Image encryption method and device based on coupled image lattice and cellular automaton

Abstract

The present application discloses an image encryption method and device based on coupled image lattice and cellular automaton, which relates to the field of image processing. The method comprises: constructing a coupled image lattice chaotic system with improved coupled structure based on elementary cellular automaton and two optimized one-dimensional mappings; performing association calculation on plaintext image and external key to generate internal key; inputting internal key into the coupled image lattice chaotic system with improved coupled structure to iterate and expand to generate chaotic sequence matrix; selecting and reorganizing the chaotic sequence matrix to generate initial cellular matrix and key matrix; using scrambling algorithm based on two-dimensional cellular automaton to scramble the plaintext image according to the initial cellular matrix to obtain scrambled image; using diffusion algorithm based on quasi-cellular automaton to diffuse the scrambled image according to the key matrix to obtain ciphertext image. The present application can simplify operation and improve encryption efficiency and security performance.

Description

Technical Field

[0001] The present application relates to the field of image processing, and in particular to an image encryption method and device based on coupled image lattices and cellular automata. Background Art

[0002] With the rapid development of information technology, digital images have become one of the main media for information dissemination. The number of images transmitted on the Internet has increased sharply, leading to increasingly serious security issues for image data. Traditional encryption algorithms such as the Advanced Encryption Standard (AES) and the Data Encryption Standard (DES) are mainly designed for text data, and are difficult to effectively deal with the characteristics of large image data volume, high redundancy, and strong pixel correlation. Therefore, encryption efficiency and performance are insufficient. To solve this problem, researchers have successively proposed new image encryption schemes based on chaotic systems, optical transformations, and DNA computing.

[0003] Among them, encryption algorithms based on the Coupled Map Lattice (CML) model and encryption schemes based on Cellular Automata (CA) have received widespread attention in recent years. However, the chaotic system constructed using the traditional CML model has certain limitations due to the limited range of parameter selection and cannot achieve the desired effect. In addition, most of the traditional encryption processes based on cellular automata are limited to the bit level, the operation is relatively complex, and the efficiency is relatively low. Summary of the invention

[0004] The purpose of this application is to provide an image encryption method and device based on coupled image lattices and cellular automata, which can simplify operations and improve encryption efficiency and security performance.

[0005] To achieve the above objectives, this application provides the following solutions.

[0006] In the first aspect, the present application provides an image encryption method based on coupled image lattice and cellular automaton, including: constructing a coupled image lattice chaotic system with an improved coupling structure based on elementary cellular automaton and two optimized one-dimensional mappings; the two optimized one-dimensional mappings include logistic tangent optimization mapping and logistic sine optimization mapping; performing association calculation on the plaintext image and the external key to generate an internal key; inputting the internal key into the coupled image lattice chaotic system with an improved coupling structure for iteration and expansion to generate a chaotic sequence matrix; selecting and reorganizing the chaotic sequence matrix to generate an initial cellular matrix and a key matrix; using a scrambling algorithm based on two-dimensional cellular automaton to scramble the plaintext image according to the initial cellular matrix to obtain a scrambled image; using a diffusion algorithm based on a quasi-cellular automaton to diffuse the scrambled image according to the key matrix to obtain a ciphertext image.

[0007] Optionally, an association calculation is performed on the plaintext image and the external key to generate an internal key, including: calculating the row and column modulus values ​​based on the sum of each row and each column of the plaintext image, and calculating the row and column sum values ​​based on the row and column modulus values; expanding the plaintext image into a one-dimensional sequence, calculating the segment quantity value, and calculating the segment plaintext value based on the segment quantity value; calculating the sum of the external keys, and calculating the plaintext key association value based on the sum of the external keys, the segment plaintext value and the row and column sum value; using a double loop to generate the internal key based on the plaintext key association value and the external key.

[0008] Optionally, the internal key is input into the coupled image lattice chaotic system of the improved coupling structure for iteration and expansion to generate a chaotic sequence matrix, including: inputting the internal key into the coupled image lattice chaotic system of the improved coupling structure for iteration to generate a chaotic sequence; expanding the chaotic sequence to generate a first sequence, a second sequence and a third sequence of the same size as the chaotic sequence; using a cyclic calculation to generate a chaotic sequence matrix according to the first sequence, the second sequence and the third sequence.

[0009] Optionally, the chaotic sequence matrix is ​​selected and reorganized to generate an initial cell matrix and a key matrix, including: expanding the chaotic sequence matrix into a one-dimensional sequence, and selecting two sequences whose lengths are equal to the expanded lengths of the plaintext image as a first selected sequence and a second selected sequence; reorganizing the first selected sequence into a matrix with the same size as the plaintext image, and rounding it to generate an initial cell matrix; reorganizing the second selected sequence into a matrix with the same size as the plaintext image, and performing cyclic calculations according to the number of iterations of the diffusion algorithm to generate a key matrix.

[0010] Optionally, a scrambling algorithm based on a two-dimensional cellular automaton is used to scramble the plaintext image according to an initial cellular matrix to obtain a scrambled image, including: adding 1 to the element values ​​in the plaintext image to obtain the plaintext image after adding 1; setting the current round to 1, and using the initial cellular matrix as the target input matrix of the current round; inputting the target input matrix of the current round into the two-dimensional cellular automaton for iteration to obtain the first iteration result of the current round; assigning the value of the first iteration result of the current round to a marking matrix of the same size; wherein, when the cell is 0, the value is -1, and when the cell is 1, the value is 1; multiplying the element values ​​of the scrambled matrix of the previous round with the element values ​​of the corresponding positions of the marking matrix to obtain the positive and negative mixed matrix of the current round; wherein the scrambled matrix of the initial round is the plaintext image after adding 1; and the positive and negative mixed matrix of the current round is assigned to the positive and negative mixed matrix of the current round. The negative mixing matrix is ​​decomposed into a first matrix of the current round with positive element values ​​and a second matrix of the current round with negative element values; the element values ​​of the second matrix of the current round are returned to positive, and the first matrix of the current round and the second matrix of the current round are combined and reconstructed into a scrambled matrix of the current round with the same size as the plaintext image; it is determined whether the current round reaches the iteration number of the scrambling algorithm; if the current round does not reach the iteration number of the scrambling algorithm, the current round is added by 1, the first iteration result of the previous round is used as the target input matrix of the current round, and the step of inputting the target input matrix of the current round into the two-dimensional cellular automaton for iteration to obtain the first iteration result of the current round is returned; if the current round reaches the iteration number of the scrambling algorithm, the element value in the scrambled matrix of the current round is subtracted by 1 to obtain a scrambled image.

