Enterprise information image encryption method based on chaotic system and biological evolution strategy

Abstract

The present invention proposes an enterprise information image encryption method based on a chaotic system and a biological evolution strategy, which comprises the following steps: converting the grayscale image to be encrypted into an image matrix; using a hash function to calculate the hash value of the image matrix, and using the hash value to calculate the initial value of the Sine map and the 3D chaotic system; iterating the 3D chaotic system to obtain three pseudo-random sequences; using the pseudo-random sequence to obtain the initial value of the Sine map and the 3D chaotic system; and LX Select the reorganization rule and reorganize and scramble each pixel in the image matrix to obtain the reorganized matrix; use the pseudo-random sequence LY Reorganized matrix P 2 to select and obtain pixel pairs; the pseudo-random sequence LZ Using random numbers, pixel pairs are sequentially cross-linked and mutated. Iterative Sine mapping generates a pseudo-random sequence, which is then fed back into the ciphertext to produce the ciphertext image. The present invention has a very large key space and high key sensitivity, effectively resisting exhaustive attacks, statistical analysis, and differential attacks, meeting the image transmission security requirements of enterprise information systems.

Description

Technical Field

[0001] The present invention relates to the technical field of digital image encryption, and in particular to an enterprise information image encryption method based on a chaotic system and a biological evolution strategy. Background Art

[0002] With the rapid development of the market economy, the scale of enterprise construction continues to expand. While this drives enterprise progress, it also brings more data and information to enterprise operations. To better adapt to the market's data informatization development trend, it is necessary to focus on improving the efficiency of information collection, processing, storage and utilization. This requires enterprises to comprehensively manage their own operational information and utilize enterprise information systems to balance the relationship between enterprise operations and data processing, thereby effectively improving operational efficiency. In the actual application of enterprise information systems, image collection, transmission, and review have become the foundation and key links of remote auditing. Therefore, the security of image information has become a critical component of enterprise information system security, and encryption of this image data is necessary.

[0003] Image encryption is an effective method for protecting digital images. Due to the large amount of data, strong correlation, high redundancy, and high identifiability of images, traditional text encryption methods such as AES and DES suffer from slow encryption and decryption speeds and weak capabilities when used for image encryption, making them inadequate for encrypting large amounts of image data. Consequently, researchers are exploring new image encryption methods. Common approaches include image encryption algorithms based on DNA random coding, dual random phase coding, filling curves, and chaotic systems.

[0004] Although these chaotic image encryption algorithms can encrypt images and improve security to a certain extent, they often fail to effectively address security threats due to varying image complexity. Since Fridrich proposed the scrambling-diffusion encryption architecture, chaotic systems, as complex nonlinear dynamic systems, are highly sensitive to initial values and parameters, exhibit unpredictable motion trajectories, and generate sequences with strong pseudo-randomness. Therefore, using chaotic systems to generate pseudo-random sequences has been widely used in image encryption.

[0005] In-depth research by researchers both domestically and internationally has revealed that single or simply structured chaotic maps can be inaccurate and lack security. Consequently, image encryption methods are becoming increasingly diverse, often employing a combination of methods rather than a single one. Pandurang employs both chaotic mapping and Latin squares to achieve pixel permutation and replacement, respectively, to enhance the encryption system's resistance to attacks.

[0006] Biological evolutionary strategies are an exploratory study. Genetic algorithms, developed based on biological evolutionary strategies, are random search and optimization algorithms based on the principle of natural selection. Genetic algorithms continuously cycle through selection, crossover, and mutation until constraints are satisfied. These operations make genetic algorithms highly capable of searching. To enhance the strength of cryptographic systems and provide greater security, this invention leverages the pseudo-randomness and ergodicity of biological evolutionary strategies and chaos theory to address security threats and inefficiencies encountered in image encryption. The use of selection, recombination, crossover, and mutation operations in the encryption diffusion process further exacerbates the avalanche effect of image encryption systems. Summary of the Invention

[0007] In response to the technical problems that the existing image encryption methods based on chaotic systems have weak resistance to differential attacks and unstable performance of chaotic systems, the present invention proposes an enterprise information image encryption method based on chaotic systems and biological evolution strategies. The method integrates the pseudo-randomness of chaotic systems with biological evolution strategies for image encryption to obtain stronger security performance and enhance the security of image data transmission.

[0008] In order to achieve the above-mentioned purpose, the technical solution of the present invention is implemented as follows: a method for encrypting enterprise information images based on a chaotic system and a biological evolution strategy, the steps of which are as follows:

[0009] Step 1: Convert the grayscale image P to be encrypted into an image matrix P1 of size M*N; where M and N are the number of rows and columns of the grayscale image P respectively;

[0010] Step 2: Use the hash function to calculate the hash value of the image matrix P1, and use the hash value to calculate the initial value w0 of the Sine map and the initial parameter values x0, y0, z0 of the 3D chaotic system;

[0011] Step 3: Use the initial parameter values x0, y0, and z0 to iterate the 3D chaotic system to obtain three pseudo-random sequences LX, LY, and LZ of length M*N;

[0012] Step 4: Perform data processing I on the pseudo-random sequence LX and convert it into a matrix LX'. Select a reorganization rule according to the element values of the matrix LX'. Use the selected reorganization rule to reorganize and scramble each pixel in the image matrix P1 to obtain a reorganized matrix P2.

[0013] Step 5: Sort the pseudo-random sequence LY in ascending order to obtain the sequence LY', mark the position of the elements in the new sequence LY' in the pseudo-random sequence LY to obtain the position index sequence Index, and select the reorganized matrix P2 in sequence according to the position index sequence Index to obtain the pixel pair matrix;

[0014] Step 6: Perform data processing II on the pseudo-random sequence LZ to obtain the sequence LZ', sequentially select the elements at odd positions in the sequence LZ' as random numbers, and perform crossover and mutation on the pixel pairs in the pixel pair matrix in turn to obtain the matrix P3;

[0015] Step 7: Iterate the Sine map based on the initial value w0 to obtain a pseudo-random sequence LW of length M*N, perform data processing III on the pseudo-random sequence LW to obtain sequence D; convert the matrix P3 into a one-dimensional sequence S, use sequence D to perform ciphertext feedback on each pixel of the one-dimensional sequence S, and convert it into a matrix form to obtain the ciphertext image E.

