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Digital Watermarking for Telltale Tamper Proo?ng and Authentication

DEEPA KUNDUR, STUDENT MEMBER, IEEE, AND DIMITRIOS HATZINAKOS, SENIOR MEMBER, IEEE Invited Paper

In this paper, we consider the problem of digital watermarking to ensure the credibility of multimedia. We speci?cally address the problem of fragile digital watermarking for the tamper proo?ng of still images. Applications of our problem include authentication for courtroom evidence, insurance claims, and journalistic photography. We present a novel fragile watermarking approach which embeds a watermark in the discrete wavelet domain of the image by quantizing the corresponding coef?cients. Tamper detection is possible in localized spatial and frequency regions. Unlike previously proposed techniques, this novel approach provides information on speci?c frequencies of the image that have been modi?ed. This allows the user to make application-dependent decisions concerning whether an image, which is JPEG compressed for instance, still has credibility. Analysis is provided to evaluate the performance of the technique to varying system parameters. In addition, we compare the performance of the proposed method to existing fragile watermarking techniques to demonstrate the success and potential of the method for practical multimedia tamper proo?ng and authentication. Keywords— Authentication, data hiding, digital watermarking, steganography, telltale tamper proo?ng.

I. INTRODUCTION Research in the area of digital watermarking has focused primarily on the design of robust techniques for the copyright protection of multimedia data. In such methods a watermark is imperceptibly embedded in a host signal such that its removal using common distortions on the marked signal is dif?cult without degrading the perceptible data content itself. Watermarking can also be used to address the equally important, but underdeveloped, problem of tamper proo?ng. As a great deal of multimedia is stored in digital format, it has become easier to modify or forge information using widely available editing software. In fact, almost all

Manuscript received February 27, 1998; revised December 1, 1998. This work was supported in part by the Natural Sciences and Engineering Research Council (NSERC) of Canada and by the Communications and Information Technology Ontario (CITO). The authors are with the Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ont. M5S 3G4 Canada (email: deepa@comm.toronto.edu; dimitris@comm.toronto.edu). Publisher Item Identi?er S 0018-9219(99)04950-6.

published imagery is edited to some extent using computerbased tools. A problem arises when the possibly tampered data are to be used as evidence; in such situations, the multimedia data must be credible. By “credible” we mean that the signal source is authentic and that the information content in the signal has not been modi?ed in transit to its destination. In this paper, we present a technique for signal tamper proo?ng. Previously proposed methods for images [1]–[5] place the watermark in the spatial domain of the signal; they provide information on the spatial location of the changes but fail to give a more general characterization of the type of distortion applied to the signal. In contrast, our scheme places the watermark in the discrete wavelet domain, which allows the detection of changes in the image in localized spatial and frequency domain regions. This gives our approach the versatility to detect and help characterize signal modi?cations from a number of distortions such as substitution of data, ?ltering, and lossy compression. In addition, we embed the mark by quantizing the coef?cients to a prespeci?ed degree, which provides the ?exibility to make the tamper-proo?ng technique as sensitive to changes in the signal as desired. We call such a method a telltale tamper-proo?ng scheme. The main objectives of this paper are: 1) to introduce a set of well-de?ned goals for a telltale tamper-proo?ng scheme; 2) to present a novel tamper-proo?ng and authentication technique which provides more complete information on how the image is modi?ed; 3) to demonstrate the potential of tamper-proo?ng methods through implementations of our method and existing techniques; 4) to provide a comparative study of the strengths and limitations of the proposed and existing tamperproo?ng methods. In Section II we de?ne the speci?c problems we address in this paper and provide a review of existing techniques for the tamper proo?ng of images. We propose and intro-

0018–9219/99$10.00 ? 1999 IEEE

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Fig. 1.

The traditional tamper-proo?ng problem.

duce a set of objectives for the novel problem of telltale tamper proo?ng. The proposed technique is developed and analyzed using concepts from signal detection theory in Section III. Implementation issues are discussed in Section IV. Simulation results and comparisons of the performance of the technique to previously proposed methods are provided in Section V, followed by concluding statements in Section VI. II. PROBLEM FORMULATION A. Tamper Proo?ng Versus Telltale Tamper Proo?ng The problem we address is that of the telltale tamperproo?ng of multimedia signals for authentication. The traditional problem of tamper-proo?ng can be stated as follows. Consider the existence of an original or authentic digital multimedia signal . Given a signal , which is a possibly modi?ed version of , determine to a high degree without explicit knowledge of probability, whether of the original signal . Thus, if it can be shown that is equal to almost for certain, then the signal is considered to be credible. There are two basic stages to the process of tamper proo?ng. In the ?rst stage (at the source) the original signal is passed through a hash function to produce a piece of data separate from the signal1; these data are then used in the second stage (at the receiver) to verify that the received image has not been modi?ed. Alternatively, it has been shown that the veri?cation data can be directly embedded imperceptibly into the signal [2]. These data are extracted from the signal itself in the second stage to check for tampering. Fig. 1 gives an overview of the tamper-proo?ng problem. Several approaches have been recently proposed to address the issue of tamper proo?ng. In [1], Friedman describes a “trustworthy digital camera” in which a digital camera image is passed through a hash function and then is encrypted using the photographer’s private key to produce a piece of authentication data separate from the image. These data are used in conjunction with the image to ensure that no tampering has occurred. Speci?cally, the photographer’s public key is used to decrypt the hashed original image and the result is compared to the hashed version of the received

