Watermark with DSA signature using predictive coding
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Abstract
This paper presents a predictorbased watermark scheme that embeds secret bit streams and a DSA signature into an image. For the copyrighting of digital media, a DSA signature is appropriate as a watermarking technique. To improve security, we apply an Arnold transform (AT) to secret messages. We propose new predictors, LeftTop, which the predict current pixel values using neighboring pixel values. Our proposed scheme conceals secret messages by using the difference between current pixel values and predictive pixel values. Experimental results show that our method has low complexity and achieves a higher embedding performance with good perceptual quality compared to the earlier arts. Experimental results verified our proposed watermark method in multimedia communications.
Keywords
Watermarking DSA signature Predictors1 Introduction
A digital watermark is added to a digital file to impart additional information or features. Sometimes the mark is obvious and sometimes it is imperceptible. Imperceptible watermarks are unnoticeable to human eyes. Recently, these have most commonly been used in forensic or tracking applications. Because the watermark is added to the underlying content file, it can impart unique information. For example, watermarks are added to copies of motion pictures and television programs. The ability to track illegal copies to their source is a powerful piracy deterrent. An important advantage of a watermark is its ability to survive digitaltoanalog conversion. Thus anyone recording a TV broadcast also records its watermark. If the recording is later posted on the Internet the forensic watermark gets posted as well.
This kind of data hiding is suitable for some specific applications where images are sensitive to further processing, such as medical images, satellite images, and artwork. Data hiding [10, 27] has applications in secure communications [5, 11, 14, 15, 17, 18, 20, 21, 23] where an insecure but readily available medium such as the Internet is used to transmit hidden data. It can also be used for transmitting different kinds of information securely over an existing channel dedicated to transmitting something else, such as transmitting hidden speech over a channel meant for transmitting H.263 video.
Fragile watermarking [26] is used for the authentication of the cover image. A fragile watermark is destroyed, even in the case of minimal modification of the cover image. The digital image is popularly used as a host image to convey side information in the image. In a watermark system, the image used to embed secret data is referred to as the host image (i.e., cover image). The image with the embedded secret data is called a stego image. The stegoimage should be perceptually identical to the host image in order to not come under attack from a hacker. Stego images can be used as a copyright and safety channel for data communication. On the Internet, a receiver can extract the secret data from a stego image.
To hide secret data, it is possible to use the spatial domain [10, 12, 27] or frequency domain [3, 9] of an image. The first scheme conceals secret data by flipping the rightmost, four least significant bits (LSB) per pixel.
The second scheme is based on the frequency domain and uses a transformation function such as the discrete cosine transforms (DCT) [9] and the discrete wavelet transforms (DWT) [3]. These schemes are very resistant to attacks; however, their hiding capacities are limited.
Galand and Kabatiansky [8] proposed a new data hiding scheme called matrix encoding. The F5 algorithm [24] implemented by Westfeld was based on matrix. One can find the definition of the cover coding [1, 2, 8] in [7]. Westfeld showed matrix encoding using Hamming codes. The performance of “+ / − steganography” was introduced by [25]. Zhang and Wang [29] showed ternary Hamming codes using the concept of efficiency by exploiting the modification direction (EMD). Chang et al. [4] proposed (7, 4) Hamming code for data hiding, which improves on the “Hamming+1” scheme [30]. Yu et al. [28] proposed a data hiding scheme via predictive coding and showed good image quality using MED and GAP predictors, Yu et al. [28] which hide secret data in an image. This scheme shows the high quality and high capacity of stego images.
BCH codes were applied to achieve a tradeoff between the embedding complexity and efficiency [16]. The CPT method [22] shows embedding efficiency by hiding messages based on the weighted value of a block.
In this paper, we propose a novel steganographic watermarking scheme, which is used to conceal a bit in each pixel to predict the original pixel’s value using a LeftTop Predictor. This will help securely transmit secret data to the receiver. Based on this, we propose an imagehiding scheme based on predictive coding, which exploits the prediction error values to hide secret data.
The advantage of our technique is that we can conceal more bits in an image than previous schemes. Hence, our technique is robust to attacks such as noise and cropping.