[0016] Preferably, the hash function is a SHA-256 algorithm, and the image matrix P1 is encrypted using the SHA-256 algorithm to obtain a 256-bit binary hash value H;

[0017] The method for calculating the initial value w0 of the Sine map and the initial parameter values x0, y0, z0 of the 3D chaotic system is:

[0018] The hash value H is divided into 32 bytes, represented as: h1, h2, ..., h 32 ;but

[0019]

[0020] Among them, Q1, Q2, Q3, Q4, α, β, γ and ω are all intermediate variables of calculation. is the floor function, q n is the average value of the M pixel values in the nth column of the image matrix P1; is the XOR operation, mod(,) is the modulo operation; x′0, y′0, z′0 and w′0 are the given initial values of the parameters.

[0021] Preferably, the Sine mapping is: t+1 =μsin(πw t );

[0022] Where w is the state variable, w t+1 and w t denote the values of the state variables at the t+1th and tth iterations, respectively, and μ is the system parameter. When the system parameter μ∈(0.87,0.93) and (0.95,1), the Sine map is in a good chaotic state.

[0023] The mathematical expression of the 3D chaotic system is:

[0024]

[0025] Among them, a and b are system parameters. When the system parameters are (a, b) = (2.6, 1.5), the 3D chaotic system is in a good chaotic state.

[0026] Preferably, the iteration of the 3D chaotic system in step 3 and the iteration of the Sine map in step 7 both discard iteration values greater than 1000 times to remove transient effects;

[0027] In step 4, the data processing I makes the value range of each element of the pseudo-random sequence LX between 1 and 8, and

[0028] lx′ i =mod(floor(10 14 ×lx i ),8)+1;

[0029] Among them, floor(·) is the rounding down operation, mod(,) is the modulus operation, lx i is the i-th element of the pseudo-random sequence LX, lx′ i is the i-th element in the sequence after data processing, i = 1, 2, ... M * N;

[0030] The data processing II in step 6 makes each element value of the pseudo-random sequence LZ within the range of 0 to 255, and

[0031] lz′ i =mod(floor(10 14 ×lz i ),256);

[0032] Among them, lz i and lz′ i are the i-th element of the pseudo-random sequence LZ and the sequence after data processing, respectively.

[0033] Preferably, the method for reorganizing and scrambling each pixel in the image matrix P1 is: converting the grayscale value of the pixel at any position (m, n) in the image matrix P1 into an eight-bit binary sequence, and using the element value at position (m, n) of the matrix LX' to select a reorganization rule to scramble the binary sequence, where m = 1, 2, ... M, n = 1, 2, ... N;

[0034] The reorganization rules include: rule (i) pixel values are rotated right by 1 bit; rule (ii) pixel values are rotated left by 1 bit; rule (iii) pixel values are rotated right by 2 bits; rule (iv) pixel values are rotated left by 2 bits; rule (v) the upper and lower four bits of the pixel values are rotated right by 1 bit respectively; rule (vi) the upper and lower four bits of the pixel values are rotated left by 1 bit respectively; rule (vii) the positions of two adjacent pixel values are swapped; rule (viii) the upper and lower three bits of the pixel values are rotated right by 1 bit respectively, and the middle two bits are swapped.

[0035] Preferably, the method of sequentially selecting the reorganized matrix P2 according to the position index sequence Index is:

[0036] According to the values of two adjacent elements of the position index sequence Index, the pixels at the corresponding positions in the reorganized matrix P2 are selected to obtain pixel pairs. The formula is described as:

[0037]

[0038] Among them, i1 is an odd number, i1 <M*N;Pixel Ai1 and Pixel Bi1 They respectively represent the pixel values of the i1-th pixel pair in the pixel pair matrix, and the pixel pairs are arranged in a zigzag shape to form a pixel pair matrix.

[0039] Preferably, the crossover and mutation in step 6 is implemented by: changing the pixel value Pixel of the i1-th pixel pair to Ai1 and Pixel Bi1 ; Use 8-bit binary to represent Pixel A =a8a7a6a5a4a3a2a1 and Pixel B =b8b7b6b5b4b3b2b1, the pixel pair that generates the offspring is recorded as Pixel′ A =a′8a′7a′6a′5a′4a′3a′2a′1 and Pixel′ B =b′8b′7b′6b′5b′4b′3b′2b′1, the random number is recorded as C=lz′ i1 =c8c7c6c5c4c3c2c1,lz′ i1 is the i1th element in the sequence LZ', i1 is an odd number, i1 <M*N;

[0040] Crossover is: According to the random number C, if c f =0, pixel Pixel′ A Inheriting Pixel B Corresponding to the value of the binary bit, pixel Pixel' B Inheriting Pixel A The value of the corresponding binary bit; if c f=1, pixel Pixel′ A Inheriting Pixel A The value of the corresponding bit, pixel Pixel' B Inheriting Pixel B The value of the corresponding bit;

[0041] Mutation adopts non-uniform mutation, that is, for the pixel to be mutated, according to the random number C, if c f =0, the corresponding bit of the pixel changes: 0 becomes 1 or 1 becomes 0; if c f =1, the bit where the new pixel is located inherits the value of the bit where the original pixel is located.

[0042] Preferably, the formula for crossover and mutation is:

[0043]

[0044] Where, f=1,2,...,8;~ represents the inversion sign; a f 、b f 、c f 、a f ′, b′ f Represents 8-bit binary Pixel A 、Pixel B , random number C, Pixel′ A Pixel B The value of the fth bit of .

[0045] Preferably, the data processing III is implemented as follows: i =mod(floor(10 14 ×lw i ),256);

[0046] Among them, lw i and d i They are the pseudo-random sequence LW and the i-th element of the sequence D after data processing; the value of each element of the sequence D is in the range of 0 to 255.

