Chaotic image encryption system and method based on discrete fractional-order neural network with dynamic transcription of RNA and DNA coding

Abstract

The application belongs to the technical field of image encryption and discloses a discrete fractional-order neural network chaotic image encryption system and method based on RNA dynamic transcription and DNA coding, which comprises a model construction module, a key generation module and an image encryption module; the model construction module is used for constructing a fractional-order neural network and making the encryption system in a hyperchaotic state based on the fractional-order neural network; the key generation module generates an RNA key stream through three rounds of dynamic transcription with a seed sequence as a starting point; the image encryption module encrypts an image through triple hybrid diffusion and then diffuses the image again based on the RNA key stream to obtain an encrypted image; the application realizes deep confusion and diffusion of image pixels by constructing a high-complexity fractional-order chaotic neural network and combining an RNA+DNA dual biological coding mechanism, thereby improving the security, randomness and robustness of the encryption system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of image encryption, and particularly relates to a discrete fractional-order neural network chaotic image encryption system and method based on RNA dynamic transcription and DNA coding. BACKGROUND

[0002] With the development of information technology, the security demand of image data in transmission and storage is increasingly prominent. Traditional encryption methods (such as symmetric encryption and asymmetric encryption) have limitations such as high computational complexity and limited attack resistance when processing high-dimensional complex images; although the existing encryption schemes based on chaotic neural networks use the sensitivity of chaotic initial values to improve security, they generally have problems such as insufficient key space and single dynamic characteristics, which are difficult to meet the needs of high-security scenarios.

[0003] Specifically, the defects of the prior art are as follows: (1) the dynamic characteristics of integer-order chaotic systems are simple, the key space is limited, and it is easy to be cracked by differential attack or statistical analysis; (2) a single encryption mechanism (such as relying only on chaotic diffusion or a single biological coding) is difficult to achieve deep confusion of pixels, and the correlation between adjacent pixels is high; (3) the robustness to noise, clipping and other attacks is insufficient, and the decryption effect is seriously degraded after local damage of the encrypted image.

[0004] Therefore, there is an urgent need for an encryption scheme that combines high-complexity chaotic systems and multiple biological coding mechanisms to improve the security and robustness of image encryption. SUMMARY

[0005] The application aims to solve the problems of the prior art and provides the following solutions:

[0006] The discrete fractional-order neural network chaotic image encryption system based on RNA dynamic transcription and DNA coding comprises a model construction module, a key generation module and an image encryption module.

[0007] The model construction module is used to construct a fractional-order neural network and make the encryption system in a hyperchaotic state based on the fractional-order neural network.

[0008] The key generation module generates an RNA key stream through three rounds of dynamic transcription starting from a seed sequence.

[0009] The image encryption module performs triple hybrid diffusion encryption on the image to be encrypted, and then performs another diffusion based on the RNA key stream to obtain an encrypted image.

[0010] Preferably, in the model construction module, the process of constructing the fractional-order neural network comprises:

[0011] A discrete fractional Caputo operator is defined.

[0012] ,

[0013] in, C Indicates the identifier of a Caputo-type fractional operator. Represents the difference operation of fractional order. q Indicates the fractional order. p This represents the discrete time step parameter. Represents the neuron's state variables. Γ Represents the gamma function. m express q Round up. n Representing discrete time points, This represents the time shift operator. s Represents state variables, express m Integer-order difference;

[0014] A locally active memristor model is introduced to simulate synaptic connections. The locally active memristor model is as follows:

[0015] ,

[0016] in, i ( n () indicates the output current. v ( n () indicates the input voltage. W Indicates the conductance of the memristor. α , β , γ Indicates the adjustment parameter;

[0017] Constructing the activation function of the four-dimensional neuron dynamics equation tanh ( x ):

[0018] The fractional neural network is constructed based on the discrete fractional Caputo operator, the locally active memristor model, and the activation function of the four-dimensional neuron dynamics equation:

[0019] ,

[0020] ,

[0021] ,

[0022] ,

[0023] ,

[0024] in, y ( n ),z n ) and w n denotes a state variable of a neuron, m n denotes a state variable of a memristor, w denotes a synaptic weight, j denotes a discrete-time history traversal index, w 11 denotes the connection strength of the 1st neuron to the 1st neuron, w 12 denotes the connection strength of the 1st neuron to the 2nd neuron, w 13 denotes the connection strength of the 1st neuron to the 3rd neuron, w 14 denotes the connection strength of the 1st neuron to the 4th neuron, w 21 denotes the connection strength of the 2nd neuron to the 1st neuron, w 22 denotes the connection strength of the 2nd neuron to the 2nd neuron, w 23 denotes the connection strength of the 2nd neuron to the 3rd neuron, w 24 denotes the connection strength of the 2nd neuron to the 4th neuron, w 32 denotes the connection strength of the 3rd neuron to the 2nd neuron, w 33 denotes the connection strength of the 3rd neuron to the 3rd neuron, w 34 denotes the connection strength of the 3rd neuron to the 4th neuron, w 41 denotes the connection strength of the 4th neuron to the 1st neuron, w 42 denotes the connection strength of the 4th neuron to the 2nd neuron, w 43 denotes the connection strength of the 4th neuron to the 3rd neuron, w 44 denotes the connection strength of the 4th neuron to the 4th neuron, k 1 denotes the coupling strength of the local active memristor model, x y and z denotes a state of a neuron, a b and c denotes a parameter regulating the dynamics of a neuron.​​​​​

[0025] Preferably, the workflow of the key generation module comprises:

[0026] Starting from the seed sequence, three rounds of dynamic transcription and gene mutation are performed to obtain RNA bases;

[0027] The RNA bases are mapped to a value of 0-255 to obtain the RNA key stream with a length of 256.