1 These data can also be an encrypted author ID independent of the signal.

image to ensure authentication. In [2], Walton proposes a technique in which a separate piece of data is not required for authentication. The method requires the calculation of the checksums of the seven most signi?cant bits of the image (or a transformed version of the image), so that they may be embedded into randomly selected least signi?cant bits. The major disadvantage of the techniques in [1] and [2] is that they produce a dichotomous result (i.e., “yesor-no” solution) to the question of tampering; it is not straightforward to determine how the image is tampered which makes the scheme highly susceptible to random bit errors during data transmission. For the tamper proo?ng of multimedia signals there is an additional issue of incidental distortions the signal may undergo due to compression, enhancement, or transmission errors. For many applications, such transformations of the signal are necessary and still maintain the integrity of the signal information. Thus, in this paper, we consider the more practical issue of identifying whether or not the tampering on the signal, if any, has an effect on its “credibility.” A few techniques which attempt to address this problem have been proposed in the literature. In [3], Schneider and Chang propose a method for content-based image veri?cation in which they de?ne a continuous interpretation of the concept of authenticity which measures the closeness of speci?c features of a possibly modi?ed image to the original one. The procedure is comprised of three stages in which: 1) the relevant signal content is extracted; 2) the results of stage 1) are hashed to reduce size; and 3) the result of stage 2) is encrypted with the author’s private key. The image content extraction could be localized histogram information, discrete cosine transform (DCT) coef?cients, or edge information. The advantage of the method is that signals that undergo incidental distortions can still be deemed credible. However, the process of selecting the image content extraction functions used in stage 1) is not straightforward for a given application. Wolfgang and Delp in [4] proposed a fragile watermarking technique involving the addition of two-dimensional sequences. They de?ne a nonbinary test statistic based sequence and the image on the inner product of the which gives a relative measure of the tampering of a particular image block. The major disadvantage is that it

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is possible to modify the data without disturbing the lower signi?cant bits which contains the veri?cation information. Similarly in [5], Yeung and Mintzer discuss a digital watermarking technique which tries to detect the modi?cation of individual pixels. The technique requires the use of a look-up table (LUT) which maps image colors to binary numbers. The original image pixel colors are modi?ed such that the associated binary numbers determined from the LUT equal the watermark bit values. Although the techniques in [4] and [5] give information about spatially localized changes in the image, they do not provide more explicit information on how the image is tampered. For example, if the image is innocently lossy compressed for convenience, then the entire image may appear tampered and its usefulness ignored. We argue that traditional authentication approaches for data are not well suited for images, sound, and video; to be practically useful a tamper-proo?ng technique must not only detect the presence of modi?cations in a signal but should also provide information helpful to characterize the distortions. A telltale tamper proo?ng method must be able to do the following: 1) indicate with high probability that some form of tampering has or has not occurred; 2) provide a measure of the relative degree of distortion of the signal; 3) characterize the type of distortion, such as ?ltering, compression or replacement, without access to the original host signal or any other signal-dependent information; it should be possible to detect changes due to compression or random bit errors and make application-dependent decisions concerning whether or not the signal still has credibility; 4) validate the signal and authenticate the source without requiring the maintenance and synchronization of additional data separate from the signal. There has been a recent trend toward addressing the problems of tamper proo?ng and authentication using a digital watermarking approach. The attraction of such an approach is that no additional data are required for signal veri?cation. In addition, the veri?cation information is discretely watermarked which adds an additional level of security against attacks to modify both the signal and the veri?cation data. In the next section, we discuss the digital watermarking problem. B. The Digital Watermarking Approach Traditionally, digital watermarking has been used to embed author and copyright identi?cation into a multimedia signal [6]–[11]. The watermark must be retained in the signal even under intentional signal distortion attacks to remove it. In contrast, fragile watermarking refers to the process of marking a signal such that any modi?cation causes the extracted mark to be different than the original which indicates that tampering has taken place.

