CN103606126A - Image duel scrambling method based on three-dimensional Logistic mapping - Google Patents

Abstract

The invention relates to an image double reset scrambling method based on three-dimensional Logistic mapping, which belongs to the field of digital image processing. Image positive scrambling process: first obtain the size of the image to be scrambled IMAGE is M×N, respectively obtain 5×M×N three-dimensional Logistic mapping function values according to the three-dimensional Logistic mapping formula, and take the last M of 5×M×N respectively Logistic function values of the first dimension, the last N second dimensions of 5×M×N and the last M×N third dimensions of 5×M×N, and sort them in ascending order respectively to obtain the position sequences index1, index2 and index3; Use the sequence index1 and index2 to scramble the pixel position of IMAGE to obtain the image Image, and then convert the Image into an image; then use the result of taking the remainder 255 of index3 to perform XOR operation with image, change the pixel value of the image, and obtain the image fig, and convert fig to the size of the IMAGE image to obtain the image FIG, which is a scrambled image. The invention uses the function value sequence of the three-dimensional Logistic mapping to respectively change the pixel position and the pixel value of the image to be scrambled, and realizes double-reset scrambling of the image; it has the advantages of strong universality of scrambling and good security.

Description

A Method of Image Double Reset Scrambling Based on 3D Logistic Mapping

technical field

The invention relates to an image double reset scrambling method for three-dimensional Logistic mapping, is an information hiding preprocessing method and an image encryption means, and belongs to the field of digital image processing. the

Background technique

In recent years, with the development of social science and technology and information technology, digital information is being transmitted quickly and conveniently in various forms on the network, and digital images have overcome the difficulties caused by the large storage capacity in the past, and have gradually become a An important carrier of information exchange. But in real life, most of the image information is required to be kept secret, so the security and confidentiality of the image information has gradually been paid close attention to by people. Therefore, digital image scrambling technology has developed rapidly and has been widely used. Over the years, scholars have studied many scrambling methods, which are mainly divided into two categories: one is pixel position scrambling, such as: Arnold scrambling, magic square scrambling, knight parade scrambling and life game scrambling etc.; the other type is pixel value scrambling, such as: Gray code scrambling and chaos scrambling. Among them, the first type of scrambling method only changes the pixel position, without considering whether the scrambled pixel position is evenly spread to the whole image, so the security of the scrambling method cannot be fully guaranteed; the other type of scrambling method only changes the pixel value , the method is relatively monotonous, and there is still a great correlation between adjacent pixels in some methods. the

The existing two types of scrambling methods have been proposed by researchers one after another, and each has its own advantages and disadvantages, but there are few methods that combine these two types of scrambling methods, and the combination of the two can cover the shortcomings of the two. Therefore, it is quite challenging to study a dual reset scrambling method with high security and good applicability. the

Contents of the invention

In order to solve the above-mentioned technical problems, the present invention proposes a double scrambling method for images of three-dimensional Logistic mapping. The method is simple to implement, has good security, high degree of scrambling, good versatility, and can resist certain attacks. It can be better used for information hiding preprocessing and image encryption, and can meet the robustness requirements of digital image encryption and hiding. the

The object of the present invention is achieved through the following technical solutions: a double-reset scrambling method for images based on three-dimensional Logistic mapping, characterized in that: the scrambling method is divided into two parts: forward scrambling of images and reverse scrambling of images;

The image is being scrambled as follows:

Set the image to be scrambled as IMAGE, the number of iterations as cycle, the key of random number as key, and the image after scrambling as FIG; use the function value sequence of three-dimensional Logistic mapping to change the pixel position and pixel value of the image to be scrambled respectively, so that Obtain the scrambled image; the steps are as follows:

1) Define the number of iterations cycle=k;

2) The size of the image IMAGE to be scrambled is obtained as M×N, and 5×M×N three-dimensional Logistic mapping function values are respectively obtained according to the three-dimensional Logistic mapping formula, and the last M first dimensions of 5×M×N, 5 Logistic function values of the last N second dimensions of ×M×N and the last M×N third dimensions of 5×M×N, and sort them in ascending order respectively to obtain the position sequences index1, index2 and index3;

3) Start of an iteration: use the sequence index1 and index2 to scramble the pixel position of IMAGE, get the image Image, and assign it to IMAGE, and an iteration ends;

4) If the cycle is not equal to k, it means that the number of iterations has not been completed, go to step 3) continue to iterate until the number of iterations is k, and the image result obtained at this time is Image;