[0011] Optionally, a diffusion algorithm based on a cellular automaton is used to diffuse the scrambled image according to the key matrix to obtain a ciphertext image, including: performing high-four-bit and low-four-bit segmentation processing on the scrambled image to obtain a high-four-bit matrix and a low-four-bit matrix; setting the current round to 1, and using the high-four-bit matrix as the first input matrix of the current round, and using the low-four-bit matrix as the second input matrix of the current round; inputting the first input matrix of the current round and the second input matrix of the current round into the cellular automaton for iteration to obtain the second iteration result of the current round; calculating the diffusion matrix of the current round according to the second iteration result of the current round and the key matrix, and using the diffusion matrix of the previous round as the first input matrix of the next round. Array, use the diffusion matrix of the current round as the second input matrix of the next round; wherein the diffusion matrix of the initial round is the lower four-bit matrix; determine whether the current round reaches the iteration number of the diffusion algorithm; if the current round does not reach the iteration number of the diffusion algorithm, add 1 to the current round, and return to the step of inputting the first input matrix of the current round and the second input matrix of the current round into the cellular automaton for iteration to obtain the second iteration result of the current round; if the current round reaches the iteration number of the diffusion algorithm, reconstruct the first input matrix of the next round and the second input matrix of the next round into an eight-bit binary number matrix according to the upper four bits and the lower four bits, and then convert it into a decimal numerical matrix to obtain a ciphertext image.

[0012] Optionally, the state quantity of the two-dimensional cellular automaton is a binary number, the boundary adopts a two-dimensional fixed boundary, the boundary value is set to 0, the neighbor adopts a von Neumann neighborhood, and the iteration rule is that the state of the cell at the next moment is equal to the state of the upper neighbor, lower neighbor, left neighbor and right neighbor of the cell at the current moment, and then the state is modulo 2; the state quantity of the quasi-cellular automaton is a decimal value corresponding to a four-bit binary number, the boundary adopts a two-dimensional periodic boundary, the neighbor adopts a von Neumann neighborhood, and the iteration rule is that the state of the cell at the next moment is equal to the state of the right neighbor and upper neighbor of the cell at the current moment, and then the state is XORed with the state of the lower neighbor, and then the state is added with the state of the left neighbor, and then the state is modulo 16.

[0013] In a second aspect, the present application provides a computer device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the image encryption method based on coupled image lattices and cellular automata.

[0014] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the image encryption method based on coupled image lattices and cellular automata.

[0015] According to the specific embodiments provided by the present application, the present application discloses the following technical effects: the present application provides an image encryption method and device based on coupled image lattice and cellular automaton, and constructs a coupled image lattice chaotic system with improved coupling structure based on elementary cellular automaton and two optimized one-dimensional mappings. On the one hand, the two proposed optimized one-dimensional mappings are used to replace the classical logistic mapping, and the chaotic performance is significantly improved. On the other hand, elementary cellular automaton is used to improve the coupling equation structure of the coupled image lattice, and the iterative equation of each lattice is judged and selected by cellular automaton, so that the randomness is enhanced; during the encryption process, the scrambling operation uses a two-dimensional cellular automaton to indirectly control the change of pixel position in parallel, and the diffusion operation uses a cellular automaton-like automaton to further encrypt the scrambled image, which is no longer limited to the bit level, and can achieve better encryption effect. Therefore, the image encryption method and device based on coupled image lattice and cellular automaton provided by the present application have good security, high encryption rate, and simple operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the embodiments of the present application or related technologies, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0017] Figure 1 A flowchart of an image encryption method based on coupled image lattices and cellular automata provided in this application.

[0018] Figure 2 A bifurcation comparison diagram of the two optimized one-dimensional mappings provided in this application and the classical logistic mapping; Figure 2 Part (a) in the figure shows the bifurcation diagram of the classic Logistic mapping. Figure 2 Part (b) in the figure shows the bifurcation diagram of the LTO mapping. Figure 2 Part (c) in Fig. 2 shows the bifurcation diagram of the LSO mapping.

[0019] Figure 3 Comparison chart of Lyapunov exponents of two optimized one-dimensional mappings and classical logistic mapping provided in this application; Figure 3 Part (a) in the figure represents the Lyapunov index graph of the classic Logistic mapping. Figure 3 Part (b) in the figure shows the Lyapunov index graph of the LTO mapping. Figure 3 Part (c) in Fig. 2 shows the Lyapunov index diagram of the LSO mapping.

[0020] Figure 4 Access provided for this application Example diagram of .

[0021] Figure 5 KS entropy density comparison diagram of ICSCML chaotic system and CML chaotic system provided in this application; Figure 5 Part (a) shows the KS entropy density diagram of the CML chaotic system. Figure 5 Part (b) shows the KS entropy density diagram of the ICSCML chaotic system.

[0022] Figure 6 KS entropy breadth comparison diagram of ICSCML chaotic system and CML chaotic system provided in this application; Figure 6 Part (a) in the figure shows the KS entropy breadth diagram of the CML chaotic system. Figure 6 Part (b) in the figure shows the KS entropy breadth diagram of the ICSCML chaotic system.

[0023] Figure 7 The overall flow chart of the image encryption method based on coupled image lattice and cellular automaton provided in this application.

[0024] Figure 8 The encrypted and decrypted images of the three images of "pepper", "baboon" and "airplane" provided for this application; Figure 8 Parts (a), (b), and (c) in the figure represent the plaintext image, ciphertext image, and decrypted image of the “chili” image, respectively. Figure 8 Parts (d), (e), and (f) in the figure represent the plaintext image, ciphertext image, and decrypted image of the “baboon” image, respectively. Figure 8 Parts (g), (h) and (i) in the figure represent the plaintext image, ciphertext image and decrypted image of the “airplane” image respectively.