[0047] Preferably, the ciphertext feedback method is:

[0048] Among them, the initial element c(0) = 127, s i is the i-th element of the one-dimensional sequence S, c i and c i-1 are the image sequences {c1, c2, c3, ...c M×N} the i-th and i-1-th elements, d i is the i-th element of sequence D;

[0049] The image sequence {c1,c2,c3,…c M×N} converted into a matrix is the ciphertext image E.

[0050] Compared with existing technologies, the present invention offers the following advantages: First, a method for generating a pseudo-random sequence associated with the plaintext is designed. After a small change in the plaintext pixel value, the change rate of the ciphertext pixel value reaches above 0.996, significantly improving the plaintext sensitivity and the algorithm's resistance to chosen-plaintext attacks. Second, a reorganization operation is used to achieve bit-level scrambling, and a selection strategy is used to achieve pixel-level scrambling. Finally, crossover and mutation operations are introduced into image encryption. To enhance the randomness of the pairing, a pseudo-random sequence generated by a chaotic system is used as a crossover and mutation operator. A diffusion operation is performed on selected pixel pairs, and finally, ciphertext feedback is performed. This invention organically combines the biological evolution strategy with the pseudo-randomness of a chaotic system. In the encryption scheme, the biological evolution strategy can better break the correlation between adjacent pixels, and the introduced crossover and mutation operations achieve excellent results in enhancing resistance to differential attacks. Experimental results and performance analysis demonstrate that the present invention has a very large key space, high key sensitivity, and is effective against exhaustive attacks, statistical analysis, and differential attacks. It can meet the image transmission security requirements of enterprise information systems and provide effective security protection in practical applications. The present invention not only improves the security of encrypted images, but also can resist noise and cropping attacks, thus meeting the demand for secure transmission of images in the network. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] Figure 1 It is a schematic diagram of the process of the present invention.

[0053] Figure 2 This is a planar phase diagram of the 3D chaotic system of the present invention, where (a) is the xy plane, (b) is the yz plane, and (c) is the xz plane.

[0054] Figure 3 Schematic diagram of hybridization operation, where (a) is single-point hybridization and (b) is multi-point hybridization.

[0055] Figure 4 Schematic diagram of the recombination rules of the present invention.

[0056] Figure 5Schematic diagram of the selection strategy of the present invention, where (a) is a pseudo-random sequence, ascending sequence and position index sequence with a length of 4*4, (b) is the pixel position pair representation corresponding to the 4*4 matrix, and (c) is a schematic diagram of the 4*4 matrix and its pixel pair selection.

[0057] Figure 6 Schematic diagram of hybridization and mutation of the present invention.

[0058] Figure 7 The original image and the corresponding encrypted image of the present invention, wherein (a) is the plaintext image, (b) is the ciphertext image, and (c) is the decrypted image.

[0059] Figure 8 is the histogram analysis result of the present invention, where (a) is the histogram of the original image of Lena, (b) is the histogram of the ciphertext image of Lena, (c) is the histogram of the original image of Pens, (d) is the histogram of the ciphertext image of Pens, (e) is the histogram of the original image of Saturn, (f) is the histogram of the ciphertext image of Saturn, (g) is the histogram of the original image of Bank, (h) is the histogram of the ciphertext image of Bank, (i) is the histogram of the original image of Finger, and (j) is the histogram of the ciphertext image of Finger.

[0060] Figure 9 Pixel statistics of randomly selected pixels and their adjacent pixels of the present invention, where (a) is the statistics of adjacent pixels in the horizontal direction of plaintext, (b) is the statistics of adjacent pixels in the horizontal direction of ciphertext, (c) is the statistics of adjacent pixels in the vertical direction of plaintext, (d) is the statistics of adjacent pixels in the vertical direction of ciphertext, (e) is the statistics of adjacent pixels in the diagonal direction of plaintext, and (f) is the statistics of adjacent pixels in the diagonal direction of ciphertext.

[0061] Figure 10 These are the encrypted and decrypted images of the present invention after being attacked by salt and pepper noise of different intensities, where (a) is the 1% intensity Pens encrypted image, (b) is the 5% intensity Pens encrypted image, (c) is the 10% intensity Pens encrypted image, (d) is the 1% intensity Pens decrypted image, (e) is the 5% intensity Pens decrypted image, and (f) is the 10% intensity Pens decrypted image.

[0062] Figure 11 These are the encrypted and decrypted images of the present invention after being attacked by salt and pepper noise of different intensities, where (a) is the 1% intensity Pens encrypted image, (b) is the 5% intensity Pens encrypted image, (c) is the 10% intensity Pens encrypted image, (d) is the 1% intensity Pens decrypted image, (e) is the 5% intensity Pens decrypted image, and (f) is the 10% intensity Pens decrypted image. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without creative work are within the scope of protection of the present invention.

[0064] like Figure 1 As shown in the figure, a corporate information image encryption method based on chaotic systems and biological evolution strategies includes two parts: biological evolution strategies and ciphertext feedback. The biological evolution strategies include recombination, selection, hybridization, and mutation. These operations achieve dual-reset chaos and diffusion of the image at the bit and pixel levels, thereby obfuscating the original image. Ciphertext feedback is performed using a pseudo-random sequence generated by a Sine map to obtain a ciphertext image. Ciphertext feedback can transmit changes during the encryption process, affecting encryption operations before and after the change point, giving the algorithm a good avalanche effect. The detailed encryption process steps are as follows:

[0065] Input a grayscale image P of size M*N, with initial parameter values x′0, y′0, z′0, and w′0; M and N are the number of rows and columns of the image respectively; output the ciphertext image E.

[0066] Step 1: Convert the grayscale image P to be encrypted with a size of M*N into an image matrix with a size of M*N, which is recorded as image matrix P1.

[0067] Step 2: Use the hash function to calculate the hash value of the image matrix P1, and use the hash value to calculate the initial value w0 of the Sine map and the initial parameter values x0, y0, and z0 of the 3D chaotic system.