Identication of the copyright of an image through watermarking as an important and technically challenging problem for multimedia.

Experiment of the robustness and effectiveness of the proposed technique to demonstrate the feasibility of watermarking images.
The remainder of this paper is organized as follows. In Section 2, descriptions of some schemes related to this paper are provided. In Section 3, we present our proposed scheme. The experimental results are given in Section 4. Finally, the conclusions are given in Section 5.
2 Related works
2.1 Arnold transform (AT)
In 1960, Vladimir Arnold proposed Arnolds cat map (ACM) or the Arnold Transform (AT) [19], which is a chaotic map that randomizes a digital image when applied to it, rendering the image imperceptible or noisy. However, it has a period p and if iterated p number of times, the original image reappears.
Definition 1
2.2 Prediction of JPEGLS
The predictor in (2) switches between three simple predictors: it tends to pick b in cases where a vertical edge exists to the left of the current location, a in cases of an horizontal edge above the current location, or a + b − c if no edge is detected. The guessed value is seen as the median of three fixed predictors, a, b, and a + b − c. By combining both interpretations, this predictor was renamed during the standardization process as “median edge detecto” (MED).
2.3 DSA Digital Signature Algorithm
The Digital Signature Algorithm (DSA) [13] is a United States Federal Government standard or FIPS for digital signatures. It was proposed by the National Institute of Standards and Technology (NIST) in August 1991 for use in their Digital Signature Standard (DSS).
Definition 2
Lemma 1
Let (r , s ) be a given signature of message m to be verified. Then the value v computed during the signature verification is equal to r , if (r , s ) was generated using the DSA signing operation described in Definition 1.
Proof
3 Proposed scheme
In this section, we shall present the proposed image hiding based on the predictive coding technique.
3.1 LeftTop pixel predictor
3.2 Embedding procedure
 Input:

Cover image I with size H ×W and binary secret message m.
 Output:

A watermarked image I′ with size H×W.

Step 1: Scramble a copyright image (watermark) m using (1). After scrambling, we get m′, which is the scrambled secret message.

Step 2: The scrambled watermark is encrypted using a one way hash function SHA1, i.e., sm = h(m′).

Step 3: A DSA signature is applied to sm to get r and s using (3). From the next step, we will show the procedure for concealing encryption value s, which is composed of {0, 1}^{160}. The triplet (p, q, r) is generated based on Definition 1.
 Step 4: Concatenate r, s, sm, and m′.$$\label{eq6} b = rssmm^{prime} $$(6)
 Step 5: A block of pixels is assigned to variables such as a, b, c, d, and x, which are read as a 2 × 2 pixel block from the cover image I of Fig. 2a. To read the next block, move from left to right 1 pixels, as seen in Fig. 2b.$$\label{eq7} [a,b,x] = \sum\limits_{i=1}^{n} \sum\limits_{j=1}^{m} (I_{i,j} : I_{i+1,j+1}) $$(7)
 Step 6: Compute prediction value x′ of a block using (5). Choose one bit out of b.$$\label{eq8} d = \sum\limits_{i=1}^{n} b(i) $$(8)
 Step 7: The “⊕” operator denotes “Exclusive Or.” This equation can be used to hide a binary bit at this stage. The x in the following equation is the current pixel.$$\label{eq9} I_{i,j}^{^{prime}} = \left\{ \begin{array}{rl} no~change~ ~~&\mbox{$ if~~LSB(x)=d \oplus LSB(x_{i}^{^{prime}} $}) \\ x=x+1~~ ~&\mbox{$ otherwise~~~ $} \end{array} \right. $$(9)

Step 8: If count = 0, then exit. Otherwise, count = count − 1. Go to Step 5.
3.3 Extraction procedure
 Input:

Stego image I′ with size H×W, ls is number of blocks, and cnt = 0.
 Output:

Secret message b, DSA signature bits v = r.

