CN106127669B - Based on the New chaotic image encryption method for protecting area B aker mapping - Google Patents

Abstract

The present invention relates to a kind of image encryption methods, in particular to a kind of New chaotic image encryption method based on guarantor's area B aker mapping, this method process is simple, can not only enhance Space-time Complexity, Computer Precision restricted problem is solved, and is capable of increasing the complexity of Encryption Algorithm.Simultaneously because chaos system uses the quantumchaoticsystem more complicated than common chaos in text, in quantumchaoticsystem, the addition of disturbance quantity is so that chaos system aperiodicity is more preferable, sequence randomness is stronger, at the same common chaos system have " fixed point " and " stability window " the problem of be also improved and solve.

Description

Chaotic Image Encryption Method Based on Area Preserving Baker Map

technical field

The invention relates to an image encryption method, in particular to a chaotic image encryption method based on area-preserving Baker mapping.

Background technique

Traditional encryption methods (such as DES, RSA, etc.) are used in an environment with a small amount of data, although they can effectively protect multimedia copyrights and enhance data security. However, multimedia data (including video, audio, image, etc.) has strong correlation and a large amount of data. Using traditional encryption methods requires a lot of system overhead in most occasions. Therefore, any operation that may increase the complexity of the algorithm will reduce the efficiency of the entire encryption system and affect the practical effect.

The chaotic system is very sensitive to the initial value, the initial state changes slightly, and the chaotic sequence produced after iteration is quite different. Moreover, the chaotic sequence also has good randomness, and these two characteristics meet the requirements of cryptographic key uncertainty. The mixed nature of the chaotic orbit also coincides with the diffusion in the encryption system. The correlation of theoretical characteristics makes the combination of the two inevitable. Theoretically speaking, the random number sequence generated by the chaotic system is an infinite, non-cyclic, and non-periodic sequence; but in fact, the computer is limited by the calculation accuracy, and each operation will lose part of the data, resulting in a certain error. At present, people propose the following three new chaotic image encryption methods: 1. Image encryption methods based on complex chaotic systems. Such as: two successive diffusion encryption methods based on the hyper-chaotic system, etc. 2. Carry out image encryption method in transform domain. Such as: combined with DCT to diffuse and scramble the DC coefficient encryption method, WT-based satellite chaotic encryption method, FrWT-based chaotic image encryption method, etc. 3. Image encryption method based on quantum chaotic system. Such as: use the physical process of quantum chaos to encrypt the image, and use the nonlinear equation of quantum chaos to encrypt the image.

Contents of the invention

The purpose of the present invention is to overcome the shortcomings and deficiencies of the prior art, and provide a chaotic image encryption method based on area-preserving Baker mapping. The process of the method is simple, not only can enhance the space-time complexity, solve the problem of computer precision limitation, but also can increase the complexity of the encryption algorithm. At the same time, because the chaotic system in this paper uses a quantum chaotic system that is more complex than ordinary chaos, the addition of disturbances in the quantum chaotic system makes the chaotic system more non-periodic, and the sequence randomness is stronger. At the same time, the "fixed point" of the ordinary chaotic system And "stability window" issues have also been improved and resolved.

A chaotic image encryption method based on area-preserving Baker mapping, comprising the following steps:

(1) Input the original image whose size is N×M pixels, where the length and width of each pixel are defined as 1.

(2) Segmented image: the image is divided into k (k is a positive integer divisible by N, which can be arbitrarily defined to meet the requirements) small rectangular blocks along the horizontal direction, and each rectangular block has N×n _i pixels. After that, the width of each rectangular block is m. The divided small rectangular block is further divided into n _i sub-blocks along the vertical direction. Each large rectangular block contains N×n _i pixels, and the length of the divided sub-block is n. Therefore, after it is divided into n _i small rectangles, each small rectangle has exactly N pixels, and the size of the divided sub-block is n×m.

(3) In each divided rectangular block of n×m size, read and read sequentially from left to right and from top to bottom to obtain the following sequence of pixel positions:

Then use the area-preserving Baker map to perform operations on its pixels in turn. Carry out the Baker mapping operation on each divided rectangular block sequentially according to the above method. Complete a Baker mapping scrambling operation. In order to meet the needs of practical applications, the entire image needs to be scrambled multiple times. Here, the number of times is defined as S, and S is used as one of the keys (its size can be set according to needs. Considering that too many times will affect performance, in actual use The number of scrambling in the middle is between 50 and 200 times). The area-preserving Baker mapping used is as follows:

In order to use the Baker mapping in this method, some transformations are needed on the mapping. In the original mapping, x∈(0,1), in order to adapt to this method, it needs to be enlarged. The following area-preserving Baker map is obtained.

