EA034104B1 - Method of authenticating images based on digital watermarks formed with use of chaotic imaging - Google Patents

Abstract

The invention relates to computer technology, and in particular to methods of protecting digital images during their transmission by communication channels. The objective of the invention is to provide a method of authenticating images based on digital watermarks (DWM) formed using chaotic imaging, which allows to detect the presence of DWM in an image and identify modified areas of an image in the presence of noise in the communication channel. The solving of this problem is achieved by this method of authenticating images based on digital watermarks generated with use of chaotic imaging, which includes: embedding a DWM in an image according to the following algorithm: obtaining a digital image, generating, based on the original image, the value of a parameter of chaotic sequence, generating a chaotic sequence representing DWM, embedding DWM in the image; decoding of the DWM according to the following algorithm: extracting the DWM from an image, recovery of the parameter of chaotic sequence, characterized by the fact that the initial value of the variable of chaotic imaging is used as the recovered parameter of chaotic sequence, the obtained chaotic sequence is embedded in the least significant bits of the image pixel values of the image, the modified image areas are detected, performing element-by-element comparison of the embedded and extracted DWM.

Description

The invention relates to computer technology, and in particular to methods of protecting digital images during their transmission over communication channels.

At the present stage of development of information technology, digital images have become widespread. Image transmission is carried out through various telecommunication channels. Since not all communication channels can provide the necessary level of security, there is a need to solve problems related to the protection of digital images [1]. One of the approaches used for these purposes is called digital watermarks. A digital watermark (CEH) is a special label embedded in an image (or other digital data) in order to be able to control its use [2].

There is a huge variety of schemes for embedding CEH in images [3]. At the same time, new types of attacks are constantly being developed, aimed at the CEH. Most of these attacks are aimed at destroying the CEH present in the image. A copy attack occupies a special place, the purpose of which is to copy the CEH from one image and add it to another [4]. This can lead to inoperability of protocols that use the CEH to solve identification problems. In order to increase the resistance of the CEH to this type of attack, it is proposed to carry out its formation taking into account the image into which it is embedded [5]. However, as a result of interference in the communication channel, part of the information about the original image may be lost or distorted. This can lead to the inability to detect the CEH in the image.

There is a method of forming fragile CEH for image authentication [6], which includes embedding CEH into an image according to the following algorithm: generating a binary sequence C using a chaotic mapping, obtaining CEH We by eliminating by elementary logic operation either to sequence C and CEH W, replacing the values of the smallest significant bits of the original image H by the values of the sequence We; extracting the CEH from the image according to the following algorithm: generating a binary sequence C using a chaotic mapping, obtaining the extracted Wext CEH by elementwise applying a logical operation to either the C sequence and the least significant bits of the image; identification of modified image regions H by element-wise comparison of the CEH W and Wext.

The disadvantage of this method is the formation of the CEH without taking into account the image into which it is embedded, which allows an attacker to modify the image according to the following algorithm: 1) extract the CEH from the image, 2) make changes to the image, 3) embed the CEH extracted at stage 1 into the modified picture. When conducting this attack, the considered method will be unable to establish the fact of image modification.

A known method of generating digital watermarks for images [7], including embedding a digital watermark in an image according to the following algorithm: 1) splitting the image into non-overlapping blocks of IxJ size, 2) modifying the selected bits for each block, 3) computing a hash value using a cryptographic function, for which input parameters are a user key, image dimensions, a modified image block, 4) combining the resulting hash value with a binary CEH B by excluding the operation more or, 5) adding the resulting C to the image; extracting the CEH from the image according to the following algorithm: 1) modification of the selected bits for each image block of size IxJ, 2) calculation of the hash value using a cryptographic hash function for which the input parameters are a user key, image size, modified image block, 3) extraction of values preset bits from each block; 4) combining the obtained values in the previous step with the calculated hash values by applying the logical operation exclusive or.

The disadvantage of this method is the use of hash values calculated by using a cryptographic hash function for image blocks when embedding the CEH. This leads to the fact that when changing one pixel of an image block, the entire block is considered modified. Thus, in the presence of noise in the communication channel, the considered method does not allow detecting image blocks modified by an attacker.

Closest to the proposed method is a method for generating chaotic watermarks for digital images [8], which includes embedding a digital watermark in an image according to the following algorithm: 1) obtaining a digital image, 2) generating a value for the chaotic display parameter based on the original image, 3) forming based on the selected value of the parameter of the chaotic sequence, which is a CEH; 4) embedding the CEH into the image; decoding the CEH according to the following algorithm: 1) extracting the CEH from the image, 2) demodulating the chaotic sequence using an ergodic demodulator to determine the average value of the chaotic sequence, 3) determining the value of the chaotic mapping parameter.

