Encryption and Hiding Watermarking Using A Chaotic Modified Wavelet Transform

Received on: 02/01/2011 Accepted on: 16/05/2011 ABSTRACT In this letter, a new digital watermarking algorithm is proposed to hide binary image watermark inside gray image to increase authentication and robustness, DWT are used in embedding because it has many features in image processing. To increase the effective of this algorithm chaotic logistic map are used to select the embedding position in host chaotically which increase the security and make it hard to be detected, experimental result which be measured by using (Mean Square error, Peak signal to noise ratio , Signal to Noise Ratio, CORLLATION) has value (0.3195, 53.0867, 45.9152, 0.9998) respectively reflect the effective of this algorithm, the watermarked image has no noticeable change, some image processing operation such as(filter ,noise and compression) are used to test the robustness which measured by calculate similarity between extracted watermark after attack and the original one, Programming based on Matlab9.


1-Introduction
Digital watermarking is defined as the process of hiding apiece of digital data in the cover data which is to be protected and extracted later for ownership verification. Some of the important applications of watermarking technique are copyright protection, ownership verification, finger printing, and broadcast monitoring [1]. Watermarking can be embedded in the spatial domain or a transform domain. In spatial domain, the

College of Computer Sciences and Mathematics
University of Mosul, Iraq watermark is embedded directly by modifying the intensity value of pixels, In frequency domain, the watermark is embedded by changing the frequency coefficients. To transform image into frequency domain, the transformation technique such as discrete wavelet transformation (DWT), discrete cosine transformation (DCT) and discrete Fourier transformation are used. Spatial domain watermarking technique is easier and its computing speed is high, than transform domain. But the disadvantage is that it is not robust against common image processing operations. Transform domain technique are introduced to increase the robustness of the digital media [2].There are three kinds of digital watermarking technique according to their embedding purpose: robust, fragile, and semi-fragile. A robust watermark withstands malicious attacks, such as scaling, rotating, filtering, and compression. This kind of watermarking is usually used for copyright protection. Fragile watermarks can detect any unauthorized modification in an image, and therefore, they are quite suitable for an authentication purpose. However a semi-fragile watermark is adopted to detect the unauthorized modification, and at the same time, it must survive some authorized image processing operations [3]. In addition, non Blind, semi-Blind, and Blind methods are the division of watermarking. In non-Blind methods the original image itself are employed for the extraction of watermark, While the certain characteristics of the original image are engaged by the semi-Blind methods, whereas the detection process in the Blind methods do not necessitate the original image. A good watermarking scheme should be robust enough to define against attacks while being invisible such that the dissimilarity between the watermarked image and the host image should not be distinguishable by the human eyes [4] In this paper a simple and efficient security system is introduced to protect the ownership of digital image using non-blind imperceptibly encrypted binary image watermarking based on DWT using chaotic function to generate random sequence used to select DWT coefficient that will be used in embedding. Chaotic Logistic map function was used twice, first time for watermarking encryption and second for watermarking hiding in host image.
The rest of this paper is organized as follows: section 2 introduces the related works. Section 3 defines different notations used in this paper. Section 4 illustrated the steps of using chaotic in watermarking encryption. Section 5 defines how to use chaotic in embedding. Section 6 and 7 introduce watermarking embedding and extraction respectively. Experimental results and attack analysis are discussed in section 8 and 9 respectively. Finally concluding remarks are made in section 10.

In 2006, S. Mabtoul, E. Ibn-Elhaj and D. Aboutajdin present a Blind
watermarking procedure for digital image in complex wavelet domain. The procedure has many steps: first a watermark image as copyright sign is preprocessed with a random location matrix then split the host image into many non-overlapping small blocks with 8*8 pixels and by using chaotic logistic map function generate a random sequence which is used to select the blocks to construct sub image, perform a Dual tree Complex Wavelet Transform on sub image then hide the watermark into coefficients by compare each pixel of low pass subband with its eight neighbors [5]. 2. In 2007, Xianyong Wu and Zhi-Hong Guan, proposed anew watermarking algorithm by using two type of chaotic maps function first Arnold cat map was used to select the embedding position in host image, second using logistic map to determine the pixel bit of host image for watermark embedding, they use spatial domain for embedding [6]. 3. in 2009,Guang yang and yang zhon present research to compress watermark using Huffman coding and embedding it using LSB and chaotic logistic function [7]. 4. In 2009, Chen yongqiang and others present an algorithm to encrypted binary image watermarking using chaotic stream encryption and embedding it by selecting and modifying DWT coefficient using genetic algorithm and used neural network in watermarking identification [8].