[0068] A chaotic system refers to a deterministic system with seemingly random irregular motions. Its behavior is uncertain, non-repeatable, and unpredictable. To balance the relationship between the complexity and efficiency of a chaotic system, the present invention adopts two chaotic systems: Sine mapping and 3D chaotic system.

[0069] In classic chaotic mapping equations, the sine function plays an important role and is always related to its own mapping. The Sine map is a chaotic mapping based on the sine function. It has extremely complex dynamic behavior and is widely used in the field of image encryption due to its simple structure and high transmission efficiency. The mathematical expression of the Sine map is as follows:

[0070] w n+1 =μsin(πw n ) (1)

[0071] Where w is the state variable, w n+1and w n denote the results of the state variables at the n+1th and nth iterations, respectively, and μ is the system parameter. When the system parameter μ∈(0.87,0.93) and (0.95,1), the Sine map is in a good chaotic state, and the pseudo-random sequence it generates is more suitable for image encryption.

[0072] Since Lorenz discovered the first classic three-dimensional autonomous chaotic system, it has attracted the attention of numerous researchers, leading to the discovery of many new three-dimensional chaotic systems, such as the Chern system and the LV system. This paper utilizes a novel 3D chaotic system with linear equilibrium. This chaotic system is highly sensitive to initial conditions and exhibits richer and more complex dynamic behaviors than most known chaotic systems, providing a good theoretical basis for the generation of more complex encrypted chaotic sequences. The mathematical expression of the 3D chaotic system is as follows:

[0073]

[0074] Among them, a and b are system parameters. When the system parameters are (a, b) = (2.6, 1.5), the 3D chaotic system is in a good chaotic state and can be used to generate the pseudo-random sequence required by the image encryption algorithm. Figure 2 is the plane phase diagram of the 3D chaotic system, through Figure 2 It can be seen that the chaotic system has good chaotic characteristics.

[0075] To ensure that different images use different keys, the present invention associates the key with the plaintext image and uses the pixel value and hash value of the plaintext image to update the key. The plaintext image is encrypted using the SHA-256 algorithm to obtain a 256-bit binary hash value H, which is used to update the initial key. The hash value H is divided into 32 bytes, represented as: h1, h2, ..., h 32 According to formulas (3)-(5), the updated key set is calculated and used as the initial value of the two chaotic systems.

[0076]

[0077] Among them, Q1, Q2, Q3, Q4, ɑ, β, γ and ω are all calculated intermediate variables. is the floor function, q m is the average value of the M pixel values in the mth column of the image matrix P1, which is determined by the average value of the pixel values in each column of the plaintext image; is an XOR operation, mod(·) is a modulo operation; x′0, y′0, z′0, and w′0 are the given initial values of the parameters.

[0078] Step 3: Iterate the 3D chaotic system, discard a certain number of iteration values to remove transient effects, and obtain three pseudo-random sequences LX, pseudo-random sequence LY and pseudo-random sequence LZ with a length of M*N.

[0079] Using a given external key and the plaintext image, the initial parameters of the chaotic system are generated. The system is then iterated to produce a pseudo-random sequence. This key is associated with the plaintext, achieving a one-time, one-pad effect. A certain number of iterations is discarded to eliminate the adverse effects of transient effects; here, 1000 iterations is acceptable.

[0080] Step 4: Process the pseudo-random sequence LX according to formula (6) so that the value range of each element is between 1 and 8 and reshape it into a matrix form, namely matrix LX1, for selecting the recombination rule. Use the selected recombination rule to reorganize and scramble each pixel in the image matrix P1 to obtain the reorganized matrix P2.

[0081] lx′ i =mod(floor(10 14 ×lx i ),8)+1 (6)

[0082] Among them, floor(·) is the rounding operation, lx i is the i-th element of the pseudo-random sequence LX, lx′ i is the i-th element in the sequence after data processing, i=1,2,...M*N.

[0083] Biological evolution strategies are similar to the genetic operations of genetic algorithms, primarily including recombination, selection, hybridization, and mutation. The primary goal of biological evolution is to generate new populations from existing populations, thereby producing new, better individuals. Genes can be encoded using binary coding, value coding, tree coding, or permutation coding. Binary coding is the most popular method because genes can be encoded in binary strings of 0s and 1s. The present invention employs binary coding.

[0084] Recombination is the foundation of genetic variation and species evolution. It refers to the reassortment of genes controlling different traits during sexual reproduction. It occurs in every generation of diploid organisms. The two copies of each chromosome may have different alleles at certain positions. By swapping corresponding parts between chromosomes, recombinant chromosomes can be produced that differ from the parental chromosomes.

[0085] The purpose of the selection operation is to select the parent to participate in the crossover and mutation operations.

[0086] Crossover is also called hybridization. Hybridization is a major link in the process of biological inheritance and evolution. It is the main way to cultivate new individuals. It refers to the exchange of some genes of two paired chromosomes in a certain way to form two new individuals. The commonly used pairing strategy is random pairing, that is, the individuals in the population are randomly organized into paired groups. The genes between individuals are crossed in pairs to achieve gene exchange, thereby forming two new individuals. Crossover methods include single-point crossover, two-point crossover, multi-point crossover, uniform crossover, arithmetic crossover, etc. For binary coding, single-point crossover refers to randomly selecting a bit in the binary string and exchanging the binary strings after that bit in the two parents to produce a new individual; multi-point crossover is performed by selecting two points on the parent sequence and exchanging bits between the two points in the two parent sequences to obtain two subsequences. Operation Figure 3 As shown, the crossover operation is usually performed on a single point, multiple points, or uniform points.

[0087] The basis of genetic variation lies in biological mutation, which introduces diversity from one generation to the next. Genetic mutation alters one or more genes in the current generation to create the next generation's genes, potentially completely changing the genes involved. This allows genetic algorithms to generate better genes through the mutation process.