[0025] Fig. 9 A comparison of the histogram test results of the three images of "pepper", "baboon" and "airplane" provided for this application; Fig. 9 Parts (a), (b), and (c) in the figure represent the plaintext image histogram test results of the images of “pepper”, “baboon”, and “airplane”, respectively. Fig. 9 Parts (d), (e), and (f) in the figure represent the ciphertext image histogram test results of the “pepper”, “baboon”, and “airplane” images, respectively.

[0026] Fig.10 A comparison chart of the correlation test results of the three images of "pepper", "baboon" and "airplane" provided for this application; Fig.10 Parts (a), (b), and (c) in the figure represent the plaintext image correlation test results of the images of “chili”, “baboon”, and “airplane”, respectively. Fig.10Parts (d), (e), and (f) in the figure represent the ciphertext image correlation test results of the “pepper”, “baboon”, and “airplane” images, respectively.

[0027] Fig.11 A comparison chart of the robustness test results of the "chili" image with different cropping sizes provided for this application; Fig.11 Parts (a), (b), and (c) in the figure represent the ciphertext images after being cropped to 67×67, 137×137, and 257×257, respectively. Fig.11 Parts (d), (e), and (f) in the figure represent the decrypted images corresponding to the ciphertext images cropped to 67×67, 137×137, and 257×257, respectively. DETAILED DESCRIPTION

[0028] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0029] This application proposes an image encryption method and device based on coupled image lattices and cellular automata. The scheme has excellent performance, good security, high encryption rate, and is very easy to operate. Two optimized one-dimensional mappings are used instead of classical logistic mappings, and the chaotic performance is significantly improved. Elementary cellular automata are used to improve the coupling equation structure of the coupled image lattice, and the iterative equation of each lattice is judged and selected by the cellular automaton, so that the randomness is enhanced. During the encryption process, the scrambling operation uses a two-dimensional cellular automaton to indirectly control the change of pixel positions in parallel. The high four-bit and low four-bit concepts are used to decompose the scrambled image into high four-bit matrices and low four-bit matrices of the same size, which are used as the initial states of the first two rounds of the cellular automaton used for diffusion, and the iteration rules set by the cellular automaton are directly applied to integer values ​​between [0,15], and are no longer limited to the bit level.

[0030] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below in conjunction with the accompanying drawings and specific implementation methods.

[0031] In an exemplary embodiment, the present application provides an image encryption method based on coupled image lattices and cellular automata. In the embodiment of the present application, Figure 1 As shown, the method includes the following steps 1 to 6.

[0032] Step 1: Construct a coupled image lattice chaotic system with improved coupling structure based on elementary cellular automata and two optimized one-dimensional mappings, including logistic tangent optimization mapping and logistic sine optimization mapping.

[0033] This application proposes a CML chaotic system constructed with the participation of CA, namely, the Improved Coupling Structure Coupled Map Lattice (ICSCML) chaotic system. ICSCML is constructed based on two optimized one-dimensional mappings and elementary cellular automata. It uses the proposed two optimized one-dimensional mappings to replace the classical logistic mapping, specifically the logistic tangent optimized (LTO) mapping and the logistic sinusoidal optimized (LSO) mapping, and the expressions are as follows.

[0034] .

[0035] .

[0036] in, represents the control parameter, Represents the mapping status value, Represents the modulo operation, and n represents the time dimension variable. The bifurcation diagrams and Lyapunov index diagrams of the two optimized one-dimensional mappings proposed above are compared with the classical Logistic mapping. Figure 2 and Figure 3 As shown, Figure 2 The x(n) on the vertical axis represents the mapping state value. Figure 3 The LE on the vertical axis represents the Lyapunov exponent. Figure 2 and Figure 3 It can be seen that compared with the traditional mapping, the two newly proposed mappings have no periodic window within the parameter range and are both in a chaotic state. The Lyapunov exponent is always greater than 0 and its value has been significantly improved.

[0037] The mathematical expression of the proposed new coupled image lattice model, namely the ICSCML model, is as follows.

[0038] .

[0039] Among them, x represents the state value of the lattice, n represents the time dimension variable, is the coupling coefficient of the system, i represents the lattice index, and its value range is (1, L), L is the total number of lattices, that is, the coupling lattice length, and L=100 in this model. represents the state value of the i-th lattice at the n-th time, represents the state value of the i-th lattice at the n+1th time, represents the state value of the i-1th lattice at the nth time, represents the state value of the i+1th lattice at the nth time. The current lattice coupling equation , the left lattice coupling equation of the current lattice And the right lattice coupling equation of the current lattice Represents the coupled equation index of this model and is defined as follows.

[0040] .

[0041] in, Indicates that the cellular automaton CA uses an elementary cellular automaton and the iteration rule is R30, the formula is , represents the exclusive OR operation, represents an OR operation, that is, the current cell performs an OR operation with its right neighbor and then performs an XOR operation with its left neighbor. S represents the state value of the cell, t represents the iteration round of the elementary cellular automaton, j represents the cell index, , Refers to the state value of the jth cell after t rounds of CA iteration (i.e., the tth round), Represents a three-bit binary number, and is defined as follows.

[0042] .

[0043] in, represents the state value of the j-1th cell in the tth round, represents the state value of the j+1th cell in the tth round, . The values ​​0 and 1 correspond to the two optimized one-dimensional mappings mentioned above, namely the logistic tangent optimization mapping and the logistic sine optimization mapping, respectively. and It is expressed as follows.

[0044] .

[0045] .

[0046] in, represents the logistic tangent optimization mapping, represents the logistic sinusoidal optimization mapping, represents the control parameter, , are the tangent function and the sine function respectively. The specific coupling equation structure of each lattice is determined by the following steps.

[0047] (1) By iterating t rounds of elementary cellular automata ECA with the same length L under the R30 rule, we obtain Model, and get all status values ​​of ECA .

