Combined Digital Signature and Digital Watermark Scheme for Image Authentication 1
Tao Chen1, Jingchun Wang1, 2 and Yonglei Zhou1 Deptartment of Automation, Tsinghua University, Beijing, 100084, P.R. China 2 State Key Lab on Pattern Recognition, Beijing, 100080, P.R. China {chentao, wang-jc}@proc.au.tsinghua.edu.cn;
[email protected]
ABSTRACT Conventional digital signature schemes for image authentication encode the signature in a file separate from the original image, thus require extra bandwidth to transmit it. Meantime, the watermark technique embeds some information in the host image. In this paper, a combined digital watermark and digital signature scheme for image authentication is proposed. The scheme extracts signature from the original image and embeds them back into the image as watermark, avoiding additional signature file. Since images are always compressed before transmission in the Internet, the proposed scheme is tested for compression tolerance and shows good robustness against JPEG coding. Furthermore, the scheme not only can verify the authenticity and the integrity of images, but also can locate the illegal modifications. Keywords: Digital Signature, Digital Watermark, Image Authentication, Internet Security.
1. INTRODUCTION The rapid growth of Internet distributions of digital media has created an urgent need for copyright protection because of easy replication and modification. The state-of-the-art image authentication research and technology fall into two broad classes: digital watermark [1] and digital signature [2]. Digital watermark techniques embed an invisible signal (for example, company logo or personal symbol) into image so as to attest the owner identification of the image and discourage the unauthorized copying. The watermark should be undeletable, perceptually invisible, statistically undetectable and resistant to lossy data compression and common signal processing operations [3][4]. While watermark techniques emphasize protecting the right of service providers, digital signature focuses on that of the customers. For example, an image purchaser may want to know whether the product he or she bought is from the legal seller and is the authentic one. Digital signature scheme can be used to solve this problem. First the image seller extracts some information dependent on the content of the original image and encrypts it into a small-size file, which is called signature. Then the signature file is sent to the purchaser with the original image. The purchaser uses the same algorithm to extract the content-dependent information of the received image. If the purchaser-extracted information matches with the signature, the ownership and the integrity of the received image are authenticated. Since images are always compressed before transmission in the Internet, which is emerged as the main method for digital media transactions, many research efforts have been done to make the signature tolerant to conventional compression methods [5~7]. It is hoped that the extracted content-dependent information is robust to reasonable distortion caused by compression, while still sensitive to modification of the content of the image. An obvious drawback of conventional digital signature schemes is the extra bandwidth needed for transmission of the signature. In this paper, we will introduce the combined digital signature and digital watermark scheme for image authentication. The basic idea of the combination is as follows. The image provider extracts the content-dependent signature from the original image, and then embeds it back into the image as a watermark. The receiver extracts the signature and the watermark from the received image at the same time. If the signature and the watermark match, the received image is thought to be authentic. However, the embedded watermark will degrade the original image, which makes the signature extracted from the watermarked image different from the original one. Thus the robust signature extraction method is of great importance. J. Fridrich [8] proposed robust bits extraction method in digital watermark technique. This idea is extended to digital signature applications here, forming the block-based digital signature extraction and embedding scheme, which is robustness against conventional compression algorithms.
Furthermore, the combined scheme not only can verify the authenticity and the integrity of images, but also can locate the illegal modifications. The rest of the paper is organized as follows. In Section 2, we describe the proposed scheme in detail. Section 3 demonstrates some experimental results of the scheme. Section 4 concludes this work.
2. THE PROPOSED DIGITAL SIGNATURE SCHEME The proposed authentication scheme is a kind of sender-receiver protocol. The sender generates the signature and inserts it back into the original image as watermark. In the receiver’s side, the ownership and integrity is verified by comparing the signature and watermark both extracted from the received image. The procedures in both sender and receiver sides are described in detail below.
2.1 Digital Signature Generation In signature generation, the content-dependent robust bits are extracted from the original image by the method proposed in [8]. We will extend its use in image authentication. Given an image, we divide it into blocks of 16 × 16 pixels. Assuming there are N blocks after division, k bits will be extracted from each block, forming a signature of length k×N bits. Using a secret key, k×N random matrices are generated whose entries are uniformly distributed in the interval [0, 1]. Then a low-pass filter is applied to each random matrix to obtain k×N random smooth patterns. After subtracting the mean of each pattern, each block is projected on k patterns successively, obtaining k×N scalar values vi, altogether. Then the absolute values of them are compared with a threshold T to obtain k×N bits bi:
− 1, if | vi |< T . bi = 1, if | vi |≥ T
(1)
Experiments in [8] showed that these extracted bits are robust to some image processing operations. In our application, these bits are considered content-dependent digital signature and will be embedded back into the original image as watermark. We will show in experiments that these bits can be re-extracted from the degraded image, although watermark insertion degrades the image a little.