[0088] The present invention uses the idea of gene recombination to convert the grayscale value of the pixel of the image to be encrypted into an eight-bit binary sequence, and then reorganizes the binary sequence of the pixel to achieve the effect of bit-level scrambling. Figure 4 As shown, the present invention defines eight recombination rules: Rule (i) pixel values are rotated right by 1 bit; Rule (ii) pixel values are rotated left by 1 bit; Rule (iii) pixel values are rotated right by 2 bits; Rule (iv) pixel values are rotated left by 2 bits; Rule (v) the upper and lower four bits of the pixel value are each rotated right by 1 bit; Rule (vi) the upper and lower four bits of the pixel value are each rotated left by 1 bit; Rule (vii) adjacent two bits are swapped; Rule (viii) the upper and lower three bits are each rotated right by 1 bit, and the middle two bits are swapped. For a given pixel, a recombination rule is randomly selected to scramble its binary sequence to achieve a change in the pixel value. The random selection here can be achieved by a pseudo-random sequence generated by a chaotic system. Figure 4 Schematic diagram of the recombination rules (i)-(viii).

[0089] The value of each element in the matrix LX1 is used to determine the rule for selecting the pixel at the corresponding position. For example, if the value of the element in the 3rd row and 5th column of the matrix LX1 is 3, and the pixel value in the 3rd row and 5th column of the pixel matrix P1 is 50, then the binary representation of the pixel value 50 is reorganized using Rule 3. That is, 50 (binary representation 00110010) becomes 140 (binary representation 10001100) after reorganization. The pixel value is changed by the reorganization rule.

[0090] Step 5: Sort the pseudo-random sequence LY in ascending order to obtain a new sequence LY'; mark the position of the elements in the new sequence LY' in the pseudo-random sequence LY to obtain a position index sequence Index; select the matrix P2 in sequence according to the position index sequence Index to obtain two pixel pairs.

[0091] Given a matrix P2 of size M*N, the present invention uses a random traversal to traverse all pixels, unlike the selection in optimization algorithms. Because pseudo-random sequences generated by chaotic systems are easy to generate, highly sensitive to initial conditions, and completely reproducible, the present invention uses pseudo-random sequences to achieve random selection.

[0092] The pseudo-random sequence LY generated by the 3D chaotic system is rearranged in ascending order to obtain an ordered sequence LY'. Find the position of each element of the ordered sequence LY' in the original sequence LY, and compose these position sequences into a new sequence in order, that is, the position index sequence Index = {Index1, Index2, Index3, ... Index M*N}, Index1, Index2, Index3,…Index M*N is the element value of the position index sequence Index. According to the values of two adjacent elements of the position index sequence Index, the pixel at the corresponding position in the matrix P2 is selected according to formula (7). For example, according to the values of two adjacent elements Index in the index sequence Index i1 and Index i1+1 , get pixel pair Pixel Ai1 Pixel vs. Pixel Bi1 , represented by 8-bit binary as Pixel A =a8a7a6a5a4a3a2a1 and Pixel B =b8b7b6b5b4b3b2b1, the pixel pair that generates the offspring is recorded as Pixel′ A =a′8a′7a′6a′5a′4a′3a′2a′1 and Pixel′ B =b′8b′7b′6b′5b′4b′3b′2b′1, Figure 5 Schematic diagram of the selection strategy. Figure 5 (a) is a chaotic sequence of length 4*4, namely a pseudo-random sequence, an ascending sequence and a position index sequence. Figure 5 (b) is the pixel position pair representation corresponding to the 4*4 matrix, Figure 5 (c) is a schematic diagram of a 4*4 pixel matrix and its pixel pair selection. The selection formula is described as follows:

[0093]

[0094] Among them, mod(·) is the modulo operation; floor(·) is the integer operation, i1 is an odd number, i1 <M*N。Pixel Ai1 and Pixel Bi1 They respectively represent the pixel values of the i1th pixel pair in the pixel pair matrix.

[0095] Step 6: Process the pseudo-random sequence LZ according to formula (8) so that the value of each element is in the range of 0 to 255. Sequentially select the elements at odd positions in the processed sequence LZ' as random numbers, and perform crossover and mutation on the two pixel pairs selected in step 5 to obtain the matrix P3.

[0096] lz′ i =mod(floor(10 14 ×lz i ),256) (8)

[0097] Among them, lz i and lz′ i are the i-th element of the pseudo-random sequence LZ and the sequence after data processing, respectively, i=1,2,...M*N.

[0098] The present invention uses hybridization and mutation to change the bit sequence, thereby improving the robustness and security of encryption. Given two parents and a random number, two offspring individuals are obtained after hybridization. The individuals here are the pixels in the image. Each pixel value in the image has 256 gray levels, and the pixel value can be represented by 8-bit binary. According to the previous selection strategy, the pixel value of the selected pixel pair is recorded as Pixel A =a8a7a6a5a4a3a2a1 and Pixel B =b8b7b6b5b4b3b2b1, the pixel pair that generates the offspring is recorded as Pixel′ A =a′8a′7a′6a′5a′4a′3a′2a′1 and Pixel′ B =b′8b′7b′6b′5b′4b′3b′2b′1. The random number is recorded as C=c8c7c6c5c4c3c2c1.

[0099] (1) Hybridization: According to the random number C = c8c7c6c5c4c3c2c1, if c f =0, pixel Pixel′ A Inheriting Pixel B Corresponding to the value of the binary bit, pixel Pixel' B Inheriting Pixel A The value of the corresponding binary bit; if c f =1, pixel Pixel′A Inheriting Pixel A The value of the corresponding bit, pixel Pixel' B Inheriting Pixel B The value of the corresponding bit. Here, the value of f is 1-8.

[0100] (2) Mutation: Non-uniform mutation is used, that is, for the pixel to be mutated, according to the random number C, if c f =0, the corresponding bit of the pixel changes: 0 becomes 1, or 1 becomes 0; if c f =1, the bit where the new pixel is located inherits the value of the bit where the original pixel is located. Thus, two new individual Pixel' A and Pixel′ B ,like Figure 6 shown.