[0048] (2) Use and j can get the i-th lattice , where i=j.

[0049] (3) Example Figure 4 As shown, . That is, .

[0050] The ICSCML chaotic system and the CML chaotic system proposed in this application are compared and evaluated using the highly recognized and commonly used KS entropy density and KS entropy breadth. The KS entropy density comparison diagram and the KS entropy breadth comparison diagram of the two are shown in Figure 2. Figure 5 and Figure 6 As shown. Figure 5 The vertical coordinate , The corrected Lyapunov index. h represents the state indicator value. When h>0, it is in a chaotic state, and when h<0, it is in a periodic state. Figure 6 The vertical coordinate , represents the number of grids with positive Lyapunov exponents, It represents the proportion of lattices in a chaotic state. Figure 5 and Figure 6 It can be seen that the ICSCML chaotic system is in a chaotic state within the parameter range (0,4) and has excellent performance. The subsequent overall encryption scheme process is as follows Figure 7 shown.

[0051] Step 2: Perform association calculation on the plaintext image and the external key to generate the internal key.

[0052] Step 2 includes: calculating the row and column modulus values ​​according to the sum of each row and each column of the plaintext image, and calculating the row and column sum values ​​according to the row and column modulus values; expanding the plaintext image into a one-dimensional sequence, calculating the segment quantity value, and calculating the segment plaintext value according to the segment quantity value; calculating the sum of the external keys, and calculating the plaintext key associated value according to the sum of the external keys, the segment plaintext value and the row and column sum value; using a double loop to generate an internal key according to the plaintext key associated value and the external key.

[0053] The first step is to read the plaintext image P to be encrypted, which has a size of M×N, and convert it into grayscale values. Enter the external key , It includes 10 real numbers between (0,1), using the plaintext image P and the external key Calculate and generate the initial value of ICSCML chaotic system , which is the internal key. The specific plaintext association steps are as follows.

[0054] (1) Read the plaintext image P of size M×N and calculate the sum of each row The sum of each column . use and Calculate the row and column modulus RCM, the calculation formula is as follows.

[0055] .

[0056] Where a=1,2,...max(M,N), M and N are image sizes, min means minimum value, and max means maximum value. When M=N, RCM calculation is directly used But when M≠N, use the above formula for piecewise calculation. Then use RCM to calculate the row and column sum value SRC, the calculation formula is as follows.

[0057] .

[0058] in, Represents a sum operation.

[0059] (2) Expand the plaintext image P into a one-dimensional sequence with a length of M × N. Calculate the number of segments num, and the calculation formula is as follows.

[0060] 。

[0061] Where L is the coupling lattice length, M and N are the image sizes, and floor represents the rounding down operation. The following formula is then used to calculate the segmented plaintext value SP.

[0062] .

[0063] Where b=1,2,...L, and num refers to the number of segments.

[0064] (3) Calculate the sum of external keys , and then use the above-calculated row and column sum value SRC and segmented plaintext value SP to calculate the plaintext key association value PKA, the calculation formula is as follows.

[0065] .

[0066] Where c=1,2,...L, refers to the sum of external keys, is the segment plaintext value, For the rows, columns and values.

[0067] (4) Define a double loop to calculate Let d and e be index variables of two loops respectively, and the value range of d is: , the value range of e is: The calculation process for each cycle is as follows.

[0068] Initial calculation: For each index d and e, calculate The calculation expression is as follows.

[0069] .

[0070] Where, d=1,2,...10, e=1,2,...10, Specifies the value associated with the text key. Represents an external key.

[0071] After the above calculations, Perform an update calculation, the formula is as follows.

[0072] .

[0073] Among them, n represents the time dimension variable, Indicates the nth moment , Represents the n+1th moment .

[0074] The above two steps form a small cycle. After the above double cycle, we can get value.

[0075] Step 3: Input the internal key into the coupled image lattice chaotic system of the improved coupling structure for iteration and expansion to generate a chaotic sequence matrix.

[0076] Step 3 includes: inputting the internal key into the coupled image lattice chaotic system of the improved coupling structure for iteration to generate a chaotic sequence; expanding the chaotic sequence to generate a first sequence, a second sequence and a third sequence of the same size as the chaotic sequence; and using a cyclic calculation to generate a chaotic sequence matrix according to the first sequence, the second sequence and the third sequence.

[0077] The initial value After being input into the ICSCML chaotic system, the chaotic sequence is iteratively generated, and then a concise and effective expansion is performed on the generated chaotic sequence to generate the chaotic sequence matrix CSM. The specific steps are as follows.

[0078] (1) Set the initial value Enter the chaos system and set , , ICSCML iterates (n0+t0) rounds, discards the first t0 rounds, and n0=100, and obtains the chaotic sequence of n0 rounds of iteration results .

[0079] (2) Yes Perform an expansion to generate a sequence of the same size , namely the first sequence, the second sequence and the third sequence. The specific expansion formula is as follows.

[0080] .

[0081] in, refers to chaotic sequence, It means that the base is 10, is the logarithm of a real number, It means that the base is e (here the base of natural logarithms), is the exponential value of the exponent.

[0082] (3) Using the sequence generated above The chaotic sequence matrix CSM is generated through a loop calculation, and the calculation formula is as follows.

[0083] .

[0084] in, , n represents the time dimension variable, represents the CSM at the nth moment, Represents the CSM at the n+1th moment.

[0085] Step 4: Select and reorganize the chaotic sequence matrix to generate the initial cell matrix and key matrix.

[0086] Step 4 includes: expanding the chaotic sequence matrix into a one-dimensional sequence, and selecting two sequences whose lengths are equal to the expanded length of the plaintext image as the first selection sequence and the second selection sequence; reorganizing the first selection sequence into a matrix with the same size as the plaintext image, and rounding it to generate an initial cell matrix; reorganizing the second selection sequence into a matrix with the same size as the plaintext image, and performing cyclic calculation according to the number of iterations of the diffusion algorithm to generate a key matrix.

[0087] The chaotic sequence matrix CSM is used to generate the initial cell matrix IC required for scrambling and the key matrix KM required for diffusion. The specific generation steps are as follows.