(4) Read each pixel of the scrambled image in the form of a one-dimensional array C, and represent the pixels as elements in the one-dimensional array C in binary form.

(5) Use the external key x _o , y ₀ , z ₀ , r ₀ , β as the initial value of the quantum Logistic chaotic system to iterate, and discard the value of the first k times of iteration (for convenience, the k value here uses ( 1) k) in step. Iterate again N×M times, and save the values of x, y, and z for each iteration in three sequences of EX, EY, and EZ, where EX represents the chaotic sequence in the x direction, and EY represents the chaos in the y direction sequence, EZ represents the chaotic sequence in the z direction. The quantum logistic chaotic system is as follows:

where r is an adjustable parameter, β is a dissipation parameter, x _n , y _n , z _n are the state values of the system, are the complex conjugates of x _n and z _n , respectively. The value range of system parameters r∈(3.74,4.00), β≥3.5, state values x∈(0,1), y∈(0,0.2461), z∈(0,0.2461) The values of these parameters can satisfy the above Under the premise of the conditions, it can be selected arbitrarily.

(6) Then transform the three sequences of EX, EY, and EZ into the following transformation:

Transform to get FX, FY, FZ sequence. The purpose of the transformation is to convert the obtained decimal sequence into an integer sequence. In order to facilitate subsequent calculations, the sequence in decimal form needs to be converted into binary form.

(7) XOR FX _i to FY _i , and then XOR the result to FZ _i again to obtain the encrypted sequence P.

(8) Then perform the following calculation on the scrambled image sequence C:

The encrypted sequence C ₁ can be obtained.

(9) Restoring the encrypted sequence into an image to complete the entire image encryption process.

In this paper, a composite chaotic encryption algorithm is used to encrypt images. First, the area-preserving Bakert map is used to scramble the image multiple times, and then the quantum Logistic chaotic system is used to perform XOR encryption on the scrambled image. This new image encryption algorithm is used for the first time. The physical structure of the quantum Logistic chaotic system used in this paper is relatively simple, but the existence of disturbances in the quantum chaotic system makes the nonlinear dynamics of the system complex, and also solves the problem of loss of computer precision, which increases the difficulty of deciphering. Moreover, the algorithm has good encryption effect and strong sensitivity. Therefore, this method can effectively protect image security.

Description of drawings

Figure 1 is a flowchart of the entire encryption process;

Figure 2 is the original image before encryption;

Fig. 3 is the image after overall scrambling;

Figure 4 is the image after completing the encryption process.

Detailed ways

The present invention will be further described in detail below in conjunction with the embodiments and the accompanying drawings, but the embodiments of the present invention are not limited thereto.

Example

As shown in Figure 1, the specific process of image encryption by the chaotic image encryption method based on the area-preserving Baker map is as follows:

(1) Select an image with a size of 256×256 as shown in Figure 2 above as the experimental object.

(2) Segment the image: set k value, choose k=32 here. Divide the picture into 32 rectangular blocks along the horizontal direction. Each rectangular block has 256×8 pixels. Then divide the image into 8 rectangular blocks along the vertical direction, then each small rectangle consists of 256 pixels, and the size of each rectangular block is 32×8.

(3) In each divided rectangular block of size 32×8, the position of each pixel is sequentially read from left to right and from top to bottom (that is, the coordinates of the first pixel are (0, 0), and so on) to get the following sequence:

For each coordinate in turn, use the area-preserving Baker map to perform calculations to obtain the new position of the coordinate. And the pixels are rearranged according to each new position to complete the encryption process of the small rectangular block. Then, the same operation as above is performed on each pixel in all the divided small rectangular blocks to complete this round of scrambling operation. In order to achieve a better encryption effect, the entire image needs to be scrambled multiple times. Here, the value S is 83, and the scrambling encryption is performed 83 times, and the image is scrambled multiple times. After completing the entire scrambling process, the image is shown in Figure 3.

(4) Read the scrambled image from top to bottom and from left to right in the form of a one-dimensional array C to obtain the following one-dimensional array C={00101101,0101110,10111010,11011011,...,C _256×256 }.

(5) Generating an encrypted sequence: the encrypted sequence is iteratively obtained by quantum Logistic chaotic mapping, and the following parameters are used in this example: x ₀ =0.85845654, y ₀ =0.03624551548, z ₀ =0.02548634197 r ₀ =3.821, β ₀ =4.231 as quantum Logistic Initial value iteration for a chaotic system. Substitute the initial iteration value into the quantum Logistic chaotic mapping equation, discard the value of the first 16 times, and then iterate 256*256 times, take the iteration value of x to get the chaotic sequence EX={0.8319321839,0.8081942841,0.7391382913...,EX _256×256 } , take the iterative value of y to get the chaotic sequence EY={0.0321817542,0.0301387401,0.0279164138...,EY _256×256 }, take the iterative value of z to get the chaotic sequence EZ={0.0235964183,0.0211387403,0.0207916438...,Y _{6 256}×} .