KUNDUR AND HATZINAKOS: DIGITAL WATERMARKING

We brie?y discuss some terminology and requirements for a successful fragile watermarking method. We assume without loss of generality that the signal to be marked is de?ned as a is a still image. A fragile watermark signal (which is often a randomly generated binary stream), containing information used to assess whether an image was modi?ed. The watermark is considered to be fragile because it is embedded in a way such that any slight modi?cation of the resulting image will distort the watermark as well. The embedding procedure involves modifying a host image to re?ect the information content in . The modi?cation must be imperceptible in the sense that the owner and recipient of the signal show no preference to the information content in either the original or marked signal. Watermark extraction is the process of detecting the presence of watermark information in a given image and is performed to recover the mark and to assess whether tampering has been performed. Some recent work in fragile watermarking [2], [4], [5] has demonstrated the potential of the approach. We specifically de?ne the problem of fragile watermarking for the application of telltale tamper-proo?ng as follows. Given a digital multimedia signal and a digital watermark , embed into by imperceptibly modifying to produce a tamper-proofed signal such that: can be extracted from without 1) the watermark requiring explicit knowledge of ; 2) if the information content in is unmodi?ed, then the extracted watermark exactly matches ; 3) if is modi?ed, then is different from the embedded with a probability vanishing close to one; 4) the differences between the embedded and extracted watermarks provide useful information to assess whether the signal modi?cation maintains or destroys credibility. We present a watermarking technique which attempts to address the above criteria. III. PROPOSED TECHNIQUE A. General Approach Our technique is described in the context of watermarking still images, but it also works for general multimedia signals. We make use of the discrete wavelet domain opposed to spatial or DCT domains to embed the watermark because it provides both a simultaneous spatial localization and a frequency spread of the watermark within the host image. The localization of the watermark gives the ability to identify distinct regions of the watermarked image which have undergone tampering and the global spreading of the mark makes it sensitive to large-scale signal distortions. We argue that characterizing the modi?cations in terms of localized space-frequency distortions is more effective and practical for tamper proo?ng than attempting to parameterize the distortion. Parametric models can be highly inaccurate in estimating a wide class of image transformations and are often costly to compute for larger images.

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(a)

(b) Fig. 2. Proposed telltale tamper-proo?ng approach: (a) embedding process and (b) tamper assessment process.

The fundamental advantage of our technique lies in its ability to detect, with high probability, the spatial and frequency components of the image which are untampered and, hence, still credible. We embed the mark by quantizing the coef?cients to a prespeci?ed degree which provides the ?exibility to make the tamper-proo?ng technique as sensitive to changes in the signal as desired. The general scenario is shown in Fig. 2(a). A validation key comprised of the author’s watermark, a coef?cient selection key (which we describe later), the quantization parameter , and possibly the speci?c mother wavelet function are necessary for embedding and extracting the mark. The watermark can be an encrypted version of the author identi?cation which is used to establish sender authenticity. There are three main stages to the watermark embedding procedure. In the ?rst stage, we compute the th-level discrete wavelet decomposition of the host image to produce a detail images, corresponding to the sequence of three horizontal, vertical, and diagonal details at each of the resolution levels, and a gross approximation of the is image at the coarsest resolution level. The value of user de?ned. We denote the th detail image component , at the th resolution level of the host by where (which stands for “horizontal,” “ver1170

tical,” and “diagonal” detail coef?cients, respectively), and is the particular spatial location index at resolution . The gross approximation is represented by where the subscript is used instead of to denote “approximation.” In the second stage, we embed the watermark bit stream by modifying selected wavelet coef?cients. Speci?cally, to embed a binary watermark of denoted , , a user-de?ned length , is coef?cient selection key employed. The particular wavelet coef?cient at which to is given by . embed the th watermark bit Each element of is distinct so that two bits are not marked at the same location, causing an ambiguity or error. In addition, the selection of the coef?cients is random and well spread spatially and throughout each resolution level to be able to assess changes to these image was components. In the simulations for this paper, generated by randomly selecting a coef?cient from the , , for each and set . Thus, one detail coef?cient at each resolution and spatial location was marked. The binary watermark was also randomly generated using a uniform distribution and . The watermark was set to be the same length as is embedded into the coef?cient through bit

PROCEEDINGS OF THE IEEE, VOL. 87, NO. 7, JULY 1999

Fig. 3. The quantization function. Each possible real value of the detail coef?cient has an associated binary number given by (1).