[0088] (1) Expand the CSM into a one-dimensional sequence, and select two sequences xx1 and xx2 of length M×N, namely the first selected sequence and the second selected sequence, in the following manner.

[0089] .

[0090] Among them, ST represents the starting point of sequence selection, Sn is the selection interval between two sequences, and both are integers between (0,100).

[0091] (2) Reorganize the above xx1 into The matrix of , and then round it to the integer, can get the initial cell matrix IC.

[0092] (3) Recombining the above xx2 into The key matrix KM is generated by the following loop formula.

[0093] .

[0094] Among them, m=1,2,...r2, r2 represents the number of iterations in the diffusion algorithm.

[0095] Step 5: Use a scrambling algorithm based on two-dimensional cellular automata to scramble the plaintext image according to the initial cellular matrix to obtain a scrambled image.

[0096] Step 5 includes: adding 1 to the element values ​​in the plaintext image to obtain the plaintext image after adding 1; setting the current round to 1, and taking the initial cell matrix as the target input matrix of the current round; inputting the target input matrix of the current round into the two-dimensional cellular automaton for iteration to obtain the first iteration result of the current round; assigning the value of the first iteration result of the current round to a marking matrix of the same size; wherein, when the cell is 0, the value is -1, and when the cell is 1, the value is 1; multiplying the element value of the scrambled matrix of the previous round with the element value of the corresponding position of the marking matrix to obtain the positive and negative mixed matrix of the current round; wherein, the scrambled matrix of the initial round (i.e., the previous round of the first round) is the plaintext image after adding 1; decomposing the positive and negative mixed matrix of the current round into the current positive and negative mixed matrices with positive element values. The method comprises the following steps: a first matrix of a round and a second matrix of the current round whose element values ​​are negative; performing an element value restoration operation on the second matrix of the current round, and combining and reconstructing the first matrix of the current round and the second matrix of the current round into a scrambled matrix of the current round having the same size as the plaintext image; judging whether the current round reaches the iteration number of the scrambling algorithm; if the current round does not reach the iteration number of the scrambling algorithm, adding 1 to the current round, taking the first iteration result of the previous round as the target input matrix of the current round, and returning to the step of inputting the target input matrix of the current round into the two-dimensional cellular automaton for iteration to obtain the first iteration result of the current round; if the current round reaches the iteration number of the scrambling algorithm, subtracting 1 from the element value in the scrambled matrix of the current round to obtain a scrambled image.

[0097] First, input the plaintext image P and the initial cellular matrix IC, where the size of IC is the same as the plaintext P. The encryption algorithm at this stage is a scrambling algorithm based on the cellular automaton CA, where each round of scrambling includes the iteration of CA based on the "odd-even game rule" and the use of CA as a control matrix to disrupt the position of pixels.

[0098] The state quantity of the two-dimensional cellular automaton is a binary number, the boundary adopts a two-dimensional fixed boundary, the boundary value is set to 0, the neighbor adopts a von Neumann neighborhood, and the iteration rule is that the state of the cell at the next moment is equal to the state of the upper neighbor, lower neighbor, left neighbor and right neighbor of the cell at the current moment, plus the state, and then modulo 2. The specific definition of the two-dimensional cellular automaton in the scrambling algorithm is as follows.

[0099] (1) State quantity S1: S1=(0, 1).

[0100] (2) Boundary B1: A two-dimensional fixed boundary is used, and the boundary value is set to 0.

[0101] (3) Neighbor N1: Using the von Neumann type neighborhood, that is, the cell ( , )'s neighbors are [( -1, ),( , -1),( +1, ),( , +1)].

[0102] (4) Iteration rules :This model adopts the "odd-even game rule", and its specific formula is as follows.

[0103] .

[0104] in, , , . represents the cell state at the next moment, It represents the neighbor state of the cell at the current moment. That is, the state of the cell at the next moment is equal to the sum of the states of the upper, lower, left and right neighbors at this moment, modulo 2.

[0105] The method of disturbing pixel positions based on two-dimensional cellular automata is as follows.

[0106] (1) First, the plaintext image P+1 is recorded as P´. The reason for adding 1 first is to prevent the plaintext image pixel value from being 0.

[0107] (2) The initial cell matrix IC is sent into the two-dimensional cellular automaton model defined above to start the first round of iteration. The result of the first round of iteration is recorded as SC1.

[0108] (3) Assign the value of SC1 to the labeling matrix TP of the same size, where TP(SC1==0)=-1, TP(SC1==1)=1, that is, assign the value of -1 to the cells whose original SC1 state quantity is 0, and assign the value of 1 to the cells whose original SC1 state quantity is 1.

[0109] (4) Then multiply P' by the corresponding position elements of the labeling matrix TP to obtain the positive and negative mixing matrix PP, that is, PP = P' × TP.

[0110] (5) Since the PP element values ​​can be positive or negative, the above PP can be used to decompose PP into a first matrix PP1 (PP>=0) with positive element values ​​and a second matrix PP2 (PP<0) with negative element values.

[0111] (6) Perform an element value restoration operation on the second matrix PP2, that is, PP2×(-1), and then combine the first matrix PP1 and the second matrix PP2 to reshape into a scrambled matrix PP3 of size M×N, that is, PP3=reshape([PP1;PP2],M,N).

[0112] After the above steps, the first round of scrambling using cellular automata is completed.

[0113] Going back to the two-dimensional cellular automaton iteration step, repeating the above steps r1 times (r1=15) can complete the scrambling of the pixels of the plaintext image P. The final result is subtracted by 1 to obtain the scrambled image, that is, B=PP3-1.

[0114] Step 6: Use a diffusion algorithm based on cellular automata to diffuse the scrambled image according to the key matrix to obtain the ciphertext image.

