An image encryption method based on five-dimensional conservative hyperchaotic system and bit-plane decomposition diffusion

Abstract

The application discloses an image encryption method based on a five-dimensional conservative hyperchaotic system and bit plane segmentation diffusion, and comprises the following steps: constructing a five-dimensional Hamilton energy conservative hyperchaotic system; obtaining an encryption key through a hash value and an initial key; taking the encryption key as an initial value of the five-dimensional Hamilton conservative hyperchaotic system to obtain five groups of chaotic sequences; reconstructing a to-be-encrypted plaintext image into a one-dimensional array, performing a permutation operation on the to-be-encrypted plaintext image to obtain a scrambling result; performing bit plane segmentation processing on the scrambling result, merging the processing result to obtain a first diffusion result; performing an exclusive OR operation on the diffusion result and a chaotic sequence X1 to obtain a second diffusion result, and obtaining an encrypted image. The application utilizes the high complexity and wide variable value range of the conservative hyperchaotic system to improve the key space of the encryption method; and combines the bit plane segmentation method to perform a diffusion operation, thereby improving the diffusion effect and the security of the encryption.

Description

Technical Field

[0001] This invention relates to the field of image encryption technology, specifically to an image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion. Background Technology

[0002] With the rapid development of 5G network communication technology and the widespread adoption of internet infrastructure, multimedia data such as images, audio, and video have become the main content of information exchange on the internet. However, while facilitating communication, internet technology has also brought significant security risks. Ensuring the security of information during network transmission has become an urgent problem to solve. Encrypting digital images using encryption algorithms can effectively protect image security during transmission. However, due to the characteristics of digital images, such as large data volume, high information redundancy, and strong correlation, traditional text encryption algorithms such as DES, AES, and IDEA are no longer suitable for image encryption. Therefore, it is necessary to research new encryption technologies to achieve encrypted processing of image data.

[0003] Because chaotic systems possess characteristics similar to those in cryptography, such as sensitivity to parameters and initial values, and unpredictability, many image encryption methods based on chaotic systems have been proposed. These methods are mostly based on the fundamental framework of "permutation and diffusion." Permutation rearranges the pixel positions of the original image without changing the pixel values; diffusion achieves encryption by altering the pixel values. A chaotic system, acting as a pseudo-random number generator, is applied to the encryption method, providing the permutation index sequence and the diffusion sequence. The diffusion result is obtained by taking the remainder of the diffusion sequence with the original pixel values ​​or by performing an XOR operation. After permutation and diffusion processing, the encrypted image is obtained. Currently, most image encryption methods are based on low-dimensional traditional chaotic systems such as Logistic chaos, Tent chaos, and Lorenz chaos, as well as some improved chaotic systems based on traditional methods.

[0004] In recent years, in order to improve the security of image encryption methods based on chaotic systems, scholars have constructed higher-dimensional dissipative chaotic systems and applied them to image encryption algorithms. However, current chaotic image encryption methods still have certain limitations: (1) Most encryption methods are based on low-dimensional chaotic systems, which have small key spaces, poor security, and are subject to prediction; (2) Most are based on dissipative chaotic systems, which have attractors, and once the attractors are located, they can provide decryption information to the decipherer; (3) The encryption methods only use one round of permutation and diffusion operations, resulting in strong correlation of ciphertext and low security of encryption results; (4) The key is not related to the plaintext image, and its resistance to differential attacks is relatively poor. Summary of the Invention

[0005] The purpose of this invention is to propose an image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion. This method utilizes the high complexity and wide range of variable values ​​of the conservative hyperchaotic system to improve the key space of the encryption method; and combines the bit-plane segmentation method to perform diffusion operations, thereby improving the diffusion effect and encryption security.

[0006] To achieve the above objectives, this application proposes an image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion, comprising:

[0007] Constructing a five-dimensional Hamiltonian energy-conserved superchaotic system;

[0008] Obtain a plaintext image P of size M×N to be encrypted, calculate the hash value of the plaintext image P using the hash function SHA-256, and obtain the encryption key using the hash value and the initial key;

[0009] Using the encryption key as the initial value of the five-dimensional Hamiltonian conservative hyperchaotic system, five sets of chaotic sequences are obtained. The chaotic sequences are quantized to obtain a pseudo-random integer chaotic sequence X1 with a value range of 0 to 255, and pseudo-random sequences Y1, Z1, U1, and V1 with a value range of 0 to 3.