Q

an appropriate quantization procedure. The speci?cs of the quantization are discussed in the next section. In the ?nal stage, the corresponding th-level inverse wavelet transform of the marked image components is computed to form the tamper-proofed image. Watermark extraction on a given image is performed as shown in Fig. 2(b). The th-level discrete wavelet transform (DWT) is applied to the given image and the is used to determine the coef?cient selection key (also marked coef?cients. A quantization function discussed in the next section) is applied to each of these coef?cients to extract the watermark values. For authentication, the author’s public key is applied to the extracted watermark to obtain the author identi?cation code. Almost any tampering of the image will cause the authentication procedure to fail as the decryption procedure is highly sensitive to changes in the watermark. Thus, authentication is possible only if the extracted watermark is identical to the embedded. If public key authentication fails, then we employ tamper assessment to determine the credibility of the modi?ed multimedia content. To assess the extent of tampering, we compute the following function which we call the tamper assessment function (TAF) TAF (1)

compression is applied to an image, the method can assess that most of the changes have occurred to the details at the higher resolution levels. If a part of the image has been replaced/changed in addition to compression, the watermark in the lower resolutions will not remain the same. Hence, the lower resolution image can be authenticated. In addition, when ?ltering is applied to an image the technique can assess the frequency regions most tampered with [12]. B. Details of the Quantization Process For an arbitrary wavelet transform, the detail coef?cients are real numbers. We perform quantization on the wavelet coef?cients in the following manner. Every real number is assigned a binary number, as shown in Fig. 3. We which maps the real number denote this function by set to {0, 1}. Speci?cally if if for for (2) is a positive real number called the quantization where parameter and is shown in Fig. 3. The following assigninto ment rule is used to embed the watermark bit . We denote the coef?cient the selected coef?cient as . selected by , then no change in the 1) If coef?cient is necessary. so that we force 2) Otherwise, change , using the following assignment: if if

is the true author watermark, is the extracted where is the length of the watermark, and is the mark, exclusive-OR (XOR) operator. The value of TAF ranges between zero and one. To determine image modi?cations for speci?c frequencies and/or spatial regions the watermark can be extracted from the corresponding marked wavelet coef?cients alone. The presence of tampering is determined if TAF , where is prespeci?ed threshold. If TAF , then the modi?cations on the image are considered to be incidental and negligible. For higher can be set to be smaller. The security applications, magnitude of TAF can be used to assess the extent of tampering. We show in Section V that if JPEG

KUNDUR AND HATZINAKOS: DIGITAL WATERMARKING

(3)

is the same parameter as in Fig. 3 and (2), where is the assignment operator. and The nature of the assignment in (3) has been experimentally found to change the image with the least visual degradation is user for a given magnitude of . The parameter

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Fig. 4. Effect of noise on the extracted watermark bit. Perturbation of the wavelet coef?cient from tampering can cause the extracted watermark to be different than the embedded.

de?ned and is set to establish an appropriate sensitivity will make to changes in the image. A smaller value of the quantization process of the second stage ?ner and hence makes minor changes in the image easier to detect. It is assumed that the speci?c wavelet transform used is unknown to make forgery dif?cult. If the wavelet transform were known, it would be possible for a tamperer to apply it to any arbitrary image and quantize the coef?cients in the same way in which using the knowledge of it appears in the original watermarked image so that the forgery appears authentic. We discuss how to overcome this handicap in Section IV with the use of an image-dependent quantization key. C. Performance Analysis In this section, we assess the performance of our general technique as a function of the system parameters. We concentrate on two types of degradations on a given region of the image. 1) Mild distortion, in which we model the degradation on the associated wavelet coef?cients as additive noise with a probability density function (pdf) with rapidly decaying tails.2 We speci?cally model the distortion on the wavelet coef?cients as zero mean additive Gaussian noise (AGN) with variance . We is “small,” such that the Gaussian assume that pdf rapidly decays. Examples of image distortions which can fall under this category are mild ?ltering and JPEG compression. 2) Severe distortion, in which the degradation is assumed to be additive noise consisting of heavy tails (i.e., is “large”) and the value of the distorted wavelet coef?cients becomes dif?cult to predict given

2 The tails of a pdf refer to the behavior of the function as the independent variable approaches in?nity and negative in?nity.

the true values. In fact, we consider that the probability of false watermark detection in such a degraded coef?cient be 1/2. Heavy linear or nonlinear ?ltering, random bit errors, and image region substitution fall under this class of distortions. We consider each type of distortion in turn to assess the performance of our method. We evaluate the effectiveness of the approach to tamper proo?ng by introducing a measure we call the tamper sensitivity function (TSF). We de?ne this as the probability that tampering is detected for given that coef?cients in the wavelet domain are modi?ed. 1) Sensitivity of the Technique to Mild Distortion: To assess the TSF for mild distortion we model the effects of the image degradation on a given wavelet coef?cient as (4) where is the undistorted wavelet coef?cient, is the distorted coef?cient, and is the associated zero mean AGN with variance . Without loss . Fig. 4 of generality we assume that shows how the additive noise can perturb the wavelet coso that the extracted ef?cient such that watermark is different from that embedded. for the tampering The probability of false negative of a given coef?cient (i.e., the probability that tampering is not detected in a particular wavelet coef?cient) is given by . That is the probability that (5) Given that of imation: is small, we can neglect the probability and we make the following approx(6)