Step 1: A block of pixels is assigned to variables such as a, b, and x read as 2×2 pixel block from the watermarked image I′ of Fig. 2a. To read the next block, move from left to right 1 pixels, as can be seen in Fig. 2b.

Step 2: Compute prediction value x′ of x with a and b using (5).
 Step 3: If (cnt > ls), go to step 4. Otherwise, go to step 1.$$\label{eq10} b(cnt++) = LSB(x) \oplus LSB(x^{prime}) $$(10)
 Step 4: Extract the keys and digital values from string b.$$ (r, s, sm, m^{prime}) = {\rm division} (b); $$
function division (b) {
[r, s, sm, m’] = (b(1:16), b(17:32), b(33:193),
b(194:size(m’));
return ([r, s, sm, m’]);
}

Step 5: Compute v as follows. That is, w = s ^{ − 1} mod q, u _{1} = h(sm)w mod q, u _{2} = rw mod q, \(v=(g^{u_1}y^{u_2} ~mod~ p) ~mod~ q\).

Step 6: Recover original watermark with vector m′ using (1).

Step 7: If v = r, the signature is accepted, else the signature is not accepted.
4 Experimental results
In (13), p denotes the bitsperpixel (bpp), which is the embedding payload. Our experiment compared the number of secret bits that can be carried by a cover pixel. b is the number of bits for watermark b. There is a tradeoff between the payload and quality of an image. Increasing the embedding rate clearly requires a sacrifice in image quality.
Comparison results of Matrix encoding, Hamming+1 scheme, and proposed scheme
Images  Matrix coding [6]  Hamming+ 1 [30]  SchemeMED (h = 1) [28]  SchemeGAP(h = 1) [28]  LeftTop predictor  

PSNR  Payload  PSNR  Payload  PSNR  Payload  PSNR  Payload  PSNR  Payload  
Baboon  56.44  0.43  54.71  0.499  51.11  0.25  51.12  0.25  51.17  0.9961 
Barbara  56.65  0.43  48.60  0.499  51.15  0.25  51.16  0.25  51.19  0.9961 
Boats  54.75  0.43  49.37  0.499  51.15  0.25  51.14  0.25  51.20  0.9961 
Goldhill  57.02  0.43  53.73  0.499  51.15  0.25  51.14  0.25  51.19  0.9961 
Airplane  55.84  0.43  51.61  0.499  51.15  0.25  51.15  0.25  51.18  0.9961 
Lena  56.05  0.43  52.43  0.499  51.16  0.25  51.14  0.25  51.20  0.9961 
Pepper  54.01  0.43  47.26  0.499  51.16  0.25  51.12  0.25  51.118  0.9961 
Tiffany  53.40  0.43  47.46  0.499  51.14  0.25  51.12  0.25  51.22  0.9961 
Zelda  56.40  0.43  54.04  0.499  51.16  0.25  51.14  0.25  51.21  0.9961 
Average  56.44  0.43  50.91  0.499  51.14  0.25  51.13  0.25  51.30  0.9961 
5 Conclusion
Fragile watermarking is necessary for digital rights management, information protection, and concealing secrets, because it is not easy to protect a secret message from hackers and attackers. Most watermarks are based on the frequency domain. Thus, the hidden bit capacity is lower than that of a domain based scheme. In this paper, we proposed a LeftTop predictor schemes that uses the LSBs of pixels in an image, using the difference errors between the original pixels and the predicted pixels. The results of experiments showed that the watermarked images of our proposed scheme had PSNR values greater than 51.19 dB, which demonstrated that our scheme is a reasonably acceptable steganography method. Thus, we can conclude that the LeftTop predictors are suitable for steganographic applications.
Notes
Acknowledgement
This research was supported by the Basic Science Research Program Through the National Research Foundation of Korea (NRF) by the Ministry of Education, Science and Technology (20120192).
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