3-Notation and Background
a. Chaotic: the word "chaos' has appeared since 800 BC and was derived from the Greek os  , which mean complete absence of order. In the past decades, many research started to adopt chaos theory into cryptosystem the reason of applying chaotic algorithm on data encryption because of two intrinsic characteristics of chaotic algorithm [9] -Highly complex and nonlinear behaviors.
-Sensitive dependence on initial condition.   telecommunication, imagery and video coding. They are the foundation for new techniques of signal analysis and synthesis and find beautiful application to general problems such as compression and denoising [11]. The Discrete wavelet transform (DWT) is a powerful and a popular transform familiar to image processing community. In two dimensional applications, The DWT decomposes a given image into four subbands (i.e. LL1, HL1, LH1, and HH1). The subbands (LL1) represent the low frequency part where most energy is concentrated, while the other subbands represent the high frequency content in the horizontal, vertical, and diagonal directions. To obtain the next wavelet level, the subband (LL1) is further decomposed into another four subbands. This process can be repeated several times until the required decomposition level is reached. Figure 2 shows an example of three level wavelet decomposition subbands [12] [13]

Watermarking encryption
Watermarking encryption algorithm is proposed as following steps: Step1: Read a binary watermarking image W of size M*M.
Step2: Locate 0 X and r value which is key for encryption, Step3: Use Equation1 to generate real value sequence(S) of size 2 M . Step4: Transfer sequence S generated by step 3 to binary sequence by using the following equation: Where k=0, 1, 2, …. 2 M Step5: Encrypt watermarking using following equation In decryption algorithm, The same pervious steps with the same initial value of 0 X and r must be used.

Chaotic algorithm
The chaotic algorithm in embedding is proposed by [7] as follows: Step1: Choose the original number 0 X , which is the seed of the Logistic mapping, and it is another key of the embedding algorithm.
Step2: Using the Logistic Mapping n-1 times to create a sequence } ,...... , { . Sequence T, which produced from this algorithm contain value from 1 to n sorted at random and not serial.

Watermarking Embedding
An embedding algorithm in DWT domain can be presented in following: Step1: Read host gray image (Y) with size N*N.
Step2: Read a watermarking binary image (W) of size M*M.
Step3 Encrypt watermarking image using chaotic encryption algorithm to produce (W  ). Step4: Change an encrypted watermarking into sequence (W   ), where Step5: Perform one level DWT (db1) on host image(Y) to get approximation(LL subband) and details coefficients(HL,LH,HH subbands). Step6: Generate a chaotic sequence (T) of size 2 N by perform chaotic algorithm. Step7: Change each DWT approximation coefficient selected by Step8: Perform IDWT and save the watermarked image.

Watermarking Extraction:
Step1: Read watermarked image I  and host image I. Step2: Perform DWT on I  and I. Step3: Choose the same value for 0 X that was used in embedding and run chaotic algorithm to produce a sequence T.
Step4: Select each i T position in approximation coefficient of I  and I. Step5: extract the encrypted watermarking as following condition: Step5: Using decryption algorithm to decrypt the extracted encrypted watermarking.

Embedding Implementation and Security Analysis
In order to evaluate validity of the proposed schema, five grayscale images samples used as host images shown in figure3. A binary image of size 64*64 used as a watermarking is shown in figure4a.  In embedding selection r=4(which means maximum chaotic) and 0 X is chosen as0.683 which is the two key for embedding. Then By implementing the best value for  which is equal to 0.01, Figure5 shows embedding process and Figure6 shows the histogram of Lena before and after embedding,   The following table illustrates the value of the four measures for five samples. And figure 7 illustrated that any change in initial condition of logistic map has a slight affected on watermarked image quality. After each attack and after extract watermark the similarity is checked between original and extract watermark by the following equation  Where W and W  are original and extracted watermarks respectively the maximum value of sim is 1 correspond to perfect match. Table2 illustrates the watermarked image after various attacks and the extracted watermark.
The comparison are made between this watermarking approaches with chaotic LSB watermarking after exposure to attacks, the results are gathered in figure8 (a, b and c) which illustrated the robustness of chaotic DWT over chaotic LSB against noises and JPEG2000 compression attacks.

Conclusion:
In the proposed algorithm the following conclusion are made: 1. This algorithm is simple, fast but efficient and has high imperceptivity. 2. chaotic logistic map has been used in encrypting and embedding with DWT which increase the security and imperceptivity because the sensitivity of logistic map to initial condition lead to generate different sequence with different initial value, therefore watermark signal spread in all regions of the host chaotically, which make embedding hard to be detected with out known initial condition. 3. after application changing in initial condition of chaotic logistic map in embedding the sequence sort will be effected but it has slight effect on watermarking quality and robustness 4. as seen in experimental results using DWT in embedding will not damage cover which reflect by value of correlation that near to 1, it mean the high identical between the covers before and after embedding. 5. Using chaotic DWT better than using chaotic LSB because it has more robustness against attacks.