The disadvantages of this method is the use as a restored parameter of a chaotic sequence of the parameter of the chaotic mapping, which does not allow to detect

- 1,034,104 areas of the image that are differentiated by an attacker. Using the average value of the generated chaotic sequence to determine the value of the restored parameter, which makes the considered method sensitive to noise in the communication channel.

The objective of the invention is to provide a method of authenticating images based on digital watermarks generated using chaotic mappings, which allows to detect the presence of the CEH in the image and identify modified areas of the image in the presence of noise in the communication channel.

The solution of this problem is achieved by the fact that in the method of authenticating images based on digital watermarks generated using chaotic mappings, including embedding a digital watermark in an image according to the following algorithm: obtaining a digital image, generating, based on the original image, a parameter of a chaotic sequence, generating a chaotic sequence, representing CEH, embedding CEH in the image; decoding the CEH according to the following algorithm: extracting the CEH from the image, restoring the parameter of the chaotic sequence, characterized in that the initial value of the variable of the chaotic mapping is used as the restored parameter of the chaotic sequence, the obtained chaotic sequence is embedded in the smallest significant bits of the pixel values of the image, the modified image areas are detected by performing an element-wise comparison of the embedded and extracted CV .

The invention is illustrated in FIG. 1-11, where in FIG. 1 shows a block diagram of the proposed method;

in FIG. 2 - test image of Lena.bmp with integrated CEH;

in FIG. 3 - the difference between the original image and the image containing the CEH;

in FIG. 4 is a test image of Peppers.bmp with a built-in digital watermark, formed for the Lena.bmp image;

in FIG. 5 is a result of checking for the presence of the CEH in the Peppers.bmp image with the integrated CEH formed for the Lena.bmp image;

in FIG. 6 - test image of Lena.bmp with the addition of noise;

in FIG. 7 - the result of checking for the presence of CEH in the Lena.bmp image with the addition of noise;

in FIG. 8 - a modified image of sailboat.bmp;

in FIG. 9 - results of checking for the presence of modified areas for the modified image sailboat.bmp;

in FIG. 10 - modified image of sailboat.bmp with the addition of noise;

in FIG. 11 is a result of checking for the presence of modified areas for a modified image of sailboat.bmp with added noise.

The block diagram (Fig. 1) contains a CEH generation module based on chaotic mappings 1, a CEH embedding module in image 2, a CEH extraction module from image 3, a reverse permutation module 4, an initial condition recovery module 5, a comparison module for the received and restored CEH 6 Also indicated on the flowchart are: 7 — initial value x ₀ for the formation of the CEH, 8 value of the parameter λ of the chaotic mapping, 9 — initial image I, 10 — communication channel, 11 restored initial value x ′ ₀ .

The input to module 1 is the value of the parameter λ of the chaotic mapping and the initial value x ₀ . A sequence of yi values is formed, the values of the elements of which are determined according to the following expression:

y _t = floor (x _t 256) (1) where xi is the value of the variable of the chaotic map at the ith iteration;

i = 1, 2, ..., N / 8;

N is the number of pixels in the original image I;

floor (a) is the largest integer less than a.

After that, a sequence of values w _k k = 1, 2, ..., N is formed. Elements w ₈ j _-7 , w ₈ j _-6 , ..., w ₈ j of this sequence are assigned the digits of the number yj represented in binary form. To the sequence wj, the procedure of permuting elements is applied. The permutation can be carried out in any way, however, it must be reversible and look like random.

Next, the image I and the generated sequence wj are fed to the input of the embedding module of the CEH 2. In this module, the least significant bit in the binary representation of the value of the jth image element I is assigned the value l _j , which is calculated according to the following expression:

= Wj Φ S [(Ij - (IJ mod2)) / 21 (2) where © is the exclusive operation or.

After that, the image with the integrated CEH enters the communication channel 10. In this communication channel, the image can be modified due to noise or the actions of an attacker.

The modified image I 'is fed to the input of the CEH 3 extraction module, where

- 2 034104 calculating the values of w'j according to expression (3). The dash in this case indicates that the values of w'j may differ from the values of w due to interference in the communication channel

Sequence w'j values is input to the inverse permutation module 4 where carried scrambling sequence in reverse order is carried out in the module 1. The received sequence is input to restore the initial value of the module 5. The module 5 based on the values of w _'k calculated value y

Ζ = Σ < ² '· <.> W r = 0

To restore the initial conditions, the following original algorithm is proposed.

1. Formation of table T, the jth row of which contains all the possible values of y _{i + 1} , if the value of y is (j-1), where j = 1K 256.