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where is the relative distance of the wavelet coef?cient as shown in from one of the range boundaries of as follows by Fig. 4. We simplify the expression for is zero mean AGN using the assumption that

and extracted watermark bits. Using this interpretation, we conclude that [14] (18)

(7) (8) erf where erf erf (9) erf

erf

(19)

is the traditional error function given by [13] erf (10)

On average, is evenly distributed between zero and for an arbitrary image and wavelet transform. Therefore, the expected probability of a false negative of a degraded coef?cient is given by erf erf erf (11) (12)

is the length of the extracted watermark, is where . the ceiling operator, and it is assumed that Equation (19) provides a relationship between the value and the probability of tamper detecof the threshold wavelet coef?cients have been mildly tion given that distorted. This probability can be set arbitrarily high by and for a given . reducing both 2) Sensitivity of the Technique to Severe Distortion: As discussed in the beginning of Section III-C, we assume that the extracted mark is essentially independent of the embedded watermark value for severe distortion so that . Performing a similar analysis to the mild distortion case, the TSF is given by TSF (20) (21) Since the distortion is unpredictable, (21) is independent of , but there still remains a geometric relationship with . The average probability of tamper detection for given that wavelet coef?cients are severely distorted is computed to be (22) is the length of the watermark extracted from a where given region. The value of the threshold can be decreased to increase the probability of tamper detection. When a geometric transformation such as shearing or rescaling is applied to a marked image, the locations of the fragile watermark bits become “unsynchronized.” Therefore, we can model this distortion as severe since the probability of a false negative is essentially 1/2 as a watermark bit is extracted from a completely different location in the image and its value is unpredictable. Our scheme, as proposed in this paper, cannot be used to estimate the particular geometric transformation applied to the image; the tampering is merely detected. IV. IMPLEMENTATION ISSUES FOR TAMPER PROOFING A. The Algorithm In this section, we discuss the major implementation issues of realizing our telltale tamper-proo?ng technique and our strategies to overcome them. We present the speci?c algorithm implemented. The two main obstacles in implementing the method are its numerical sensitivity

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The TSF for mild distortion is given by the probability that at least one extracted watermark bit differs from the corresponding embedded bit TSF all modi?ed coef?cients produce false negative tampering results (13) (14) erf (15)

. Equation (15) gives us the average where given that probability of tamper detection for wavelet coef?cients have been modi?ed. We see that the value of dictates the sensitivity of the technique to image tampering. The value of the TSF increases monotonically with decreasing ; hence, the smaller the value of , the more sensitive the tamper detection which con?rms is user-de?ned so that the our intuition. The value of technique is ?exible for a variety of applications. Equation (15) also reveals that there is a geometric increase in the is increased. change in the TSF as We next determine the probability of tamper detection for given that coef?cients are modi?ed arbitrary TAF (16) (17) The right-hand side of (17) is equivalently the probability differences in the embedded that there are at least

KUNDUR AND HATZINAKOS: DIGITAL WATERMARKING

and its susceptibility to forgery. 1) Numerical Sensitivity: The fragile watermarking of images is somewhat different than robust watermarking because the design of the technique must be intrinsically sensitive to detect tampering. Existing fragile watermarking methods deal with the addition of integers to the spatial domain pixels of the image [2], [4], [5]. Our proposed method involves embedding the watermark in the wavelet domain. When the marked wavelet coef?cients are modi?ed and the inverse DWT is applied, the resulting marked image pixels must be rounded to integer values to form a digital image. This rounding operation is an image modi?cation that may cause the watermark in the marked image to differ from the original due to numerical sensitivity. To avoid these numerical dif?culties, we propose an algorithm in which the changes to the wavelet coef?cients guarantee integer changes in the spatial domain. We make use of the Haar wavelet transform, in which the coef?cients are rational numbers of the at each resolution level where . We modify the coef?cients by form adding or subtracting a multiple of 2 . This speci?c type of quantization guarantees that inverse DWT produces an image with integer pixel values; no rounding, which may jeopardize the accuracy of the method, is necessary. We use the following modi?ed quantization function to is equal to embed the watermark such that the watermark bit value: if if is even (23) is odd