[0101] For the selected pixel pairs, the present invention uses the same random number for hybridization and mutation, so the hybridization and mutation operations can be performed simultaneously. The hybridization and mutation can be described by the following formula:

[0102]

[0103] Where, f = 1, 2, ..., 8; Indicates the inversion operation. If x=0, then If x=1, then a f 、b f 、c f , a′ f , b′ f Represents 8-bit binary Pixel A 、Pixel B , random number C, Pixel′ A Pixel B The value of the fth bit of .

[0104] The plaintext is reorganized and selected to achieve bit-level and pixel-level scrambling of the image; the image is further diffused through crossover and mutation operations to achieve the purpose of confusing the original image.

[0105] Step 7: Iterate the Sine map based on the initial value w0, discard the iterative values after a certain number of times to remove the transient effect, and obtain a pseudo-random sequence LW of length M*N. Perform data processing on the pseudo-random sequence LW according to formula (11); convert the matrix P3 into a one-dimensional sequence S, perform ciphertext feedback on each pixel according to the ciphertext feedback operation, and restore it to matrix form to obtain the matrix P4, which is the ciphertext image E.

[0106] lw′ i =mod(floor(1014 ×lw i ),256) (11)

[0107] Among them, lw i and lw′ i They are the i-th element of the pseudo-random sequence LW and the sequence after data processing, i=1,2,...M*N.

[0108] Ciphertext feedback is an operation that strengthens the mutual influence between pixels and changes the pixel values. Ciphertext feedback allows small changes in the plaintext to propagate to the entire ciphertext, enhancing the algorithm's resistance to differential and statistical attacks. With the help of the pseudo sequence generated by the chaotic map, the previous pixel value and the pseudo sequence elements are combined to change the current pixel value, effectively propagating a small amount of plaintext image changes to the entire ciphertext image. Given a pseudo-random sequence D of length M*N = {d1, d2, d3, ... d M×N}, where the element values in D are all between 0 and 255. Convert the image matrix into a one-dimensional sequence S = {s1, s2, s3, ... s M×N}, the image sequence after feedback is recorded as C = {c1, c2, c3, ... c M×N}, the feedback process is shown in formula (12):

[0109]

[0110] Among them, the initial element c(0)=127, i=1,2,…,M*N.

[0111] Converting the image sequence C into a matrix forms the ciphertext image E.

[0112] The decryption algorithm is the inverse process of the encryption algorithm, which will not be described here. In addition, the present invention is also applicable to the encryption of color images, which only requires decomposing the pixels of the image into RGB channels.

[0113] In order to verify the feasibility and effectiveness of the present invention, five grayscale images of size 256×256, Lena, Pens, Saturn, Bank, and Finger, were selected and experiments were carried out in the Matlab2018 environment. The key was given with the value x′0=y′0=z′0=w′0=0.01. The original image, ciphertext image, and decrypted image are shown in Figure 2. Figure 7 As shown in Figure 2, through intuitive observation, the ciphertext image has completely lost the characteristics of the plaintext image. This algorithm is lossless, and the decrypted image obtained after decrypting the ciphertext image is exactly the same as the original image.

[0114] A good encryption algorithm should be sensitive to the key and be able to resist common attacks. In order to comprehensively evaluate the proposed model, common performance indicators are used, including key analysis, time complexity analysis, statistical attack analysis and differential attack analysis.

[0115] In encryption systems, keys play a crucial role and require a high level of security. The present invention is extremely sensitive to its key, original image, and encrypted image, so that even the slightest change in any of them results in a significantly different generated image. For example, if the encrypted image is subjected to even the slightest perturbation, the resulting image will appear random, primarily due to the application of chaotic systems, which are extremely sensitive to even the slightest changes.

[0116] Attackers will try to use all possible keys to crack the encryption system, so a larger key space has a higher resistance to brute force attacks. Studies have shown that even with powerful computers, if the key space is larger than 2 100 , the encryption method cannot be cracked by brute force attack within the specified time. The key stream length of the present invention reaches 10 60 >2 100 , enough to resist any brute force attack.

[0117] The performance of the image encryption scheme of the present invention is tested by statistical analysis. The statistical method analyzes any foreseeable relationship between the original image and the encrypted image.

[0118] The histogram is defined as the number of pixels in each grayscale of the image. The histograms of the original image and the ciphertext image of the present invention are as follows: Figure 8 For a good cryptographic system, the distribution of pixels in the encrypted image should be uniform and different from the histogram of the original image. Figure 8 It is obvious from the figure that the attacker will not be able to derive any statistical information from the cipher image because the distribution of pixel values is uniform in the cipher image.

[0119] In order to prove that this uniformity is not only visually uniform but also theoretically uniform, a chi-square test is performed on the ciphertext image using hist i (i=0,1,…,255) represents the histogram of the image, then the histogram χ 2 The distribution calculation formula is described in formula (13):

[0120]

[0121] The histogram follows a χ2 with 255 degrees of freedom. 2 Distribution. Given a significance level α, Right now When the significance level α=0.01, 0.05 and 0.1, there is The χ of the test image 2 The distribution is shown in Table 1. The commonly used significance level is α = 0.05, and all the ciphertext images in Table 1 pass the test. By comparison, it can be seen that the present invention greatly changes the histogram distribution of the image and has a good ability to break the statistical characteristics of the original image.

[0122] Table 1 Histogram of χ 2 Distribution Statistics

[0123]

[0124] Adjacent pixels in a plaintext image have high correlation in the horizontal, vertical, and diagonal directions. An ideal encryption algorithm can reduce the correlation between adjacent pixels in a ciphertext image, thereby effectively resisting statistical attacks. The correlation coefficient calculation formula is:

[0125]

[0126] Where x and y are pixel values, cov(x,y) is the covariance, D(x) is the variance, E(x) is the mean, and ρ xy is the correlation coefficient. N is the number of pixels tested for correlation.