5) One-dimensionalize the Image into an image; then use the result of taking the remainder 255 from index3 to perform an XOR operation with the image, change the pixel value of the image, obtain the image fig, and convert it into an image Fig of the size of the IMAGE image, and output the final result is FIG, and FIG is the image after scrambling; so far, the scrambling process is over;

Positive scrambling obtains the scrambled image FIG under the premise of scrambling the key, and no information of the original image can be seen from FIG. FIG scrambling effect is good, which ensures the security of the original information. the

The second part is the inverse scrambling of the image, that is, the restoration of the scrambled image. the

The forward and reverse scrambling process of the image is as follows: set the image to be scrambled as FIG, the number of iterations as cycle, the random number key as key, and the scrambled image as OUT; according to the obtained scrambled image, follow the reverse process of forward scrambling To restore the scrambled image, the specific steps are as follows:

1) Define the number of iterations cycle=k;

2) Same as the positive scrambling process, get the same index1, index2, index3;

3) Dimensionalize the scrambled image FIG into fig, and then use index3 to take the result of 255 and perform XOR operation with fig to obtain the image fin, and upgrade fin to the image Fig of FIG size;

4) Start of an iteration: Use the sequence index1 and index2 to inversely scramble the pixel position of Fig to obtain the image Out, and assign the result to Fig, then an iteration ends;

5) If the cycle is not equal to k, it means that the number of iterations has not been completed. Go to step 4) and continue to iterate until the number of iterations is k. At this time, the output of Out is OUT, and OUT is the image after scrambling; so far, inverse scrambling The process is over. the

Under the premise of scrambling the key, the image OUT restored through the inverse scrambling process has no slight difference from the original image, and the purpose of completely restoring the original image is achieved. the

Beneficial effects of the present invention: the scheme of the present invention uses the function value sequence of the three-dimensional Logistic mapping to change the pixel position and pixel value of the image to be scrambled respectively, realizes double reset scrambling of the image, and obtains a lossless scrambled recovery image , and the scrambled image can resist certain geometric attacks. The method adopted in the present invention includes two parts: the positive scrambling process of the image and the reverse scrambling process of the image. The first part is the positive scrambling process of the image: there are three inputs: the image to be scrambled IMAGE, the number of iterations cycle and the random number key key, an output is a scrambled image FIG; the process is to change the pixel position and pixel value of the image to be scrambled by using the function value sequence of the three-dimensional Logistic mapping, so as to obtain the scrambled image. (1) Define the number of iterations cycle=k; (2) The size of the image IMAGE to be scrambled is M×N, and 5×M×N three-dimensional Logistic mapping function values are respectively obtained according to the three-dimensional Logistic mapping formula, and 5×M are respectively taken Logistic function values of the last M first dimensions of ×N, the last N second dimensions of 5×M×N, and the last M×N third dimensions of 5×M×N, and sort them in ascending order respectively to obtain Position sequence index1, index2 and index3; (3) Start of an iteration: Use the sequence index1 and index2 to scramble the pixel position of IMAGE to obtain the image Image, and assign it to IMAGE, and an iteration ends; (4) If the cycle is not equal to k, indicating that the number of iterations has not been completed, go to step (3) and continue to iterate until the number of iterations is k, and the image result obtained at this time is an Image; (5) convert the Image into an image; then use index3 to get the remainder 255 The result is XORed with image, the pixel value of the image is changed, the image fig is obtained, and it is converted into the image Fig of the size of the IMAGE image, and the final result is FIG, which is the scrambled image; so far, the scrambling process is in progress Finish. Positive scrambling obtains the scrambled image FIG under the premise of scrambling the key, and no information of the original image can be seen from FIG. FIG scrambling effect is good, which ensures the security of the original information. The second part is the inverse scrambling of the image, that is, the restoration of the scrambled image. There are three inputs for the image to be scrambled FIG, the number of iterations cycle and the random key key, and one output is the scrambled image OUT; according to the obtained scrambled image, the scrambled image is restored according to the reverse process of the normal scrambled . (1) Define the number of iterations cycle=k; (2) Obtain the same index1, index2, and index3 as in the normal scrambling process; (3) Convert the scrambled image FIG into fig, and then use index3 to get the remainder 255 The result is XORed with fig to obtain the image fin, and the dimension of fin is increased to the image Fig of FIG size; (4) an iteration starts: use the sequence index1 and index2 to inversely scramble the pixel position of Fig to obtain the image Out, and Assign the result to Fig, and one iteration ends; (5) If the cycle is not equal to k, it means that the number of iterations has not been completed, go to step (4) and continue iterating until the number of iterations is k, and the Out output obtained at this time is OUT, OUT is the image after scrambling; so far, the scrambling process is over. the