[0115] Step 6 includes: performing high-four-bit and low-four-bit segmentation processing on the scrambled image to obtain a high-four-bit matrix and a low-four-bit matrix; setting the current round to 1, and using the high-four-bit matrix as the first input matrix of the current round, and using the low-four-bit matrix as the second input matrix of the current round; inputting the first input matrix of the current round and the second input matrix of the current round into a cellular automaton for iteration to obtain a second iteration result of the current round; calculating a diffusion matrix of the current round according to the second iteration result of the current round and the key matrix, and using the diffusion matrix of the previous round as the first input matrix of the next round, and using the diffusion matrix of the current round as the second input matrix of the next round; Among them, the diffusion matrix of the initial round (i.e., the previous round of the first round) is the lower four-bit matrix; it is determined whether the current round reaches the number of iterations of the diffusion algorithm; if the current round does not reach the number of iterations of the diffusion algorithm, the current round is incremented by 1, and the step of inputting the first input matrix of the current round and the second input matrix of the current round into the cellular automaton for iteration to obtain the second iteration result of the current round is returned; if the current round reaches the number of iterations of the diffusion algorithm, the first input matrix of the next round and the second input matrix of the next round are reconstructed into an eight-bit binary number matrix according to the upper four bits and the lower four bits, and then converted into a decimal numerical matrix to obtain a ciphertext image.

[0116] First, the scrambled image B generated above is segmented into high and low quartiles, that is, a simple high four-bit and low four-bit segmentation process is performed on B to generate high four-bit matrices and the lower four bits of the matrix , and then use the constructed cellular automaton to perform diffusion operations.

[0117] The state quantity of the cellular automaton is the decimal value corresponding to the four-bit binary number. The boundary adopts a two-dimensional periodic boundary, the neighbor adopts a von Neumann neighborhood, and the iteration rule is that the state of the cell at the next moment is equal to the state of the right neighbor and the upper neighbor at the current moment of the cell, and then the state of the lower neighbor is XORed, and then the state of the left neighbor is added, and then modulo 16. The specific definition of the cellular automaton (LCA) in the diffusion algorithm is as follows.

[0118] (1) State quantity S2: S2 = (0, 1, 2, ... 15), that is, the decimal value that can be constructed by four binary numbers.

[0119] (2) Boundary B2: A two-dimensional periodic boundary is used.

[0120] (3) Neighbor N2: Similar to scrambling, it also uses the von Neumann type neighborhood.

[0121] (4) Iteration rules : The specific formula is as follows.

[0122] .

[0123] in, , , . represents the cell state at the next moment, It represents the neighbor state of the cell at the current moment. That is, the iteration rule is no longer limited to the bit level, but is set between (0, 1, 2, ... 15). In comparison, this setting greatly improves the diffusion efficiency.

[0124] The specific diffusion steps are as follows.

[0125] (1) The scrambled image B generated by the above scrambling process is segmented into the upper four bits and the lower four bits, and is divided into the upper four bits matrix and the lower four bits of the matrix ,Right now , .

[0126] (2) , As the initial matrix (including the first input matrix and the second input matrix), the cellular automaton model defined above is input for iteration, that is, , As =0 and =1, the state of the cellular automaton, the specific calculation formula is , that is, the result of each round is calculated by the previous two rounds, for example .in, =(1,2,...r2), express +1 time CA status, express Moment CA follows the rules defined above The result of the iteration, express -1 The status of CA at time instant.

[0127] (3) After each round of calculation results are obtained, they need to be further operated with the key matrix KM to obtain the diffusion matrix. The specific operation is as follows: ,For example .in, =(1,2,...r2), n refers to the time dimension variable, represents the XOR operation, KM is the key matrix, and its matrix element values ​​are integers between [0,15].

[0128] After the above steps, a complete round of diffusion using cellular automata is completed.

[0129] The diffusion operation can be completed well by repeating the above operation r2 times (r2=3). The ciphertext image is the result of the last two rounds of calculation. , , the result of reconstructing the eight-bit binary number matrix according to the high four bits and the low four bits and then converting it into a decimal number matrix.

[0130] The decryption algorithm is the reverse process of the encryption algorithm and will not be described in detail here.

[0131] In order to evaluate the overall performance of the encryption scheme, it is necessary to conduct multiple test analyses, including key space size analysis, histogram and correlation test analysis, plaintext sensitivity and key sensitivity test analysis, and robustness test analysis.

[0132] The encrypted and decrypted images of the three images of "pepper", "baboon" and "airplane" are as follows Figure 8 shown.

[0133] Key space size: The key space size of an encryption scheme is very important and must exceed the theoretical minimum security requirement to effectively resist brute force attacks. The encryption scheme proposed in this application has a key space size of external key length, is a real number between 10 (0,1), that is . Because 64-bit double-precision floating point numbers are used, the overall key space size is: Therefore, the key space of the proposed encryption scheme is large enough, which proves that this scheme has the ability to resist exhaustive attacks.

[0134] Histogram test: The histogram of a digital image can reflect the distribution of its pixels. Therefore, the plaintext image histogram often leaks important pixel information. Therefore, the ciphertext image histogram should be evenly distributed to achieve the purpose of hiding key pixel information. The histogram test results of the encryption scheme proposed in this application are as follows: Fig. 9 As shown, from Fig. 9It can be observed that the histograms of the tested ciphertext images are uniformly distributed, and the encryption scheme has the ability to resist statistical attacks.

[0135] Correlation test: Pixels in plaintext images usually have strong neighborhood correlation, and the encrypted image needs to eliminate this feature to enhance anti-cracking capabilities. In other words, the pixels in the ciphertext image should be independent of each other. Therefore, an ideal encryption scheme should convert the original image into a ciphertext image with extremely low correlation between adjacent pixels. 2000 pairs of adjacent pixels in the plaintext image and the ciphertext image in the encryption scheme proposed in this application are extracted, and the correlation coefficients of adjacent pixels in the horizontal, vertical, diagonal, and anti-diagonal directions are calculated respectively. The correlation test results are as follows: Fig.10 As shown in Table 1, the correlation coefficients are shown in Table 1. It can be seen that the correlation between adjacent pixels of the ciphertext image in this scheme is extremely low.