Tables 1 and 2, respectively. The choice of the user-de?ned parameters are discussed in Section V. B. Key Features of the Algorithm We discuss and review the main characteristics of the technique which distinguish it from previously proposed methods for watermarking. 1) Our technique differs from existing fragile watermarking techniques in that the mark is embedded in the discrete wavelet domain. This allows information concerning the frequencies of the image that have undergone tampering and their relative degree of distortion. 2) There is a relationship between the value of the maximum wavelet decomposition level and the visibility of the watermark. Given that detail coef?cients are marked per spatial location at a particular resolution, there can be a change in . The larger the any image pixel of at most the more localized the information that value of is extracted concerning changes to lower frequencies of the image. Thus, there exists a tradeoff between the visibility of the mark and the ability to detect changes in lower image frequencies. Analogously, increasing can provide additional information the value of about tampering such as the possibility of directional ?ltering, but this increases the chance of visibility. 3) The quantization key provides the ?exibility to make the technique more or less sensitive to certain distortions. For example, if we wish to detect changes in the mean value of each 8 8 block of the image, can depend directly on this quantity so that then and hence any change in the mean will scramble cause the extracted watermark value to differ from the embedded with high probability. It should be noted maintains the integrity of the that the presence of tamper-proo?ng scheme against forgery even under the condition that the coef?cient sensitivity function is disclosed. These properties make the method appealing for other multimedia security applications. Related work has demonstrated the usefulness of telltale watermarking for tamper recovery [12] and watermark attack characterization [15]. In [12] the authors demonstrated how telltale watermarking can be used for semiblind image restoration. In this problem the marked image undergoes unknown blurring and must be recovered using information on how the corresponding fragile watermark is distorted. In [15] the authors demonstrate how a fragile watermark can be embedded in addition to a robust watermark to characterize image tampering. The characterization process allows optimal robust watermark extraction which improves security for copyright-protection applications. V. SIMULATION RESULTS AND COMPARISONS A. Basis of Comparison We evaluate the fragile watermarking techniques based on their ability to detect undesired tampering such as

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is the where is a prespeci?ed positive integer and ?oor function. 2) Susceptibility to Forgery: As discussed in Section IIIB, knowledge of the speci?c wavelet transform used to embed the watermark can jeopardize the security of the method. However, during implementation, we make exclusive use of the Haar wavelet, which is a disclosed detail of the algorithm. To combat this, we introduce an image-dependent key called the quantization key . The value of this key for each index is a function of a localized component of the image. The purpose of the quantization key is to make the forgery of an untampered image virtually impossible with. Instead of embedding the waterout knowledge of directly into the wavelet coef?cients, we embed mark where is dependent on the image. If we wanted to make the tamper proo?ng especially sensitive to changes in horizontal edges of the image, then the could be a function of . Similarly, value of if we wanted the technique to indicate changes in the can be dependent on mean value of the image, then localized averages of the image intensity. The introduction improves security against forgery and provides the of ?exibility to monitor speci?c changes to the image. Algorithmic forms of the watermark embedding, and extraction and tamper assessment routines are provided in

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Table 1 The Proposed Telltale Tamper-Proo?ng Technique for Watermark Embedding

replacement of speci?c image regions and their robustness to incidental image distortions such as high quality JPEG compression. In addition, we study the introduction of artifacts, if any, into the image as a result of the watermarking procedure using both qualitative observations and the peak signal-to-noise ratio (PSNR) which is de?ned as

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PSNR

(24)

Table 2 The Proposed Telltale Tamper-Proo?ng Technique for Watermark Extraction and Tamper Assessment

in decibels, where is the original unmarked image, is the tamper-proofed result, and are the [or alternatively in ] number of pixels in since watermarking does not increase the dimensions of the image. We compare the performance of our technique with the watermarking methods of [4] and [5]. We do not implement the approaches in [1]–[3] for comparison as these methods provide little information to characterize the distortion and, hence, fall under a different class of techniques than our proposed algorithm. B. Results We demonstrate the results of the three techniques using the 256 256 image of Lena shown in Fig. 5(a). We tamper

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proof the image using our proposed technique and use the following parameters: and .3 The watermark and the coef?cient selection key are randomly generated. The quantization key maps the amplitude of the selected detail coef?cients are set randomly to binary numbers. The values of for each argument with runs of zeros and ones no greater than two to avoid visual artifacts in the marked image. in this way to make the method We speci?ed the equally sensitive to all distortions to obtain a general sense of the behavior of our technique. The resulting watermarked

3 These parameters were chosen as they provide no noticeable visual change in the image. From experience, we ?nd that 1 is appropriate for smooth photographic images. For highly varying images, = 2 can also be used. As a rule of thumb, L may be set such that log2 (N=8) L log2 (N=4), where N is the largest dimension of the image.

=

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Table 4 The TAF Values for the Proposed Technique for Various JPEG Compression Ratios

(a)

(a) (b) Fig. 5. Original and watermarked images for the proposed method: (a) original image of Lena and (b) watermarked image with L 5 and = 1 (PSNR = 43 dB).