Under the premise of scrambling the key, the image OUT restored through the inverse scrambling process has no slight difference from the original image, and the purpose of completely restoring the original image is achieved. the

Compared with the existing image scrambling technology, the present invention has the following advantages:

Since the present invention is a method for double-resetting images of three-dimensional Logistic mapping, the method is to use the function value sequence of three-dimensional Logistic mapping to respectively change the pixel position and pixel value of the image to be scrambled, combining pixel position scrambling and pixel value scrambling The characteristics of the two types of methods realize the dual reset scrambling of the image, and the method is simple to implement, which solves the problems of low implementation efficiency of the existing methods. the

The method proposed by the invention uses the function value sequence of the three-dimensional Logistic mapping to adjust the image pixel position and change the image pixel value, and has no requirement on the image size, so the invention has strong versatility for images. the

This method can resist attacks from cutting, noise adding, compression and filtering, and the readability of the restored image will not be affected. It can be better used for information hiding preprocessing and image encryption, and can meet the requirements of digital image encryption and Hidden robustness requirements. the

Description of drawings

Figure 1(a) The overall distribution of 2000 3D Logistic mapping points in 3D space. the

Figure 1(b) The distribution of 2000 3D Logistic mapping points on the xy plane. the

Figure 1(c) The distribution of 2000 3D Logistic mapping points on the yz plane. the

Figure 1(d) The distribution of 2000 3D Logistic mapping points on the zx plane. the

Figure 2(a) is the standard lena original image. the

Figure 2(b) is the scrambling of the standard lena graph by this method. the

Figure 2(c) is the recovery map after scrambling the standard lena map. the

Figure 2(d) is a wide rectangular lena map. the

Figure 2(e) is the wide rectangular lena graph scrambled by this method. the

Figure 2(f) is the recovery map after scrambling the wide rectangular lena map. the

Figure 2(g) is a tall rectangle lena map. the

Figure 2(h) is the scrambled high rectangular lena graph by this method. the

Figure 2(i) is the recovery map after scrambling the high rectangular lena map. the

Fig. 3 is a graph showing the evaluation curve of the scrambling degree of this method by the gray value continuous scrambling degree evaluation method. the

Figure 4(a) Histogram of the standard lena raw image. the

Figure 4(b) The histogram of the image after the standard lena image is scrambled by this method. the

Figure 5(a) The scrambled image after the clipping attack by this method. the

Figure 5(b) The recovered image after the clipping attack by our method. the

Figure 5(c) This method is a scrambled image after adding a salt and pepper noise attack with a noise density of 0.15. the

Fig. 5(d) The recovered image after adding the salt and pepper noise attack with a noise density of 0.15 by this method. the

Figure 5(e) The scrambled image after this method undergoes a JPEG compression attack with a quality factor of 0.7. the

Figure 5(f) The recovered image after compression attack by this method. the

Figure 5(g) The scrambled image after the Gaussian low-pass filtering attack by this method. the

Fig. 5(h) The restored image after Gaussian low-pass filtering attack by this method. the

Detailed ways

The present invention will be further described below in conjunction with accompanying drawing:

The following is an explanation from the theoretical basis:

1) Three-dimensional Logistic mapping function

One-dimensional Logistic mapping is proposed by mathematical ecologist R.May in a review published in the British journal Nature. According to one-dimensional Logistic mapping, the form of three-dimensional Logistic mapping is as follows:

Among them, g ₁ , g ₂ , and g ₃ are coupling items, and the following situations can be taken: (1) g ₁ = rx ₃ , g ₂ = primary coupling items of rx ₁ and g ₃ = rx ₂ ; (2) g ₁ =g ₂ =g ₃ =rx ₁ x ₂ x ₃ symmetric coupling term; (3) asymmetric secondary coupling, etc. This method adopts the three-dimensional Logistic mapping under the condition (2).