[0010] The plaintext image P to be encrypted is reconstructed into a one-dimensional array. The chaotic sequence X1 is sorted to obtain the index sequence X2. The plaintext image P to be encrypted is then permuted according to the index sequence X2 to obtain the scrambling result.

[0011] The scrambling result is processed by bit-plane segmentation to obtain four sub-images with pixel ranges from 0 to 3. These sub-images are then XORed with pseudo-random sequences Y1, Z1, U1, and V1 respectively. The results are then merged to obtain the first diffusion result.

[0012] The diffusion result is XORed with the chaotic sequence X1 to obtain the second diffusion result. Based on this diffusion result, the M×N two-dimensional matrix is ​​restored to obtain the encrypted image.

[0013] Furthermore, the mathematical model of the five-dimensional Hamiltonian energy conservative hyperchaotic system is as follows:

[0014]

[0015] Where x i For system variables, Π i c are system parameters, i = 1, 2, 3, 4, 5.

[0016] Further, the encryption key is obtained through the hash value and the initial key, specifically: the hash value HK is calculated by using the hash function SHA-256 on the plaintext image P to be encrypted, and the encryption key K is obtained based on the initial key (x,y,z,u,v) input by the user.

[0017] HK = SHA_256(P);

[0018]

[0019] K=(x+hk1, y+hk2, z+hk3; u+hk4; v+hk5).

[0020] Furthermore, using the encryption key K as the initial value of the five-dimensional Hamiltonian conservative hyperchaotic system, five sets of chaotic sequences X, Y, Z, U, and V are obtained. These chaotic sequences X, Y, Z, U, and V are quantized, and the first N elements of each chaotic sequence are discarded, resulting in a pseudo-random integer chaotic sequence X1 with values ​​ranging from 0 to 255, and pseudo-random sequences Y1, Z1, U1, and V1 with values ​​ranging from 0 to 3. Specifically:

[0021]

[0022] mod() is the modulo function, and floor() is the floor function.

[0023] Furthermore, the plaintext image P to be encrypted is reconstructed into a one-dimensional array of length M×N. The chaotic sequence X1 is sorted to obtain the index sequence X2. A permutation operation is then performed on the plaintext image P to be encrypted based on the index sequence X2 to obtain the scrambling result P1, specifically as follows:

[0024] P = reshape(P, 1, M × N)

[0025] [~,X2] = sort(X1)

[0026] P1(i)=P(X2(i)),i=1,2,...,M×N

[0027] The reshape() function is used to reshape the array, and the sort() function is used to sort it.

[0028] Further, the scrambling result P1 is processed by bit-plane segmentation, converting it into an 8-bit binary image sequence S of size M×N×8. The 8-bit binary image sequence is then divided into four groups of two-bit binary sequences of size M×N×2, grouped by two bits. These binary sequences are then converted to decimal to obtain four sub-images s1, s2, s3, and s4 with values ​​between 0 and 3. These sub-images are then XORed with the pseudo-random sequences Y1, Z1, U1, and V1, respectively. The processed results d1, d2, d3, and d4 are merged to obtain the first diffusion result P2.

[0029] S(:,:)=dec2bin(P1,8)

[0030]

[0031]

[0032] P2 = dec2bin([d1 d2 d3 d4])

[0033] Among them, dec2bin() is the decimal to binary conversion function, bin2dec() is the binary to decimal conversion function, and bitxor() is the bitwise XOR function.

[0034] Furthermore, the diffusion result P2 is XORed with the chaotic sequence X1 to obtain the second diffusion result. Based on this diffusion result, an M×N two-dimensional matrix is ​​recovered, resulting in the encrypted image E.

[0035] E' = bitxor(P2,X1);

[0036] E = reshape(E', M, N).

[0037] The advantages of the above technical solutions adopted in this invention compared with the prior art are as follows:

[0038] 1. This invention is based on a five-dimensional Hamiltonian energy conservative hyperchaotic system. Compared with other low-dimensional chaotic systems, this chaotic system does not have an attractor, has more complex dynamic properties and a larger range of variable values, which increases the key space, encryption complexity and security of the encryption method, and can effectively resist various common attacks.

