Chaos-based composite image encryption method

Abstract

The invention discloses a chaos-based composite image encryption method. The method comprises the following steps: 1) establishing a Logistic chaos mapping formula; 2) decomposing the image into a red component, a green component and a blue component; (3) setting values of parameters x0 and alpha, respectively taking x0 and alpha as secret values of the two communication parties, randomly generating a group of chaotic sequence values according to a Logistic chaotic mapping formula, taking the group of chaotic sequence values as sequence values of Arnold transformation matrix parameters a and b, and respectively taking a and b as public values of the two communication parties; 4) changing the initial position of each pixel point in each color component according to an image replacement formula; 5) randomly generating another group of chaotic sequence values according to a Logistic chaotic mapping formula, multiplying the group of chaotic sequence values by the pixel points respectively, and diffusing the graph of each color component to form an encrypted image of each color component; and 6) combining the encrypted color component images into an encrypted image.

Description

Technical Field

[0001] The present invention relates to the technical field of image encryption, and in particular to a chaos-based composite image encryption method. Background Art

[0002] Images are important carriers of information transmission and play an important role in various fields. For example, product information is displayed through product pictures, and personal identity is verified through face pictures. However, image information may be lost, intercepted, or leaked during transmission. In order to prevent security risks caused by loss, interception, or leakage during transmission, the image is generally encrypted into ciphertext by encryption technology at the image sending end, and then transmitted to the image receiving end. After receiving the encrypted image, the image receiving end restores the encrypted image by decryption technology to obtain the original image, thus ensuring the security of image data during transmission.

[0003] In the prior art, Du Yongkang and others from Tianjin University of Technology proposed a color image scrambling encryption technology, which uses Arnold transform and row-column scrambling to encrypt color images. However, this method does not have randomness and chaotic behavior, is easy to be cracked, and has low security. Zhou Xiangzhen and others proposed a compressed image encryption method, which mainly divides the data image to be kept confidential into several image blocks by combining chaotic mapping, and then compresses it in the frequency domain to change the pixel value of the rearranged image to achieve the effect of image encryption. This method has a very large amount of calculation and is not suitable for general communication. Therefore, there is an urgent need for an image encryption method with fast encryption speed and high security. Summary of the invention

[0004] In view of the above-mentioned problems, the present invention provides a chaos-based composite image encryption method, which has fast encryption speed, strong security and good practicability.

[0005] The technical solution of the present invention is: a chaos-based composite image encryption method, comprising the following steps:

[0006] 1) According to the red component, green component and blue component of the image, a Logistic chaotic mapping formula is established;

[0007] 2) Decompose the image to be encrypted into red component, green component and blue component;

[0008] 3) Set the values ​​of the two parameters x0 and α of the Logistic chaotic mapping formula, and use the two parameters x0 and α as the secret values ​​of the asymmetric encryption of the communicating parties respectively, and then randomly generate a group of chaotic sequence values ​​according to the Logistic chaotic mapping formula, use the group of chaotic sequence values ​​as the sequence values ​​of the parameters a and b of the Arnold transformation matrix, and use the parameters a and b as the public values ​​of the asymmetric encryption of the communicating parties respectively;

[0009] 4) According to the Arnold transformation matrix, the initial position of each pixel in each color component is changed through the image permutation formula;

[0010] 5) Another set of chaotic sequence values ​​is randomly generated according to the Logistic chaotic mapping formula, and the set of chaotic sequence values ​​is multiplied by the pixel points after the position change, and the graphics of each color component are diffused to form encrypted images of each color component;

[0011] 6) Combine the encrypted color component images to form an encrypted image.

[0012] Preferably, in step 1), the Logistic chaotic mapping formula is:

[0013] x n+1 =αx n (1-x n )

[0014] In the formula, x n+1 is the value of the next iteration, α is the control parameter, x n is the value of the nth iteration.

[0015] Preferably, in step 3), the Arnold transformation matrix is:

[0016]

[0017] Where T is the Arnold transformation matrix, and a and b are parameters.

[0018] Preferably, in step 3), the image replacement formula is:

[0019] [x ′ ,y ′ ]=[x,y]×T(mod256)

[0020] In the formula, [x ′ ,y ′ ] is the transformed position coordinate of each pixel in the color image, [x, y] is the initial position coordinate of each pixel in the color image, T is the Arnold transformation matrix, and mod256 is the modulus operation on the pixel values ​​in the range of [0, 255].

[0021] The advantages of the present invention are:

[0022] 1) The present invention adopts an asymmetric encryption method, the algorithm strength is complex, and therefore has high security.

[0023] 2) Chaotic mapping is used to calculate encryption keys. Chaos is topologically mixed, sensitive to initial conditions, must have dense periodic orbits, and is nonlinear and irregular. It has good averageness and security, and can encrypt images better.

[0024] 3) The histogram of the encrypted ciphertext image is relatively uniform and flat, making it difficult for attackers to obtain information about the original text from the ciphertext, and it has a high resistance to system attacks in statistics.

[0025] 4) The encryption method can efficiently decrypt images infected by Gaussian noise, Poisson noise and other noises, and has high resistance to noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of an encryption algorithm implementation diagram of an embodiment of the present invention;

[0027] Figure 2 This is an example diagram of encryption and decryption implementation in an embodiment of the present invention;

[0028] Figure 3 Grayscale histogram comparison diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0029] See also Figure 1 , a chaos-based composite image encryption method, comprising the following steps:

[0030] 1) According to the red component, green component and blue component of the image, a Logistic chaotic mapping formula is established; the Logistic chaotic mapping formula is:

[0031] x n+1 =αx n (1-x n )

[0032] In the formula, x n+1 is the value of the next iteration, α is the control parameter, x n is the value of the nth iteration.

