is said to be effected by cropping attack. The effects of these attacks can be visualize in Figure 5 and results are listed in Table III. 123
(a)
(b)
(c)
Fig. 5: Effects of image processing operations on watermarked image, (a) Noise attack, (b) Compression attack and (c) Cropping attack.
TABLE III: Numerical values of confidence measure for baboon, lena and pepper images for different image processing attacks. Attacks
Baboon
Lena
Pepper
Noise Comression Cropping
74.3254 69.2563 42.1586
76.1254 71.2984 44.5198
75.9815 71.5698 41.3695
V.
[6] [7]
[8] [9] [10]
C ONCLUSION
Digital watermarking is one of the best technologies developed for copyright of digital contents, although with some loopholes. The basic drawbacks associated with the traditional watermarking techniques are discussed. To embedd more watermark in quantity and to be robust against several attacks, this paper present a technique which is based upon spatial and frequency domains and employ chaos to embedd the watermark. With the employment of chaos in our technique, the resuts shown are good as can be visualized through security statistical analysis, also the robustness of our technique has checked through confidence measure. The similarity between original watermark and extracted watermark after passing through image processing operations has the percentage values between 42-77%, so base on these results we can say that our proposed technique lies between semifragile and fragile watermarking schemes. R EFERENCES [1] [2]
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