The three-dimensional Logistic mapping function of the symmetrical cubic coupling term is as follows:

Let f: R ³ ×R ^3→ R ³ , X'=f(X,v), have

Among them, u ₁ , u ₂ , u ₃ and r are the four parameters in the three-dimensional Logistic mapping function, and the values of the parameters will affect the final state of the system; when u ₁ =u ₂ =u ₃ , when r is greater than 0.69, the system Enter the chaotic state (the chaotic state refers to the similar random process in the nonlinear dynamical system, which is neither periodic nor convergent), when u ₁ , u ₂ , u ₃ are all different (u ₁ , u ₂ , When u ₃ can be generated by a random number generator), the system enters a chaotic state when r is greater than 0.76; this method takes r=0.78; in addition, x ₁ , x ₂ , and x ₃ are the function values of the previous state of the three-dimensional Logistic mapping function (No. A state is used as the initial value of the function, which can be generated by a random number generator), and x' ₁ , x' ₂ , x' ₃ are the function values of the next state.

2) Three-dimensional Logistic mapping function distribution diagram

Set the parameter values of the three-dimensional Logistic mapping function u ₁ =0.6, u ₂ =0.65, u ₃ =0.7; the initial value of the function is generated by a random number generator (the random number seed is rand('state', key), where key=12 ); r=0.78; 100,000 points were generated using the three-dimensional Logistic mapping function formula, and the three-dimensional Logistic distribution diagram of these points was drawn by taking the 2,000 points at the end, as shown in Figure 1. Among them, Figure 1(a) is the overall distribution map of 2000 points in three-dimensional space, and Figure 1(b)(c)(d) is the distribution map of these 2000 points on the xy, yz and zx planes respectively. It can be seen that these 2000 points are basically hashed to the entire space of the plane, which shows that its hashing property is good, basically in a chaotic state, and can be better suitable for scrambling.

3) Image scrambling

The purpose of image scrambling is to convert the image information that originally displayed rules into a disordered display, which lays a good foundation for further processing such as encryption or data embedding. the

The first part: Using the function value sequence of the three-dimensional Logistic mapping to change the pixel position and pixel value of the image to be scrambled, the double scrambling of the image is realized, and the scrambled image FIG is obtained. the

This part has three inputs for the image to be scrambled IMAGE, the number of iterations cycle and the random key key, and one output is the scrambled image FIG; the process is to use the function value sequence of the three-dimensional Logistic mapping to change the pixels of the image to be scrambled respectively position and pixel value to get the scrambled image. The scrambling key is the number of iterations cycle and the random number key. the

1) Define the number of iterations cycle=k;

Among them, cycle is one of the scrambling keys, defined by the user, for example: cycle=1;

2) The size of the image IMAGE to be scrambled is obtained as M×N, and 5×M×N three-dimensional Logistic mapping function values are respectively obtained according to the three-dimensional Logistic mapping formula, and the last M first dimensions of 5×M×N, 5 ×M×N at the end of the N second dimension and 5×M×N at the end of the M×N third dimension of the Logistic function values, and sort them in ascending order respectively to obtain the position sequence index1, index2 and index3; where, in Before obtaining the value of the three-dimensional Logistic mapping function, you must first set its parameter value and its function initial value;

Here we use the random number generator rand() to set the initial value of the function and some parameter values. The random number generator needs the user to define the random number seed rand('state', key), and key is one of the scrambling keys, which is any Integer, such as: key=12; in addition, the setting of the function parameter value must reach the chaotic state to obtain the ideal scrambling effect, and this chaotic state is related to the definition of the random number seed; it is also related to the generated 5× M×N three-dimensional The value of the Logistic mapping function is related to the value of the Logistic mapping function. The reason why the value of the function is more than the number of image pixels is that in the obtained 3D Logistic mapping function value, the farther the position is, the better the chaotic hashability is, so we usually take the last one function value of the number. The position sequence index1, index2, index3 is a set of integer sequence numbers; for example: a is such a set of numbers: 0.1230, 0.3450, 0.7853, 0.2970, 0.0972, the position sequence indexa of a is 1, 2, 3, 4, 5; After a is sorted in ascending order, b is obtained: 0.0972, 0.1230, 0.2970, 0.3450, 0.7853, and the position sequence indexb of b is also obtained as 5, 1, 4, 2, 3;

3) Start of an iteration: use the sequence index1 and index2 to scramble the pixel position of IMAGE, get the image Image, and assign it to IMAGE, and an iteration ends;

Among them, the pixel position scrambling of the image is to change the pixel position of the image; the position scrambling adopted here is: a pixel coordinate is (i, j), the image to be scrambled is IMAGE, and the image after scrambling is f, then the The position scrambling process of this pixel point is: f(index1(i), index(j))=IMAGE(i, j), that is to say, adjust the pixel point at coordinate (i, j) to (index1(i ), index (j)); the other pixels of the image are adjusted in this way in turn. the