[0039] 2. The diffusion method based on bit-plane segmentation processing in this invention improves the utilization rate of chaotic sequences, enhances diffusion efficiency, and makes the diffusion results more complete.

[0040] 3. This invention uses the SHA-256 method, which incorporates plaintext image information as a component of the key, thereby improving the plaintext sensitivity of the encryption method and enhancing its ability to resist plaintext attacks. Attached Figure Description

[0041] Figure 1 The flowchart shows an image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion.

[0042] Figure 2 Lyapunov exponent diagram and bifurcation diagram for a five-dimensional Hamiltonian energy conservative hyperchaotic system;

[0043] Figure 3 Phase trajectory diagram of a five-dimensional Hamiltonian energy conservative hyperchaotic system;

[0044] Figure 4 This is a flowchart of the overall encryption process;

[0045] Figure 5 The original plaintext image to be encrypted;

[0046] Figure 6 A diagram illustrating the scrambling of the index sequence;

[0047] Figure 7 This is a schematic diagram of bit-plane segmentation processing;

[0048] Figure 8 In response to Figure 5 The encryption and decryption results of the original image are shown below;

[0049] Figure 9 In response to Figure 5 Histogram of the encryption / decryption experiment of the original image shown;

[0050] Figure 10 In response to Figure 5 Correlation distribution of plaintext and ciphertext images in Lena images along the horizontal, vertical, and diagonal directions;

[0051] Figure 11 In response to Figure 5 Images showing the effects of cropping Lena images to varying degrees.

[0052] Figure 12 In response to Figure 5 Images of Lena images subjected to different levels of salt and pepper noise attack. Specific implementation methods

[0053] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit the application; that is, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0054] Example 1

[0055] like Figure 1 As shown, this embodiment provides an image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion, specifically including:

[0056] S1. Construct a five-dimensional Hamiltonian energy-conservative hyperchaotic system;

[0057] Specifically, the mathematical model of a hyperchaotic system with Hamiltonian energy conservation and two positive Lyapunov exponents is shown in equation (1):

[0058]

[0059] Where x i For system variables, Π i c are system parameters, i = 1, 2, 3, 4, 5.

[0060] The parameters (Π1,Π2,Π3,Π4,Π5,c) are set to (9,7,5,4,8,1), with initial values ​​of (1,x). 20 ,1,1,1.5). For example Figure 2 As shown, within a large range of initial values, there are always two Lyapunov exponents greater than 0, and the sum of the exponents is always 0, indicating that the chaotic system has a stable hyperchaotic state. Furthermore, from... Figure 3 As can be seen from the phase diagram, the system lacks an attractor, and the trajectory of motion almost traverses the entire system space, exhibiting strong complexity and randomness.

[0061] S2. Obtain a plaintext image P of size M×N to be encrypted, calculate the hash value of the plaintext image P using the hash function SHA-256, and obtain the encryption key using the hash value and the initial key;

[0062] The specific encryption process is as follows: Figure 4 As shown, using Figure 5 The following explanation uses the grayscale image Lena as an example. The image is denoted as P and its size is denoted as M×N, where M=N=256.

[0063] Using the plaintext image P to be encrypted as input to the SHA-256 function, we obtain a 64-bit hexadecimal hash sequence HK:

[0064] HK='b745b123052c072920e6970815e4cbe9719

[0065] f983c129334bf0e26d71d0781ef6a'

[0066] Convert HK to decimal form bit by bit, and you get the following result:

[0067] HK(:) = hex2dec(HK(:))

[0068]

[0069] Based on the initial key (1,1,1.5,1,1) input by the user, the system encryption key is calculated as follows:

[0070] K=(1.1479,1.1502,1.7394,1.1878,1.1690).

[0071] S3. Using the encryption key as the initial value of the five-dimensional Hamiltonian conservative hyperchaotic system, five sets of chaotic sequences are obtained, and the chaotic sequences are quantized to obtain a pseudo-random integer chaotic sequence X1 with a value range of 0 to 255, and pseudo-random sequences Y1, Z1, U1, and V1 with a value range of 0 to 3.

[0072] Specifically, the encryption key obtained above is substituted as an initial value into the mathematical model of the hyperchaotic system. Using the Runge-Kutta algorithm, iterations are performed 1000+M×N times to obtain five sets of pseudo-random chaotic sequences X, Y, Z, U, and V, discarding the first 1000 elements of each sequence. Further quantization is performed on each chaotic sequence to obtain sequences X1, Y1, Z1, U1, and V1 of length M×N.