=

Table 3 The TAF Values for the Proposed Technique for Various Mean Filter Lengths

image is shown in Fig. 5(b). No visual difference is noticed when viewed on a computer screen. The PSNR of the marked image is 43 dB. for the untampered marked As expected, TAF image. If a watermark is extracted from the unmarked image or from any other unmarked image the value of TAF is approximately 0.5. We demonstrate the effects of various image distortions such as mean ?ltering and JPEG compression in Tables 3 and 4. As we can see, for high-quality JPEG compression, the lower resolution subimages are still deemed credible by our method. For mean ?ltering, we can see from the magnitude of the TAF that the lower frequencies are less distorted than the higher frequencies. Tests were also conducted to determine

KUNDUR AND HATZINAKOS: DIGITAL WATERMARKING

(b) Fig. 6. (a) Tampered image. The feathers on the hat have been smoothed using an image-editing package. (b) Undistorted watermarked image.

whether localized tampering could be detected. The marked image was modi?ed by smoothing out the feathers in the hat using an image editing package as shown in Fig. 6. The differences in the extracted watermark and embedded are shown in white in Fig. 7 for the various resolution levels. The value of the threshold to detect for tampering is application dependent. From our simulations we found that a value of approximately 0.15 allows the method to be robust to high quality compression, but detects the

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(e) Fig. 7. Tamper detection at the various resolutions for the distorted image of Fig. 6(a) for: (a) l 1; (b) l = 2; (c) l = 3; (d) l = 4; and (e) l = 5. The differences between the embedded and extracted watermarks are shown in white for each resolution.

=

presence of additional tampering. A good way to analyze the effects of tampering would be to view the differences in the extracted and embedding marks as displayed in Fig. 7. The Lena image was also tamper proofed using the method by Yeung and Mintzer [5]. The results are shown in Fig. 8. The LUT and watermark used in the technique were randomly generated as suggested. The PSNR for the marked image is 45 dB. Perfect watermark recovery

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was possible when the marked image was untampered. Localized spatial regions of image tampering were also identi?ed accurately. We tested the effects of mild ?ltering and JPEG compression. The results are shown in Fig. 9, where the white pixels indicate that tampering has been detected at the corresponding spatial locations. As can be seen, high-quality JPEG compression has the effect of completely destroying the credibility of the image. It is

PROCEEDINGS OF THE IEEE, VOL. 87, NO. 7, JULY 1999

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(b) Fig. 8. Original and watermarked images for the method by Yueng and Mintzer [5]: (a) original image of Lena and (b) watermarked image (PSNR 45 dB).

(b) Fig. 9. Tamper identi?cation for ?ltering and compression for the technique by Yueng and Mintzer [5]: (a) tamper identi?cation for high-quality JPEG compresion CR 3 and (b) tamper identi?cation 3 mean ?ltering. for 3

=

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not possible to distinguish between an image which is compressed with perceptual information in tact and one that is compressed in addition to being severely tampered. In general, we found that the method in [5] produced no noticeable artifacts in the marked images. The changes in the image were similar to the effect of mild dithering. We tested the watermarking method by Wolfgang and Delp [4] on the same image of Lena. The results are shown sequence of order 16, and for block sizes of 8 8, an a bipolar watermark scaled by a factor of two in Fig. 10. The PSNR of the resulting image is 41 dB. As expected, no tampering was detected for the original marked image. The method detected the 8 8 blocks containing spatially localized changes (similar to that shown in Fig. 6) in the image for a threshold of zero. We found that the method identi?ed the changes even in the presence of high quality JPEG compression (CR 3) for a threshold set to 1.5 times the mean value of the associated autocorrelation matrix [4]. For mean ?ltering, the regions of high variance were detected to be tampered, but for JPEG compression, the results were more unpredictable. To determine localized changes in the image, it is important that the block sizes be small. However, the strength of

KUNDUR AND HATZINAKOS: DIGITAL WATERMARKING

the technique lies in statistical assumptions of the embedded -sequence watermark, and reducing the block size lowers the statistical validity of the technique. Thus, we have found there to be a tradeoff between accuracy and localization of detection in this method. In addition, the technique requires that image-dependent information in the form of an inner product matrix [4] (which depends on the marked image sequence) be known for extraction. This makes the and method less portable and not well suited for automation. VI. CONCLUSIONS Tamper proo?ng of multimedia signals is a new and growing ?eld of study. Traditional approaches for data authentication are not appropriate for multimedia due to the nature of the information to be protected. In this paper we introduce the problem of telltale tamper proo?ng. We propose a fragile watermarking technique for images and compare its performance with existing methods. Our results indicate that the proposed approach has potential for multimedia information authentication applications. Future research involves extending this approach to characterize geometric distortions through appropriate design of the quantization key.