4) If the cycle is not equal to k, it means that the number of iterations has not been completed, go to step 3) continue to iterate until the number of iterations is k, and the image result obtained at this time is Image;

5) One-dimensionalize the Image into an image; then use the result of taking the remainder 255 from index3 to perform an XOR operation with the image, change the pixel value of the image, obtain the image fig, and convert it into an image Fig of the size of the IMAGE image, and output the final result is FIG, and FIG is the image after scrambling; so far, the scrambling process is over. the

Positive scrambling obtains the scrambled image FIG under the premise of scrambling the key, and no information of the original image can be seen from FIG. FIG scrambling effect is good, which ensures the security of the original information. the

The second part is the inverse scrambling of the image, that is, the restoration of the scrambled image. There are three inputs for the image to be scrambled FIG, the number of iterations cycle and the random key key, and one output is the scrambled image OUT; according to the obtained scrambled image, the scrambled image is restored according to the reverse process of the normal scrambled . the

1) Define the number of iterations cycle=k;

Among them, the cycle must be consistent with the positive scrambling process, that is, cycle=1;

2) Same as the positive scrambling process, get the same index1, index2, index3;

3) Dimensionalize the scrambled image FIG into fig, and then use index3 to take the result of 255 and perform XOR operation with fig to obtain the image fin, and upgrade fin to the image Fig of FIG size;

Among them, the two XOR operations reach the original state again, so the inverse scrambling process only needs to perform one more XOR operation on the basis of the positive scrambling process, which is the inverse process of the XOR operation in the positive scrambling process. the

4) Start of an iteration: Use the sequence index1 and index2 to inversely scramble the pixel position of Fig to obtain the image Out, and assign the result to Fig, then an iteration ends;

Among them, the inverse scrambling of the pixel position is opposite to the scrambling of the pixel position in the forward scrambling process 3), namely: f(i, j)=IMAGE(index1(i), index(j)). the

5) If the cycle is not equal to k, it means that the number of iterations has not been completed, go to step 4) continue to iterate until the number of iterations is k, and the output of Out obtained at this time is OUT, and OUT is the image after scrambling; so far, scrambling The process is over. the

Under the premise of scrambling the key, the image OUT restored through the inverse scrambling process has no slight difference from the original image, and the purpose of completely restoring the original image is achieved. the

A grayscale image can be regarded as a two-dimensional array, and the pixel position and pixel value of the image to be scrambled are changed respectively by using the function value sequence of the three-dimensional Logistic mapping, combining the characteristics of the two methods of pixel position scrambling and pixel value scrambling , to realize the dual reset scrambling of the image; and the method is relatively easy to implement, and the scrambling has no requirement on the size of the image, and has a good ability to resist illegal attacks. the

To sum up, by analyzing the 3D Logistic mapping function, and using its function value sequence to realize the double scrambling of the image, we obtained a 3D Logistic mapping image double scrambling method. the

1) Observation of scrambling effect

A standard lena map whose size is a square matrix with a size of 512×512 and a lena map whose size is a rectangular matrix with a size of 277×512 and 512×321 are selected, and the method of the present invention is used to scramble the map. The scrambling key cycle is 1, and the key is 12; as shown in Figure 2, (a) is the original lena image with a size of 512×512, (b) is the scrambling image obtained by (a) the normal scrambling process, ( c) is (b) the restored image obtained by the inverse scrambling process; (d) is the original lena image with a size of 277×512, (e) is the scrambled image obtained by (d) the positive scrambling process, (f ) is (e) the restored image obtained by the inverse scrambling process; (g) is the original lena image with a size of 512×321, (h) is the scrambled image obtained by (g) the forward scrambling process, (i) (h) The restored image obtained through the inverse scrambling process. From (b) (e) (h), it can be seen that the visual effect of image scrambling is good, and the scrambled image is the same as white noise; from (c) (f) (i), it can be seen that the restored image is the same as the original There is no loss in comparison to the image. It shows that the scrambling effect of the present invention is basically successful. the

2) Evaluation of scrambling effect

We use gray value continuous scrambling degree evaluation method to carry out scrambling degree evaluation to method of the present invention:

The degree of scrambling of digital images

Among them, ||F' _m×n || represents the number of continuous regions in the scrambled image matrix, and ||F _m×n || represents the number of continuous regions in the original image matrix.