2. The formation of a matrix E containing m rows and n columns, the ij-th element of the matrix e, j is equal to one if the representation of the value of y in binary form does not differ from the binary representation of the number j in no more than r any digits. Otherwise, e, j = 0.

3. The formation of an array of pairs B. If e, j = 1, e _{i + 1u} = 1 and the value u is present in the jth row of the matrix T, then the pair (е ^, e _{i + 1u} ) is added to the array B.

4. The choice of pairs contained in the array B, those that allow you to establish a continuous relationship between the first and last non-zero elements of the matrix E. The result is possible options for the values of y ,. It should be noted that for r = 2 the number of possible values for most elements of the sequence Y is 1.

5. Based on y _n , the values x _min and x _max are determined such that

6. The value x ' _o x'o = (f ⁿ (x _min ) + f- ⁿ (x ™ x »12 (6)

7. Calculated h'o,

where h is a positive number;

= 1, ... M.

8. Based on each x'o, the sequence y '^ _{k is} calculated.

Computed d:

<= Σ (^ · Λ) (8)

9. As x ' _{0, one} chooses x'oi, using which the value of d is minimal.

Thereafter, the found initial value x _'0 and the value of the parameter λ are input to module 1, wherein the formation sequence carried w''j.

The input of module 6 receives the sequence of values w'j and wj. This module searches for modified image areas. The search for modified regions is carried out as follows: any image block D of size a x b pixels for which the ratio of the number of elements q _b whose values differ in fragments of the sequences w'j and and wj corresponding to this block to the total number of block elements exceeds the threshold q _th value is considered modified. The threshold value q _th is selected based on the value of q _n , numerically equal to the ratio of the number of modified bytes on reception to the total number of transmitted bytes. The recommended value for q is

The inventive method of authenticating images based on digital watermarks generated using chaotic mappings was implemented programmatically on the basis of a personal computer with the installed Windows 7 operating system in the C # programming language.

The developed ChaosWatermark software can work in two modes: embedding the CEH into the image and checking for the presence of the CEH in the image. Using the ChaosWatermark dialog box, the user selects: 1) the operating mode of the application, 2) the image into which the CEH needs to be embedded, 3) the chaotic display used in the formation of the CEH, 4) sets the parameter value and the initial value of the selected chaotic display, 5) determines q _th parameter values and block sizes used when searching for modified areas.

The CEH is formed using the createWatermark function. The user calls this function by clicking on the Insert Watermark button in the program mode of embedding the CEH into the image.

The createWatermark function includes the following steps: calling the initS function, which

- 3 034104 initializes the replacement array S and permutes its elements; calling the function X2Y, which generates a sequence of integers based on the values of the variable x of the chaotic mapping and writes them to the array Y; calling the function Y2W, which converts the sequence of integers obtained in the previous step into an array of bits W; calling the permutation function, which permutes the values of the array W; a call to the InsertWatermark function, which assigns the least significant bits of the Imagel image elements to the values of the elements of the W array and writes to the disk the resulting Imagel image in bmp format. After the createWatermark function has been executed, the user is presented with a dialog box containing Complete.

To check for the presence of the CEH in the image and identify the modified areas, the checkWatermark function is called. This function is called up by pressing the check Watermark button, which is only available in the Check for CEH program mode. When the checkWatermark function is executed, the following auxiliary functions are called: initS, which performs the same operations as when the createWatermark function was called; extractWatermark, which extracts the CEH from a user-selected image and writes to the Wa array; inversePermutation, which performs the reverse permutation of the elements of the array Wa; W2Y which converts an array of bits Wa into an array of integers Ya; findX0, which, based on an array of integers Ya, computes the real value of xl; X2Y, which, based on the value of xl, fills the array of integers Yb. Next, the function Y2W is called, which, based on the array of integers Yb, fills the array of bits Wb. After that, the permutation function is called, into which the Wb array is passed. After that, the processing of each image block is carried out in a double cycle. For each image block, the SM value is calculated, which is equal to the number of cases when the values of the corresponding elements of the arrays Wb and Wa are different. If the resulting value is greater than q ^, then all pixels of the Imagel image block in question are assigned a value of 255, which corresponds to white. Recordings to the disk of the received Imagel image in bmp format is performed. At the end of the function, the user displays Complete and the resulting image is displayed.

It is worth noting that the user selects the image through the standard file selection dialog box, which is opened by clicking the Open image button.

As an example in FIG. 2-11 are the results of the proposed method for various cases. The threshold value q * was chosen equal to 0.4. The result of applying the proposed algorithm to the test image Lena.bmp is presented in FIG. 2. Since the embedding of the CEH changes the values of only the smallest significant bits in the binary representation of the values of the image elements, it is impossible to visually detect the presence of the CEH in the image. For a visual representation of the differences between the original image and the image with the integrated CEH, a new image I _s was formed (Fig. 3), the pixel values of which were determined based on a comparison of the pixel values of the compared images. If the pixel values in the image data coincided, then the corresponding pixel of the image Is was assigned a value corresponding to black, otherwise, a value corresponding to white.