[0073]

[0074] S4. Reconstruct the plaintext image P to be encrypted into a one-dimensional array, sort the chaotic sequence X1 to obtain the index sequence X2, and perform a permutation operation on the plaintext image P to be encrypted according to the index sequence X2 to obtain the scrambling result.

[0075] Specifically, first, the chaotic sequence X1 is sorted using the sort() function to obtain the index sequence. Then, the image P is reconstructed into a one-dimensional array and scrambled according to the index order to obtain P1. The scrambling process is as follows: Figure 6 As shown.

[0076] S5. Perform bit-plane segmentation on the scrambling result to obtain four sub-images with pixel values ​​ranging from 0 to 3. XOR these sub-images with the pseudo-random sequences Y1, Z1, U1, and V1 respectively. Combine the processed results to obtain the first diffusion result.

[0077] Specifically, based on the scrambling result P1, a diffusion operation is performed on it to perform bit-plane segmentation, resulting in the first diffusion result P2:

[0078] like Figure 7As shown, the scrambling result plaintext P1 is first converted into an 8-bit binary image sequence S of size M×N×8. Then, the 8-bit binary image sequence is divided into four groups of two-bit binary sequences of size M×N×2, according to the form of two-bit binary numbers per group. Further converting the binary numbers to decimal yields four sub-images s1, s2, s3, and s4 with values ​​between 0 and 3. These sub-images are then XORed with pseudo-random sequences Y1, Z1, U1, and V1 respectively. This method improves the utilization rate and diffusion effect of chaotic sequences.

[0079] S(:,:)=dec2bin(P1,8)

[0080]

[0081]

[0082] P2 = dec2bin([d1 d2 d3 d4])

[0083] S6. XOR the diffusion result with the chaotic sequence X1 to obtain the second diffusion result. Based on this diffusion result, reconstruct an M×N two-dimensional matrix to obtain the encrypted image E:

[0084] E' = bitxor(P2,X1);

[0085] E = reshape(E', M, N).

[0086] This embodiment also provides an image decryption method based on a conservative hyperchaotic system and bit-plane segmentation diffusion, specifically including:

[0087] A1. The decryption method uses the same key as the encryption method;

[0088] A2. Generate identical chaotic sequences X1, Y1, Z1, U1, and V1 based on the key;

[0089] A3. Reconstruct the encrypted image E into a one-dimensional array and perform XOR diffusion processing with the sequence X1;

[0090] A4. Based on the above results, perform bit-plane segmentation processing and spread it with the chaotic sequences Y1, Z1, U1 and V1 respectively;

[0091] A5. Based on the above results, scramble the sequence according to the index of sequence X1;

[0092] A6. Restore the scrambled result to an M×N two-dimensional matrix to obtain the decrypted image.

[0093] For example Figure 4 The image shown was used for encryption and decryption experiments, and the resulting simulation image is as follows. Figure 8As shown in the figure, the encrypted image is completely disordered, and no valid information from the original image can be discerned. Furthermore, to more intuitively demonstrate the security performance of the multi-image encryption method of this invention, this embodiment provides histograms of the Lena image before and after encryption / decryption, as shown below. Figure 9 As shown in the figure, the histogram of the encrypted image Lena is uniformly distributed, making it impossible for an attacker to extract useful information. Furthermore, to more intuitively demonstrate the security of the image encryption method of this invention, this embodiment also provides a correlation analysis diagram before and after encryption, as shown below. Figure 10 As shown in the figure, the correlation of encrypted images is effectively reduced. Furthermore... Figure 11 and Figure 12 The encryption method is shown to resist shearing and noise attacks, indicating that the method has strong robustness.

[0094] The foregoing description of specific exemplary embodiments of the invention is for illustrative and explanatory purposes. These descriptions are not intended to limit the invention to the precise forms disclosed, and it will be apparent that many changes and variations can be made in accordance with the foregoing teachings. The exemplary embodiments were chosen and described in order to explain the specific principles of the invention and its practical application, thereby enabling those skilled in the art to implement and utilize various different exemplary embodiments of the invention, as well as various different choices and variations. The scope of the invention is intended to be defined by the claims and their equivalents.