The evaluation results of the degree of scrambling are shown in Figure 3. A lena graph with a size of 512×512 is selected, and the number of scrambling times is 200. From the evaluation curve of the degree of scrambling, it can be seen that there is no period of scrambling, and there is no security recovery problem; scrambling can quickly achieve the ideal scrambling effect and stable scrambling state; the scrambling degree is relatively high. the

3) Histogram feature analysis

In Figure 4, (a) is the histogram of a lena image with a size of 512×512, and (b) is the histogram of a 512×512 lena image after being scrambled by this method. It can be seen from Figure 4(b) that the histogram of the image has changed after scrambling, and the gray value is uniformly distributed, indicating that the image after scrambling by this method appears as white noise, which increases the risk of illegal attacks. It is difficult for the attacker to attack according to the statistical characteristics of the scrambled image, thus improving the security of the method. the

4) Anti-attack test

In the experiment, a lena image of 512×512 was selected, and the scrambled image was cut, added noise, JPEG compressed and filtered. After the scrambled image is processed by these attacks, it still has good recoverability. This process is the anti-attack test of the scrambled image. In Figure 5, (a) is the scrambled image after the cut part, where the cut part is the (234:453, 244:463) and (65:191, 66:192) pixels of the image, and (b) is the cut The restored image after cutting; (c) the scrambled image after adding salt and pepper noise, the noise density is 0.15, (d) the restored image after adding noise; (e) the scrambled image after JPEG compression with a quality factor of 0.7, (f) is the restored image after compression; (g) is the scrambled image after filtering, using a 3×3 Gaussian low-pass filter with a standard deviation of 0.4, (h) is the restored image after filtering. Figure 5(a)(c)(e)(g) shows the result of the scrambled image after attack processing, and the restored image after attack processing is shown in Figure 5(b)(d)(f)(h) Show. The above experimental results show that certain attack processing on the image scrambled by the method in this paper will not affect the intelligibility of the restored image, which shows that the method has certain anti-attack ability. the

Claims (1)

1. the doubling of the image disorder method based on three-dimensional Logistic mapping, is characterized in that: this disorder method is divided into the positive scramble of image, the random two parts of the inverted of image;

The positive scramble process of described image is as follows:

If treat that scramble image is that IMAGE, iterations are that cycle, random number key are key, the image after scramble is FIG; Utilize the functional value sequence of three-dimensional Logistic mapping to change respectively location of pixels and the pixel value for the treatment of scramble image, thereby obtain the image after scramble; Step is as follows:

1) definition iterations cycle=k;

2) obtain and treat that scramble image I MAGE is of a size of M * N, according to three-dimensional Logistic mapping formula, obtain respectively 5 * M * N three-dimensional Logistic mapping function value, get respectively end M the first dimension of 5 * M * N, the Logistic functional value of end M * N third dimension of end N second peacekeeping 5 * M * N of 5 * M * N, and respectively they are carried out to ascending sort, obtain position sequence index1, index2 and index3;

3) iteration starts: with sequence index1 and index2, IMAGE is carried out to location of pixels scramble, obtains image I mage, and by its assignment to IMAGE, one time iteration finishes;

4) if cycle is not equal to k, illustrate that iterations does not complete, forward step 3) to and continue iteration, until iterations is k, the image result now obtaining is Image;

5) Image one dimension is turned to image; With result and the image of index3 remainder 255, carry out XOR again, change image pixel value, obtain image fig, and be converted into the image Fig of IMAGE picture size size, output net result is FIG, and FIG is image after scramble; So far, positive scramble process finishes;

The random process of the positive inverted of described image is as follows:

If treat that scramble image is that FIG, iterations are cycle, random number key is key, and the image after scramble is OUT; Scramble image according to obtaining, carries out the recovery of scramble image according to the inverse process of positive scramble, concrete steps are as follows:

1) definition iterations cycle=k;

2) the same with positive scramble process, obtain identical index1, index2, index3;

3) scramble image FIG one dimension is turned to fig, then carry out XOR with result and the fig of index3 remainder 255, obtain image fin, and fin is risen to the image Fig that ties up into FIG size;

4) iteration starts: with sequence index1 and index2, Fig is carried out to location of pixels inverted disorderly, obtains image Out, and by result assignment to Fig, an iteration finishes;

5) if cycle is not equal to k, illustrate that iterations does not complete, forward step 4) to and continue iteration, until iterations is k, the Out now obtaining is output as OUT, OUT is image after scramble; So far, the random process of inverted finishes.

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