2.2 Digital Watermark Insertion and Detection There are many watermark insertion and detection algorithms in the literatures. The foremost requirement of image authentication is blind detection. That is, the watermark must be extracted from the watermarked image without referring to the original one. Also, the watermark can be neither too robust to be insensitive to content modification, nor too fragile to be easily corrupted by reasonable compression. Furthermore, a block-based method is needed to insert the bits into the same block from which they are extracted. This will help locating the exact blocks which were undesirably modified by others. In the experiments, a frequency domain method is used [9], which performs wavelet transform to the image, inserts watermark to the lowest subband, and then performs inverse wavelet transform. When inserting watermark, a predefined quantization coefficient Q is selected considering the trade-off of robustness and image quality. More details can be found in [9]. While we focus on testing the efficiency of the combined scheme for image authentication, other watermark insertion and detection methods can also be used here.
2.3 Verification In the receiver’s side, the same robust bits extraction and watermark detection methods are performed to obtain the signature (that is, the robust bits) and the watermark. The signature is compared with the watermark for each block. If the number of mismatched bits exceeds a predefined threshold, the correspondent block is regarded as being modified by others. Otherwise,
the image is considered as integrity. Block based verification technique is quite useful if the image is distributed in the Internet. If only some blocks are undesirably modified, just these blocks need to be re-transmitted, which reduces the burden of the network. This is very efficient when the Internet is in congestion.
3. EXPERIMENTAL RESULTS In this section, some experiments are designed to prove the efficiency of the proposed scheme. First, the image quality after watermark insertion is investigated. Secondly, the scheme is tested to compression tolerance. Finally, we will show the scheme is capable to image authentication. The 256*256 Lean image of 8-bit grayscale is used for experiments. In signature generation, the image is divided to blocks of 16*16 pixels, forming 256 blocks. 4 bits are extracted from each block. The total length of the signature is then 1024 bits. In watermark insertion, the quantization coefficient Q is set 10.
3.1 Image Quality The peak-to-peak signal-to-noise ratio (PSNR) is computed to evaluate the watermarked image quality. PSNR is given by
PSNR = 10 log10
2552
σ q2
[dB ] ,
(2)
where σ q 2 is the mean square of the difference between the original image and the watermarked one. Fig.1 shows the Lena images before and after watermark insertion. We can see no obvious degradation in Fig. 1(b) whose PSNR is 35.541.
(a) Original Lena image
(b) Watermarked Lena image
Fig. 1: 8-bit 256 x 256 Grayscale Lena Image
3.2 Compression Tolerance The extracted watermark is hoped to be the same as the extracted signature (e.g., robust bits) after reasonable image compression. Table 1 shows the error rate after JPEG algorithm. It must be noted that even without JPEG compression, the watermarked image is different from the original one. Table 1 shows that the extracted signature and watermark are almost the same unless the compression ratio is more than 16:1. However, such high compression leads to obvious image degradation, which is rarely used in applications.
Table 1: Detection Error Rate after JPGE Compression Compression Ratio
1 : 1*
0 Error Rate * Without JPEG Compression.
4:1
6:1
8:1
16 : 1
0
0.52%
1.02%
5.86%
3.3 Image Authentication In this subsection we will show the proposed scheme is capable for image authentication. In the experiment, the signature is extracted from the original image and inserted back into the image as watermark. Then a small area of the watermarked image is modified. In the receiver’s side, the signature and watermark are extracted from the modified image. Then the modified area is detected if the signature and watermark are not the same in the corresponding blocks. Fig. 2 shows the result. In Fig.2 (a), a little star is put on the upper-left of the watermarked Lena image. In authentication, the difference of signature and watermark indicate the modified area showing in Fig. 2 (b) marked with white.
(a) Modified Lena Image
(b) Modified Area is Detected
Fig.2 Authentication Result
4. CONCLUSIONS Digital signature and digital watermark are two techniques used for copyright protection and authentication, respectively. In this paper, a combined signature and watermark scheme is proposed for image authentication. Conventional digital signature schemes usually encode the signature in a file separate from the original image, thus require extra bandwidth to transmit it. The proposed scheme extracts signature from the original image and embeds them back into the image as watermark, avoiding additional signature file. Furthermore, the scheme not only can verify the authenticity and the integrity of images, but also can locate the illegal modifications. Experiments show our scheme is robust to reasonable compression rate while preserving good image quality, and capable to authentication. Future work will be focused on more robust signature extraction method and possible ways to recover the illegally modified image without the original image.
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