[0136] Table 1 Correlation coefficient test results

[0137]

[0138] Plaintext sensitivity: Plaintext sensitivity refers to the ciphertext images C1 and C2 obtained after the same encryption algorithm encrypts two plaintext images P1 and P2 with slight differences. The difference between the two is analyzed by calculating the Normalized Pixel Contrast Ratio (NPCR) and the Normalized Average Changing Intensity (UACI). The plaintext sensitivity analysis results of the encryption scheme proposed in this application are shown in Table 2 below. It can be seen from the data in the table that the test indicators of the test images are close to the theoretical values. Therefore, the proposed encryption scheme has good plaintext sensitivity and has the ability to resist differential attacks.

[0139] Table 2 Plaintext sensitivity analysis results

[0140]

[0141] Key sensitivity: Slightly adjust the external key and calculate the difference between the ciphertexts. is a real number between 10 (0,1), that is C1 refers to minor changes (only + ) refers to the ciphertext image output after slightly changing the K1 value, C2 refers to the ciphertext image output after slightly changing the K2 value, and so on. The key sensitivity analysis results of the encryption scheme proposed in this application are shown in Table 3 below, which shows that this scheme has strong key sensitivity.

[0142] Table 3 Key sensitivity analysis results

[0143]

[0144] Robustness: Robustness is one of the key factors in evaluating image encryption algorithms. It is mainly used to measure whether the algorithm can effectively protect the image content from being destroyed or leaked when it is interfered by various noises. In the real world and in practical applications, images are often interfered with in different forms. Therefore, it is particularly important to analyze and evaluate the anti-interference ability of encryption algorithms. The ciphertext images are cropped to 67×67, 137×137, and 257×257, respectively, and then decrypted. Fig.11 As shown, it can be concluded that the encryption scheme has good robustness.

[0145] Compared with the prior art, the present application has the following advantages.

[0146] First, the ICSCML model based on cellular automata and two optimized one-dimensional mappings proposed in this application has better chaotic performance than the traditional CML model. Specifically, the Lyapunov exponents of the two optimized one-dimensional mappings in the ICSCML model are always greater than 0 within the parameter value range, and the values ​​are greatly improved, so that the entire parameter value range is a chaotic state, and there is no periodic window. The controllable coupled equation random combination model based on elementary cellular automata has the advantage of using elementary cellular automata to perturb the chaotic system, which improves the pseudo-randomness of the coupling process and can effectively alleviate the dynamic degradation of the digital system.

[0147] Second, the encryption scheme proposed in this application uses a two-dimensional cellular automaton to scramble the plaintext image, that is, the iterative results of the two-dimensional cellular automaton are used to indirectly control and change the pixel position in parallel during the encryption process, which simplifies the operation process and improves the algorithm security and efficiency.

[0148] Third, the diffusion algorithm based on cellular automata proposed in this application uses the concept of high four bits and low four bits to divide the image into high four bits and low four bits, which are used as the initial states of the first two rounds of LCA respectively, and the iteration rule is directly set on the decimal value converted from the four-bit binary number, i.e. (0, 1, 2...15), which is no longer limited to the bit level, making the diffusion process easier to operate and more efficient.

[0149] In an exemplary embodiment, the present application further provides a computer device, including a memory and a processor, wherein a computer program is stored in the memory, and the processor implements the steps in the above-mentioned method embodiments when executing the computer program.

[0150] In an exemplary embodiment, the present application further provides a computer-readable storage medium storing a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0151] In an exemplary embodiment, the present application further provides a computer program product, including a computer program, which implements the steps in the above-mentioned method embodiments when executed by a processor.

[0152] In this application, all actions to obtain signals, information or data are carried out in compliance with the relevant data protection laws and policies of the country where the application is located and with the authorization of the corresponding device owner. It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant legal provisions.

[0153] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0154] The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. The non-relational database may include a distributed database based on blockchain, etc., but is not limited thereto. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but is not limited thereto.

[0155] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0156] This article uses specific examples to illustrate the principles and implementation methods of this application. The description of the above embodiments is only used to help understand the method and core ideas of this application. At the same time, for those skilled in the art, according to the ideas of this application, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. An image encryption method based on coupled image lattices and cellular automata, characterized in that: include: Based on elementary cellular automata and two optimized one-dimensional mappings, a coupled image lattice chaotic system with improved coupling structure is constructed; The two optimized one-dimensional mappings include logistic tangent optimization mapping and logistic sine optimization mapping; the expression of the coupled image lattice chaotic system of the improved coupling structure is: ； ； ； in, represents the state value of the lattice, represents the time dimension variable, represents the lattice index, represents the state value of the i-th lattice at the n-th time, represents the state value of the i-th lattice at the n+1th time, represents the state value of the i-1th lattice at the nth time, represents the state value of the i+1th lattice at the nth time, is the coupling coefficient, represents the current lattice coupling equation, represents the lattice coupling equation on the left, represents the lattice coupling equation on the right side, represents an elementary cellular automaton with iteration rule R30, represents the state value of the cell, represents the iteration round of elementary cellular automaton, represents the cell index, represents the state value of the jth cell in the tth round, represents the state value of the j-1th cell in the tth round, represents the state value of the j+1th cell in the tth round, Represents a three-digit binary number, and the values ​​0 and 1 correspond to the logistic tangent optimization mapping and the logistic sine optimization mapping respectively; Perform association calculation on the plaintext image and the external key to generate the internal key; The internal key is input into the coupled image lattice chaotic system of the improved coupled structure for iteration and expansion to generate a chaotic sequence matrix; Select and reorganize the chaotic sequence matrix to generate the initial cell matrix and key matrix; A scrambling algorithm based on two-dimensional cellular automata is used to scramble the plaintext image according to the initial cellular matrix to obtain a scrambled image. A diffusion algorithm based on cellular automata is used to diffuse the scrambled image according to the key matrix to obtain the ciphertext image.

2. The image encryption method based on coupled image lattice and cellular automaton according to claim 1, characterized in that: Perform association calculation on the plaintext image and the external key to generate the internal key, including: Calculate the row and column modulus values ​​according to the sum of each row and each column of the plaintext image, and calculate the row and column sum values ​​according to the row and column modulus values; Expand the plaintext image into a one-dimensional sequence, calculate the segment quantity value, and calculate the segment plaintext value according to the segment quantity value; Calculate the sum of the external keys, and calculate the plaintext key associated value based on the sum of the external keys, the segmented plaintext value, and the row and column sum values; A double loop is used to generate the inner key based on the plaintext key association value and the outer key.