(6) Then transform the three sequences of EX, EY, and EZ into the following transformation:

Transform to get sequence:

FX={839,841,913...,FX _256×256 },

FY={542,401,138...,FY _256×256 },

FZ={183,403,438...,FZ _256×256 };

The decimal sequence is converted to a binary sequence, because the image is an 8-bit image. In the process of converting to binary, only the first 8 bits of the binary are used for encryption during sequence conversion. get:

FX={11010001,11010010,11100100...,FX _256×256 },

FY={10000111,11001000,10001010...,FY _256×256 },

FZ＝{10110111,11001001,11011011...,FZ _256×256 }

(7) Use FX _i to XOR FY _i to XOR FZ _i again to get the sequence:

P={11100001,11010011,10110101...,P _256×256 }.

(8) Perform scrambled image sequence C Operation, (since the first element has no preceding item, so the first element does not perform the XOR operation in the above formula.) According to the above operation, the encrypted sequence C ₁ ={00001110,00101100,10000001,....C _{256 ×256} }.

(9) Restore the encrypted sequence into an image, as shown in Figure 4 above, to complete the image encryption process.

The above-mentioned embodiment is a preferred embodiment of the present invention, but the embodiment of the present invention is not limited by the above-mentioned embodiment, and any other changes, modifications, substitutions, combinations, Simplifications should be equivalent replacement methods, and all are included in the protection scope of the present invention.

Claims (3)

1. A chaotic image encryption method based on area-preserving Baker mapping, comprising the following steps: (1) The input size is an original image of N×M pixels; (2) Segment the image, and the sub-block size after segmentation is n×m; (3) In each divided rectangular block of n×m size, read and read sequentially from left to right and from top to bottom to obtain the following sequence of pixel positions: Then use the area-preserving Baker mapping to perform operations on its pixels in turn, and perform Baker mapping operations on each of the divided rectangular blocks in turn to complete a Baker mapping scrambling operation. The area-preserving Baker mapping is: (4) read each pixel of the scrambled image in the form of a one-dimensional array C, and represent the pixel in binary form as an element in the one-dimensional array C; (5) Use the external key x ₀ , y ₀ , z ₀ , r ₀ , β as the initial value of the quantum Logistic chaotic system to iterate, discard the value of the first k times of iteration, and then iterate N×M times, and set The values of x, y, and z for each iteration are stored in three sequences EX, EY, and EZ, where EX represents the chaotic sequence in the x direction, EY represents the chaotic sequence in the y direction, and EZ represents the chaotic sequence in the z direction The sequence, quantum Logistic chaotic system is as follows: In the formula, z is an adjustable parameter, β is a dissipation parameter, x _n , y _n , z _n are the state values of the system, are the complex conjugates of x _n and z _n respectively, the value range of system parameters r∈(3.74,4.00), β≥3.5, the state value x∈(0,1), y∈(0,0.2461), z∈( 0,0.2461) The values of these parameters can be selected arbitrarily under the premise of satisfying the above conditions; (6) Then the three sequences of EX, EY, and EZ are transformed as follows: (7) transform to obtain FX, FY, FZ sequence, the purpose of transformation is to convert the obtained decimal sequence into an integer sequence, in order to facilitate subsequent calculations, the sequence in decimal form needs to be converted into binary form here; (8) XOR FX _i to FY _i , and then XOR the result to FZ _i again to obtain the encrypted sequence P; (9) Then perform the following calculation on the scrambled image sequence C: The encrypted sequence C ₁ can be obtained; (10) Restoring the encrypted sequence into an image to complete the entire image encryption process. 2. The chaotic image encryption method according to claim 1, characterized in that: the length and width of each pixel are 1. 3. chaotic image encryption method according to claim 1, is characterized in that: image is divided into k small rectangular blocks along horizontal direction, and k is the positive integer that can be divisible by N, can arbitrarily define the number that satisfies the requirement, each The rectangular block has N×n _i pixels, the width of each rectangular block after division is m, and the divided small rectangular block is divided into n _i sub-blocks along the vertical direction, and each large rectangular block contains N ×n _i pixels, the length of the divided sub-block is n, so after dividing it into n _i small rectangles, each small rectangle has exactly N pixels, and the size of the divided sub-block is n×m.