Claims

1. An image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion, characterized in that, include: Constructing a five-dimensional Hamiltonian energy-conserved superchaotic system; Obtain a plaintext image P of size M×N to be encrypted, calculate the hash value of the plaintext image P using the hash function SHA-256, and obtain the encryption key using the hash value and the initial key; Using the encryption key as the initial value of the five-dimensional Hamiltonian conservative hyperchaotic system, five sets of chaotic sequences are obtained. The chaotic sequences are quantized to obtain a pseudo-random integer chaotic sequence X1 with a value range of 0 to 255, and pseudo-random sequences Y1, Z1, U1, and V1 with a value range of 0 to 3. The plaintext image P to be encrypted is reconstructed into a one-dimensional array. The chaotic sequence X1 is sorted to obtain the index sequence X2. The plaintext image P to be encrypted is then permuted according to the index sequence X2 to obtain the scrambling result. The scrambling result is processed by bit-plane segmentation to obtain four sub-images with pixel ranges from 0 to 3. These sub-images are then XORed with pseudo-random sequences Y1, Z1, U1, and V1 respectively. The results are then merged to obtain the first diffusion result. The diffusion result is XORed with the chaotic sequence X1 to obtain the second diffusion result. Based on this diffusion result, the M×N two-dimensional matrix is ​​restored to obtain the encrypted image.

2. The image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion according to claim 1, characterized in that, The mathematical model of the five-dimensional Hamiltonian energy conservative hyperchaotic system is as follows: Where x i For system variables, Π i c are system parameters, i = 1, 2, 3, 4, 5.

3. The image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion according to claim 1, characterized in that, The encryption key is obtained by using the hash value and the initial key, specifically: the hash value HK is calculated on the plaintext image P to be encrypted using the hash function SHA-256, and the encryption key K is obtained based on the initial key (x,y,z,u,v) input by the user. HK = SHA_256(P); K=(x+hk1, y+hk2, z+hk3; u+hk4; v+hk5).

4. The image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion according to claim 1, characterized in that, Using the encryption key K as the initial value of the five-dimensional Hamiltonian conservative hyperchaotic system, five sets of chaotic sequences X, Y, Z, U, and V are obtained. These sequences are then quantized, and the first N elements of each sequence are discarded, resulting in a pseudo-random integer chaotic sequence X1 with values ​​ranging from 0 to 255, and pseudo-random sequences Y1, Z1, U1, and V1 with values ​​ranging from 0 to 3. Specifically: mod() is the modulo function, and floor() is the floor function.

5. The image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion according to claim 1, characterized in that, The plaintext image P to be encrypted is reconstructed into a one-dimensional array of length M×N. The chaotic sequence X1 is sorted to obtain the index sequence X2. The plaintext image P to be encrypted is then permuted according to the index sequence X2 to obtain the scrambling result P1, specifically as follows: P = reshape(P, 1, M×N) [~, X2] = sort(X1) P1(i)=P(X2(i)), i=1,2,...,M×N The reshape() function is used to reshape the array, and the sort() function is used to sort it.

6. The image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion according to claim 1, characterized in that, The scrambling result P1 is processed by bit-plane segmentation, converting it into an 8-bit binary image sequence S of size M×N×8. The 8-bit binary image sequence is then divided into four groups of two-bit binary sequences of size M×N×2, grouped by two bits. These two binary sequences are further converted to decimal to obtain four sub-images s1, s2, s3, and s4 with values ​​between 0 and 3. These sub-images are then XORed with pseudo-random sequences Y1, Z1, U1, and V1, respectively. The results d1, d2, d3, and d4 are merged to obtain the first diffusion result P2. S(:,:)=dec2bin(P1,8) P2 = dec2bin([d1 d2 d3 d4]) Among them, dec2bin() is the decimal to binary conversion function, bin2dec() is the binary to decimal conversion function, and bitxor() is the bitwise XOR function.

7. The image encryption method based on a five-dimensional conservative hyperchaotic system and bit-plane segmentation diffusion according to claim 1, characterized in that, The diffusion result P2 is XORed with the chaotic sequence X1 to obtain the second diffusion result. Based on this diffusion result, an M×N two-dimensional matrix is ​​recovered, resulting in the encrypted image E. E′ = bitxor(P2, X1); E = reshape(E′, M, N).

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