[0127] In order to analyze the correlation between adjacent pixels in plaintext images and ciphertext images, taking Lena, Boat, Hill and Face images as examples, 10,000 pairs of adjacent pixels are randomly selected in plaintext images and ciphertext images for testing. Figure 9 As shown in Table 2, the distribution of adjacent pixels in the plaintext images of these images is highly concentrated, resulting in a very high correlation between adjacent pixels in the plaintext images. However, the distribution of adjacent pixels in the ciphertext images is random, meaning that after encryption, the correlation between adjacent pixels in these ciphertext images decreases. The correlation coefficients in various directions between the plaintext and ciphertext images in Table 2 also show that the correlation between adjacent pixels in the ciphertext images is lower than that between adjacent pixels in the plaintext images.

[0128] Table 2 Correlation coefficients of plaintext images and ciphertext images in each direction

[0129]

[0130] Information entropy is a disordered statistical measure that reflects the randomness of information. The calculation formula for information entropy is:

[0131]

[0132] Where L is the grayscale value of the image. For an 8-bit grayscale image, L = 255. iis the i-th grayscale value on the image, P(m i ) represents the gray value m i The probability of a completely randomly generated image is 8. The ideal value of information entropy is 8. The closer the information entropy of the ciphertext image is to 8, the more random the image information is. As shown in Table 3, after encryption, the information entropy of the ciphertext images is close to 8.

[0133] Table 3 Information entropy of plaintext image and ciphertext image

[0134]

[0135] A differential attack involves studying the effect of differences in plaintext images on their ciphertext images, establishing a relationship between the plaintext image and the corresponding ciphertext image, and thereby cracking the encryption algorithm. The number of pixel change rate (NPCR) and the unified pixel average change intensity (UACI) are two methods for testing whether an encryption method is resistant to differential attacks. NPCR reflects the ratio of the number of unequal pixels at the same position in two images to the total number of pixels in the image, while UACI is the overall average change density, representing the average change intensity of a planar image. The ideal values of NPCR and UACI are 99.6094% and 33.4635%, respectively. Assuming that P1 and P2 are two ciphertext images, and their plaintext images differ by only one bit, their NPCR and UACI values are calculated as follows:

[0136]

[0137] Where P1(i,j)≠P2(i,j).

[0138] Table 4 shows the NPCR and UACI detection results of several images. It can be seen that the encryption method of the present invention is more resistant to differential attacks.

[0139] Table 4. Image test results

[0140]

[0141] During digital image transmission, noise can interfere with the image for various reasons. An effective image encryption algorithm can reconstruct a recognizable decrypted image despite noise interference or data loss. Pens' ciphertext image was decrypted after adding 1%, 5%, and 10% salt and pepper noise, respectively. Figure 10 The experimental results of encrypted and decrypted images of Pens with noise intensity of 1%, 5%, and 10%. Figure 10It can be seen from the figure that even if the noise intensity reaches 10%, the decrypted image can still be recognized. This shows that the encryption algorithm of the present invention can effectively resist the attack of noise.

[0142] When an image is transmitted over a network, data may be lost due to various reasons. By cropping a portion of the ciphertext image and decrypting the cropped ciphertext image, we can test the ability of the ciphertext image to be restored to the plaintext image when data is lost, and analyze the performance of the encryption algorithm against cropping attacks. Cropping attack analysis can reflect the scrambling effect of the encryption algorithm on the plaintext image. The better the scrambling effect, the stronger the degree of recovery of the visual features of the plaintext image by the encryption algorithm when part of the ciphertext is lost. Figure 11 As shown, the ciphertext image of Pens is cropped to 1 / 64, 1 / 16 and 1 / 4 respectively and then decrypted, and the information of the decrypted image can be identified. Therefore, the present invention can resist cropping attacks.

[0143] This invention organically combines biological evolution strategies with the pseudo-randomness of chaotic systems to propose an image encryption scheme. The use of biological evolution strategies in the encryption scheme effectively breaks down the correlation between adjacent pixels, and the introduced crossover and mutation operations achieve excellent results in enhancing resistance to differential attacks. Experimental and simulation results demonstrate that the proposed encryption scheme provides a very large key space and high key sensitivity. It can effectively resist exhaustive attacks, statistical analysis, and differential attacks, meeting the image transmission security requirements of enterprise information systems and providing effective security measures in practical applications.

[0144] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for encrypting enterprise information images based on chaotic systems and biological evolution strategies, characterized in that: The steps are as follows: Step 1: Convert the grayscale image P to be encrypted into an image matrix P1 of size M*N; where M and N are the number of rows and columns of the grayscale image P respectively; Step 2: Use the hash function to calculate the hash value of the image matrix P1, and use the hash value to calculate the initial value w0 of the Sine map and the initial parameter values x0, y0, z0 of the 3D chaotic system; Step 3: Use the initial parameter values x0, y0, and z0 to iterate the 3D chaotic system to obtain three pseudo-random sequences LX, LY, and LZ of length M*N; Step 4: Perform data processing I on the pseudo-random sequence LX and convert it into a matrix LX'. Select a reorganization rule according to the element values of the matrix LX'. Use the selected reorganization rule to reorganize and scramble each pixel in the image matrix P1 to obtain a reorganized matrix P2. Step 5: Sort the pseudo-random sequence LY in ascending order to obtain the sequence LY', mark the position of the elements in the new sequence LY' in the pseudo-random sequence LY to obtain the position index sequence Index, and select the reorganized matrix P2 in sequence according to the position index sequence Index to obtain the pixel pair matrix; Step 6: Perform data processing II on the pseudo-random sequence LZ to obtain the sequence LZ', sequentially select the elements at odd positions in the sequence LZ' as random numbers, and perform crossover and mutation on the pixel pairs in the pixel pair matrix in turn to obtain the matrix P3; Step 7: Iterate the Sine map based on the initial value w0 to obtain a pseudo-random sequence LW of length M*N, perform data processing III on the pseudo-random sequence LW to obtain sequence D; convert the matrix P3 into a one-dimensional sequence S, use sequence D to perform ciphertext feedback on each pixel of the one-dimensional sequence S, and convert it into a matrix form to obtain the ciphertext image E.

2. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 1 is characterized in that: The hash function is the SHA-256 algorithm, which is used to perform encryption operation on the image matrix P1 to obtain a 256-bit binary hash value H; The method for calculating the initial value w0 of the Sine map and the initial parameter values x0, y0, z0 of the 3D chaotic system is: The hash value H is divided into 32 bytes, represented as: h1, h2, ..., h 32 ;but Among them, Q1, Q2, Q3, Q4, α, β, γ and ω are all intermediate variables of calculation. is the floor function, q n is the average value of the M pixel values in the nth column of the image matrix P1; is the XOR operation, mod(,) is the modulo operation; x′0, y′0, z′0 and w′0 are the given initial values of the parameters.

3. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 1 or 2, characterized in that: The Sine mapping is: t+1 =μsin(πw t ); Where w is the state variable, w t+1 and w t denote the values of the state variables at the t+1th and tth iterations, respectively, and μ is the system parameter. When the system parameter μ∈(0.87,0.93) and (0.95,1), the Sine map is in a good chaotic state. The mathematical expression of the 3D chaotic system is: Among them, a and b are system parameters. When the system parameters are (a, b) = (2.6, 1.5), the 3D chaotic system is in a good chaotic state.

4. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 3 is characterized in that: The iteration of the 3D chaotic system in step 3 and the iteration of the Sine map in step 7 are both discarded with iteration values greater than 1000 times to remove transient effects; In step 4, the data processing I makes the value range of each element of the pseudo-random sequence LX between 1 and 8, and lx i ′=mod(floor(10 14 ×lx i ),8)+1; Among them, floor(·) is the rounding down operation, mod(,) is the modulus operation, lx i is the i-th element of the pseudo-random sequence LX, lx i ′ is the i-th element in the sequence after data processing, i = 1, 2, ... M*N; The data processing II in step 6 makes each element value of the pseudo-random sequence LZ within the range of 0 to 255, and lz i ′=mod(floor(10 14 ×lz i ),256); Among them, lz i and lz′ i are the i-th element of the pseudo-random sequence LZ and the sequence after data processing, respectively.

5. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 4 is characterized in that: The method for reorganizing and scrambling each pixel in the image matrix P1 is as follows: converting the grayscale value of the pixel at any position (m, n) in the image matrix P1 into an eight-bit binary sequence, and using the element value at position (m, n) of the matrix LX' to select a reorganization rule to scramble the binary sequence, where m = 1, 2, ... M, and n = 1, 2, ... N; The reorganization rules include: rule (i) pixel values are rotated right by 1 bit; rule (ii) pixel values are rotated left by 1 bit; rule (iii) pixel values are rotated right by 2 bits; rule (iv) pixel values are rotated left by 2 bits; rule (v) the upper and lower four bits of the pixel values are rotated right by 1 bit respectively; rule (vi) the upper and lower four bits of the pixel values are rotated left by 1 bit respectively; rule (vii) the positions of two adjacent pixel values are swapped; rule (viii) the upper and lower three bits of the pixel values are rotated right by 1 bit respectively, and the middle two bits are swapped.

6. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 4 or 5, characterized in that: The method for sequentially selecting the reorganized matrix P2 according to the position index sequence Index is: According to the values of two adjacent elements of the position index sequence Index, the pixels at the corresponding positions in the reorganized matrix P2 are selected to obtain pixel pairs. The formula is described as: Among them, i1 is an odd number, i1 <M*N;Pixel Ai1 and Pixel Bi1 They respectively represent the pixel values of the i1-th pixel pair in the pixel pair matrix, and the pixel pairs are arranged in a zigzag shape to form a pixel pair matrix.

7. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 6 is characterized in that: The implementation method of the crossover and mutation in step 6 is: the pixel value Pixel of the i1-th pixel pair Ai1 and Pixel Bi1 ; Use 8-bit binary to represent Pixel A =a8a7a6a5a4a3a2a1 and Pixel B =b8b7b6b5b4b3b2b1, the pixel pair that generates the offspring is recorded as Pixel′ A =a′8a′7a′6a′5a′4a′3a′2a′1 and Pixel′ B =b′8b′7b′6b′5b′4b′3b′2b′1, the random number is recorded as C=lz′ i1 =c8c7c6c5c4c3c2c1,lz′ i1 is the i1th element in the sequence LZ', i1 is an odd number, i1 <M*N; Crossover is: According to the random number C, if c f =0, pixel Pixel′ A Inheriting Pixel B Corresponding to the value of the binary bit, pixel Pixel' B Inheriting Pixel A The value of the corresponding binary bit; if c f =1, pixel Pixel′ A Inheriting Pixel A The value of the corresponding bit, pixel Pixel' B Inheriting Pixel B The value of the corresponding bit; c f represents the value of the fth bit of the random number C; Mutation adopts non-uniform mutation, that is, for the pixel to be mutated, according to the random number C, if c f =0, the corresponding bit of the pixel changes: 0 becomes 1 or 1 becomes 0; if c f =1, the bit where the new pixel is located inherits the value of the bit where the original pixel is located.

8. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 7 is characterized in that: The formulas for crossover and mutation are: Where, f=1,2,...,8;~ represents the inversion sign; a f 、b f , a′ f 、b f ' represents 8-bit binary Pixel A 、Pixel B Pixel A Pixel B The value of the fth bit of .

9. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 7 or 8, characterized in that: The implementation method of the data processing III is: i =mod(floor(10 14 ×lw i ),256); Among them, lw i and d i They are the pseudo-random sequence LW and the i-th element of the sequence D after data processing; the value of each element of the sequence D is in the range of 0 to 255.

10. The enterprise information image encryption method based on chaotic system and biological evolution strategy according to claim 9 is characterized in that: The method of ciphertext feedback is: Among them, the initial element c(0) = 127, s i is the i-th element of the one-dimensional sequence S, c i and c i-1 are the image sequences {c1, c2, c3, ...c M×N } the i-th and i-1-th elements, d i is the i-th element of sequence D; The image sequence {c1,c2,c3,…c M×N } converted into a matrix is the ciphertext image E.

Images