To test the resistance of the proposed algorithm to a copy attack, the obtained CEH for the Lena.bmp image was added to other images. The test image peppers.bmp containing the CEH formed for the Lena.bmp image is shown in FIG. 4.

In FIG. 5 shows the image I _s2 , the pixel values of which are obtained based on the results of comparing the elements of the sequences w'j and wj obtained for this image.

If the values of w'j and w _{j are} equal, the color of the corresponding image pixel I _{s2 was} chosen black, otherwise, white. From the results of comparing the values of the elements of the sequences w'j and wj, it was found that the ratio q of the number of elements whose values in these sequences differ, to the total number of elements in each sequence exceeds the value of 0.47. Since the obtained q value is greater than the q ^ value, it is concluded that the CEH was not detected in the image in question.

To assess the resistance of the proposed method to the presence of noise in the communication channel, the values of the selected number of image pixels were randomly replaced. An image of Lena.bmp when changing the values of 20% of the pixels is shown in FIG. 6. The sequence w'j was extracted from this image and the sequence wj was determined based on the values of its elements.

Based on the elementwise comparison of the values of these sequences, an image I _s3 was formed (Fig. 7). The number of different elements in the sequences w'j and wj was about 25% of the total number of elements in each sequence. Thus, for this case, the value q = 0.25 is approximately one and a half times less than the threshold value q ^, which indicates the preservation of the CEH in the image.

When checking the proposed algorithm for the ability to detect modified regions, the values of block sizes were chosen equal to 4x4 pixels. The threshold q ^ value was chosen equal to 0.5. The results obtained for the test image sailboat.bmp are presented. Changes were made to the image with the built-in CEH: a second sailboat and a house on the shore were added

- 4,034,104 lakes (Fig. 8). All pixels belonging to image blocks for which q _B > q _Bth , in FIG. 9 are white. Thus, the application of the proposed method allowed to identify all areas of the image that have been modified.

After that, the ability of the algorithm to detect modified image areas in case of distortion of the values of image elements due to the presence of noise in the communication channel was tested. For this, the values of some image elements were randomly changed. The result of the algorithm when changing the values of 15% of the elements of the modified sailboat.bmp image is shown in FIG. 10. As in the previous case, image blocks for which q> q _th are shaded in white (Fig. 11). Thus, in the case under consideration, it was also possible to determine those areas in the image that have undergone modifications.

Thus, in comparison with the prototype, the claimed method of authentication of images based on digital watermarks formed using chaotic mappings provides a higher degree of protection of digital images from modifications when they are transmitted via real communication channels. With the claimed method, it is possible to restore the parameter of a chaotic sequence with distortion of its individual elements, which makes it possible to detect the CEH in the image and identify areas of the image modified by the attacker in the presence of noise in the communication channel.

Sources of information

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2. Gribunin V.G. Digital steganography / V.G. Gribunin, I.N. Okov, I.V. Turintsev - M .: SolonPress, 2002 .-- S. 5.

3. Pushpa Mala S. Digital image watermarking techniques: a review / S. Pushpa Mala, D. Jayadevappa, K. Ezhilarasan // International Journal of Computer Science and Security. - 2015. - Vol. 9. - P. 140-156.

4. Kutter M. The Watermark Copy Attack / M. Kutter, S. Voloshynovskiy, A. Herrigel // Proceedings of SPIE: Security and Watermarking of Multimedia Content. San Jose, CA, USA, January 2000 - San Jose, 2000. P. 371-380

5. Dawei Zh. A chaos-based robust wavelet-domain watermarking algorithm / Zh. Dawei, Ch. Guanrong, L. Wenbo // Chaos, solitons and fractals. - 2004. - No. 22. - P. 47-54.

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Claims (1)

CLAIM A method for authenticating images based on digital watermarks generated using chaotic mappings, including embedding digital watermarks (CEH) in an image according to the following algorithm: obtaining a digital image, generating a chaotic sequence parameter value based on the original image, generating a chaotic sequence representing a CEH embedding the CEH in the image; decoding the CEH according to the following algorithm: extracting the CEH from the image, restoring the parameter of the chaotic sequence, characterized in that the initial value of the variable of the chaotic mapping is used as the restored parameter of the chaotic sequence, the obtained chaotic sequence is embedded in the smallest significant bits of the pixel values of the image, the modified image areas are detected , performing element-wise comparison of the integrated and extracted CEH.