3. The image encryption method based on coupled image lattice and cellular automaton according to claim 2, characterized in that: The internal key is input into the coupled image lattice chaotic system of the improved coupling structure for iteration and expansion to generate a chaotic sequence matrix, including: The internal key is input into the coupled image lattice chaotic system of the improved coupled structure for iteration to generate a chaotic sequence; Expanding the chaotic sequence to generate a first sequence, a second sequence and a third sequence having the same size as the chaotic sequence; The chaotic sequence matrix is ​​generated according to the first sequence, the second sequence and the third sequence by adopting cyclic calculation.

4. The image encryption method based on coupled image lattice and cellular automaton according to claim 3, characterized in that: The chaotic sequence matrix is ​​selected and reorganized to generate the initial cell matrix and key matrix, including: Expand the chaotic sequence matrix into a one-dimensional sequence, and select two sequences whose lengths are equal to the expanded length of the plaintext image as the first selected sequence and the second selected sequence; Reorganize the first selected sequence into a matrix with the same size as the plaintext image, and perform rounding to generate an initial cell matrix; The second selected sequence is reorganized into a matrix with the same size as the plaintext image, and a cyclic calculation is performed according to the number of iterations of the diffusion algorithm to generate a key matrix.

5. The image encryption method based on coupled image lattice and cellular automaton according to claim 4, characterized in that: The scrambling algorithm based on two-dimensional cellular automaton is used to scramble the plaintext image according to the initial cellular matrix to obtain a scrambled image, including: Add 1 to the element value in the plaintext image to obtain the plaintext image after adding 1; Let the current round be 1, and use the initial cell matrix as the target input matrix of the current round; Input the target input matrix of the current round into the two-dimensional cellular automaton for iteration to obtain the first iteration result of the current round; Assign the value of the first iteration result of the current round to the label matrix of the same size; where the value is -1 when the cell is 0, and the value is 1 when the cell is 1; Multiply the element value of the scrambled matrix of the previous round by the element value of the corresponding position of the marking matrix to obtain the positive and negative mixed matrix of the current round; wherein the scrambled matrix of the initial round is the plaintext image after adding 1; Decomposing the positive and negative mixed matrix of the current round into a first matrix of the current round with positive element values ​​and a second matrix of the current round with negative element values; Performing an element value restoration operation on the second matrix of the current round, and combining the first matrix of the current round and the second matrix of the current round and reconstructing them into a scrambled matrix of the current round having the same size as the plaintext image; Determine whether the current round has reached the number of iterations of the scrambling algorithm; If the current round does not reach the number of iterations of the scrambling algorithm, then the current round is incremented by 1, the first iteration result of the previous round is used as the target input matrix of the current round, and the target input matrix of the current round is input into the two-dimensional cellular automaton for iteration to obtain the first iteration result of the current round. If the current round reaches the number of iterations of the scrambling algorithm, the element value in the scrambling matrix of the current round is subtracted by 1 to obtain a scrambled image.

6. The image encryption method based on coupled image lattice and cellular automaton according to claim 5, characterized in that: A diffusion algorithm based on cellular automata is used to diffuse the scrambled image according to the key matrix to obtain the ciphertext image, including: The scrambled image is processed by dividing the upper four bits and the lower four bits to obtain an upper four-bit matrix and a lower four-bit matrix; Let the current round be 1, and use the upper four-bit matrix as the first input matrix of the current round, and use the lower four-bit matrix as the second input matrix of the current round; Inputting the first input matrix of the current round and the second input matrix of the current round into the cellular automaton for iteration to obtain the second iteration result of the current round; Calculating the diffusion matrix of the current round according to the second iteration result of the current round and the key matrix, and using the diffusion matrix of the previous round as the first input matrix of the next round, and using the diffusion matrix of the current round as the second input matrix of the next round; wherein the diffusion matrix of the initial round is the lower four-bit matrix; Determine whether the current round has reached the number of iterations of the diffusion algorithm; If the current round does not reach the number of iterations of the diffusion algorithm, the current round is incremented by 1, and the step of inputting the first input matrix of the current round and the second input matrix of the current round into the cellular automaton for iteration is returned to obtain the second iteration result of the current round; If the current round reaches the iteration number of the diffusion algorithm, the first input matrix of the next round and the second input matrix of the next round are reconstructed into an eight-bit binary matrix according to the high four bits and the low four bits, and then converted into a decimal numerical matrix to obtain a ciphertext image.

7. The image encryption method based on coupled image lattice and cellular automaton according to claim 6, characterized in that: The state quantity of the two-dimensional cellular automaton is a binary number, the boundary adopts a two-dimensional fixed boundary, the boundary value is set to 0, the neighbor adopts a von Neumann neighborhood, and the iteration rule is that the state of the cell at the next moment is equal to the state of the upper neighbor, lower neighbor, left neighbor and right neighbor of the cell at the current moment, and then the state is modulo 2; the state quantity of the quasi-cellular automaton is a decimal value corresponding to a four-bit binary number, the boundary adopts a two-dimensional periodic boundary, the neighbor adopts a von Neumann neighborhood, and the iteration rule is that the state of the cell at the next moment is equal to the state of the right neighbor and upper neighbor of the cell at the current moment, and then the state is XORed, and then XORed with the state of the lower neighbor, and then summed with the state of the left neighbor, and then modulo 16.

8. The image encryption method based on coupled image lattice and cellular automaton according to claim 1, characterized in that: The expression of the logistic tangent optimization mapping is: ； The expression of the logistic sinusoidal optimization mapping is: ； in, represents the logistic tangent optimization mapping, represents the logistic sinusoidal optimization mapping, represents the control parameter, represents the tangent function, represents the sine function, Represents the modulo operation.

9. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the image encryption method based on coupled image lattices and cellular automata as described in any one of claims 1 to 8.

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