[0033] 2) Decompose the image to be encrypted into red component, green component and blue component;

[0034] 3) Set the values ​​of the parameters x0 and α of the Logistic chaotic mapping formula, and use the two parameters x0 and α as the secret values ​​of the asymmetric encryption of the communicating parties respectively. Then, randomly generate a set of chaotic sequence values ​​according to the Logistic chaotic mapping formula, and use the set of chaotic sequence values ​​as the sequence values ​​of the parameters a and b of the Arnold transformation matrix, and use the parameters a and b as the public values ​​of the asymmetric encryption of the communicating parties respectively. The Arnold transformation matrix is:

[0035]

[0036] Where T is the Arnold transformation matrix, and a and b are parameters.

[0037] 4) According to the Arnold transformation matrix, the initial position of each pixel in each color component is changed by the image replacement formula; the image replacement formula is:

[0038] [x ′ ,y ′ ]=[x,y]×T(mod256)

[0039] In the formula, [x ′ ,y ′ ] is the transformed position coordinate of each pixel in the color image, [x, y] is the initial position coordinate of each pixel in the color image, T is the Arnold transformation matrix, and mod256 is the modulus operation on the pixel values ​​in the range of [0, 255].

[0040] 5) Another set of chaotic sequence values ​​is randomly generated according to the Logistic chaotic mapping formula, and the set of chaotic sequence values ​​is multiplied by the pixel points after the position change, and the graphics of each color component are diffused to form encrypted images of each color component;

[0041] 6) Combine the encrypted color component images to form an encrypted image.

[0042] After receiving the image, the image receiving end first reads the encrypted image, then extracts the red component, green component, and blue component of the encrypted image respectively, and then performs Logistic mapping decryption on the encrypted image. Then, the Arnold inverse matrix is ​​calculated using the same encryption parameters x0 and α as well as the a, b sequence, and then the ciphertext pixel [x ′ ,y ′ ] and the Arnold inverse matrix, and then perform the modulus operation to get the original pixel point. The red component, green component, and blue component are decrypted separately, and finally the red component, green component, and blue component are synthesized to get the decrypted image.

[0043] One embodiment of the present invention, see Figure 2, select the 444×333 pixel "China Anhui" art word image, such as Figure 2 (a). The encryption algorithm described in the present invention is used to encrypt the image, thereby obtaining an encrypted image as shown in FIG. Figure 2 As shown in (b), it can be seen that the original information of the image is hidden and the encryption algorithm is effective. After restoring the encrypted image, a clearer decrypted image can be obtained, as shown in Figure 2 As shown in (c), the decrypted image can clearly restore the original image, so that the information of the original image can be obtained. Figure 3 ,according to Figure 3 From the plaintext grayscale histogram of the "China Anhui" art word image and the ciphertext grayscale histogram of the "China Anhui" art word image, it can be seen that the histogram of the encrypted ciphertext image is relatively uniform and flat, making it difficult for attackers to obtain the original text information from the ciphertext, and it has a high resistance to system attacks in statistics.

[0044] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A chaos-based composite image encryption method, characterized in that: The following steps are involved: 1) According to the red component, green component and blue component of the image, a Logistic chaotic mapping formula is established; 2) Decompose the image to be encrypted into red component, green component and blue component; 3) Set the values ​​of the two parameters x0 and α of the Logistic chaotic mapping formula, and use the two parameters x0 and α as the secret values ​​of the asymmetric encryption of the communicating parties respectively, and then randomly generate a group of chaotic sequence values ​​according to the Logistic chaotic mapping formula, use the group of chaotic sequence values ​​as the sequence values ​​of the parameters a and b of the Arnold transformation matrix, and use the parameters a and b as the public values ​​of the asymmetric encryption of the communicating parties respectively; 4) According to the Arnold transformation matrix, the initial position of each pixel in each color component is changed through the image permutation formula; 5) Another set of chaotic sequence values ​​is randomly generated according to the Logistic chaotic mapping formula, and the set of chaotic sequence values ​​is multiplied by the pixel points after the position change, and the graphics of each color component are diffused to form encrypted images of each color component; 6) Combine the encrypted color component images to form an encrypted image.

2. The chaos-based composite image encryption method according to claim 1, characterized in that: In step 1), the Logistic chaotic mapping formula is: x n+1 =αx n (1-x n ) In the formula, x n+1 is the value of the next iteration, α is the control parameter, x n is the value of the nth iteration.

3. The chaos-based composite image encryption method according to claim 1, characterized in that: In step 3), the Arnold transformation matrix is: Where T is the Arnold transformation matrix, and a and b are parameters.

4. The chaos-based composite image encryption method according to claim 1, characterized in that: In step 4), the image replacement formula is: [x ′ ,y ′ ]=[x,y]×T(mod256) In the formula, [x ′ ,y ′ ] is the transformed position coordinate of each pixel in the color image, [x, y] is the initial position coordinate of each pixel in the color image, T is the Arnold transformation matrix, and mod256 is the modulus operation on the pixel values ​​in the range of [0, 255].

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