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[9] G. Voyatzis and I. Pitas, “Applications of toral automorphisms in image watermarking,” in Proc. IEEE Int. Conf. Image Processing, 1996, vol. 2, pp. 237–240. ? [10] J. J. K. O Ruanaidh, W. J. Dowling, and F. M. Boland, “Watermarking digital images for copyright protection,” in IEE Proc. Vision, Image and Signal Processing, Aug. 1996, vol. 143, pp. 250–256. [11] D. Kundur and D. Hatzinakos, “A robust digital image watermarking method using wavelet-based fusion,” in Proc. IEEE Int. Conf. Image Processing, 1997, vol. 1, pp. 544–547. [12] , “Semi-blind image restoration based on telltale watermarking,” in Proc. 32nd Asilomar Conf. Signals, Systems, and Computers, 1998, pp. 933–937. [13] M. Abramowitz and I. A. Stegun, Eds., Handbook of Mathematical Functions with Formulas Graphs and Mathematical Tables. New York: Dover, 1965. [14] A. Leon-Garcia, Probability and Random Processes for Electrical Engineering. Don Mills, Ont., Canada: Addison-Wesley, 1989. [15] D. Kundur and D. Hatzinakos, “Improved robust watermarking through attack characterization,” Opt. Express, vol. 3, pp. 485–490, Dec. 7, 1998.

(b) Fig. 10. Original and watermarked images for the method by Wolfgang and Delp [4]: (a) original image of Lena and (b) watermarked image for a block size of 8 8, an sequence of order 16, and a watermark scaling of a factor of two.

Deepa Kundur (Student Member, IEEE) was born in Toronto, Ont., Canada. She received the Bachelor of Applied Science degree in 1993 and the Master of Applied Science degree in communications and signal processing in 1995, both from the Department of Electrical and Computer Engineering, University of Toronto, Ont., Canada. She is currently pursuing the Ph.D. degree at the University of Toronto. Her research interests include digital watermarking of multimedia information, blind image restoration, and data fusion for the classi?cation of remote sensing imagery. Ms. Kundur is currently an Engineer-in-Training with the Professional Engineers of Ontario (PEO).

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REFERENCES

[1] G. L. Friedman, “The trustworthy digital camera: Restoring credibility to the photographic image,” IEEE Trans. Consumer Electron., vol. 39, pp. 905–910, Oct. 1993. [2] S. Walton, “Image authentication for a slippery new age,” Dr. Dobb’s J., vol. 20, pp. 18–26, Apr. 1995. [3] M. Schneider and S.-F. Chang, “A robust content based digital signature for image authentication,” in Proc. IEEE Int. Conf. Image Processing, 1996, vol. 3, pp. 227–230. [4] R. B. Wolfgang and E. J. Delp, “A watermark for digital images,” in Proc. IEEE Int. Conf. Image Processing, 1996, vol. 3, pp. 219–222. [5] M. M. Yeung and F. Mintzer, “An invisible watermarking technique for image veri?cation,” in Proc. IEEE Int. Conf. Image Processing, 1997, vol. 2, pp. 680–683. [6] I. J. Cox, J. Killian, T. Leighton, and T. Shamoon, “Secure spread spectrum watermarking for multimedia,” NEC Res. Inst., Princeton, NJ, Tech. Rep. 95-10, 1995. [7] J.-F. Delaigle, C. De Vleeschouwer, and B. Macq, “Digital watermarking,” in Proc. SPIE, Optical Security and Counterfeit Deterrence Techniques, Feb. 1996, vol. 2659, pp. 99–110. [8] E. Koch and J. Zhao, “Toward robust and hidden image copyright labeling,” in Proc. Workshop on Nonlinear Signal and Image Processing, I. Pitas, Ed., June 1995, pp. 452–455.

Dimitrios Hatzinakos (Senior Member, IEEE) received the Diploma degree from the University of Thessaloniki, Greece, in 1983, the M.A.Sc degree from the University of Ottawa, Canada, in 1986, and the Ph.D. degree from Northeastern University, Boston, MA, in 1990, all in electrical engineering. In September 1990, he joined the Department of Electrical and Computer Engineering, University of Toronto, where he now holds the rank of Associate Professor with tenure. His research interests span the ?elds of digital signal/image processing with applications to wireless communications and multimedia. He is the author or co-author of more than 80 papers in technical journals and conference proceedings and has contributed to four books in his areas of interest. His experience includes consulting through Electrical Engineering Consociates Ltd. and contracts with United Signals and Systems, Inc., Burns and Fry Ltd., Pipetronix Ltd., Defense Research Establishment Ottawa (DREO), and Vaytek, Inc. He has been an Associate Editor for IEEE TRANSACTIONS ON SIGNAL PROCESSING since July 1998 and Guest Editor for the Special Issue of Signal Processing on Signal Processing Technologies for Short Burst Wireless Communications, scheduled to appear in late 1999. He was a member of the IEEE Statistical Signal and Array Processing Technical Committee (SSAP) from 1992 to 1995 and Technical Program Cochair of the Fifth Workshop on Higher-Order Statistics in July 1997. He is a member of EURASIP, the Professional Engineers of Ontario (PEO), and the Technical Chamber of Greece.

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