[0028] Preferably, the workflow of the image encryption module comprises:

[0029] The pre-processing and size adjustment are performed on the image to be encrypted to obtain a processed image;

[0030] The three mixed diffusion operations of chaotic XOR diffusion, chaotic modulo addition diffusion and DNA encoding diffusion are performed on the processed image to obtain a diffused image;

[0031] The global cyclic shift operation is performed on the diffused image to obtain an enhanced diffused image;

[0032] After repeating the three mixed diffusion operations and the global cyclic shift operation for 16 rounds, the RNA key diffusion is performed based on the RNA key stream to obtain the encrypted image.

[0033] The application also provides a discrete fractional-order neural network chaotic image encryption method based on RNA dynamic transcription and DNA encoding, which is applied to the encryption system described above and comprises the following steps:

[0034] The fractional-order neural network is constructed, and the encryption system is brought into a hyperchaotic state based on the fractional-order neural network;

[0035] Starting from the seed sequence, the RNA key stream is generated through three rounds of dynamic transcription;

[0036] The three mixed diffusion encryption is performed on the image to be encrypted, and then the RNA key stream is used for further diffusion to obtain the encrypted image.

[0037] Preferably, the process of constructing the fractional-order neural network comprises:

[0038] The discrete fractional Caputo operator is defined as:

[0039] ,

[0040] wherein, C denotes the identification of the Caputo fractional operator, denotes the difference operation of the fractional order, q denotes the fractional order, pThis represents the discrete time step parameter. Represents the neuron's state variables. Γ Represents the gamma function. m express q Round up. n Representing discrete time points, This represents the time shift operator. s Represents state variables, express m Integer-order difference;

[0041] A locally active memristor model is introduced to simulate synaptic connections. The locally active memristor model is as follows:

[0042] ,

[0043] in, i ( n () indicates the output current. v ( n () indicates the input voltage. W Indicates the conductance of the memristor. α , β , γ Indicates the adjustment parameter;

[0044] Constructing the activation function of the four-dimensional neuron dynamics equation tanh ( x ):

[0045] The fractional neural network is constructed based on the discrete fractional Caputo operator, the locally active memristor model, and the activation function of the four-dimensional neuron dynamics equation:

[0046] ,

[0047] ,

[0048] ,

[0049] ,

[0050] ,

[0051] in, y ( n ), z ( n )and w ( n ) represents the neuron's state variable. m ( n ) represents the state variable of the memristor. w Indicates synaptic weight, ja history traversal index representing discrete time, w 11 a connection strength of the first neuron to the first neuron, w 12 a connection strength of the first neuron to the second neuron, w 13 a connection strength of the first neuron to the third neuron, w 14 a connection strength of the first neuron to the fourth neuron, w 21 a connection strength of the second neuron to the first neuron, w 22 a connection strength of the second neuron to the second neuron, w 23 a connection strength of the second neuron to the third neuron, w 24 a connection strength of the second neuron to the fourth neuron, w 32 a connection strength of the third neuron to the second neuron, w 33 a connection strength of the third neuron to the third neuron, w 34 a connection strength of the third neuron to the fourth neuron, w 41 a connection strength of the fourth neuron to the first neuron, w 42 a connection strength of the fourth neuron to the second neuron, w 43 a connection strength of the fourth neuron to the third neuron, w 44 a connection strength of the fourth neuron to the fourth neuron, k 1 a coupling strength of a local active memristor model, x 、 y and z a neuron state, a 、 b and c a parameter regulating the dynamics of the neuron.

[0052] Preferably, the method of generating the key stream comprises:

[0053] starting from a seed sequence, performing three rounds of dynamic transcription and gene mutation to obtain RNA bases;

[0054] The RNA base is mapped to a value of 0-255, and the RNA key stream with a length of 256 is obtained.

[0055] Preferably, the method for obtaining the encrypted image comprises:

[0056] The to-be-encrypted image is preprocessed and resized to obtain a processed image.

[0057] Based on the key stream, a triple hybrid diffusion operation of chaotic XOR diffusion, chaotic modulo addition diffusion and DNA encoding diffusion is performed on the processed image to obtain a diffused image.

[0058] A global cyclic shift operation is performed on the diffused image to obtain an enhanced diffused image.

[0059] After repeating the triple hybrid diffusion operation and the global cyclic shift operation for 16 rounds, RNA key diffusion is performed based on the RNA key stream to obtain the encrypted image.

[0060] Compared with the prior art, the present application has the following beneficial effects:

[0061] The present application realizes deep confusion and diffusion of image pixels by constructing a high-complexity fractional-order chaotic neural network and combining an RNA+DNA dual biological encoding mechanism, and improves the security, randomness and robustness of the encryption system. The information entropy of the encrypted image reaches 7.9971 (close to the theoretical maximum value of 8), the pixel distribution is close to uniform randomness, and the statistical analysis attack is effectively resisted; the NPCR (pixel change rate) is 99.6175%, and the UACI (change intensity) is 33.4638%, close to the ideal value, and highly sensitive to single-pixel modification; facing 25% clipping attack or 10% salt and pepper attack, the decrypted image still retains the main outline; the PSNR of the decrypted image and the original image is Inf dB, and the SSIM is 1.0000, completely restoring the original information. BRIEF DESCRIPTION OF DRAWINGS

[0062] In order to more clearly illustrate the technical solutions of the present application, the following briefly introduces the drawings needed in the embodiments. Obviously, the drawings described in the following embodiments are only some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without creative labor.

[0063] Figure 1 The system structure diagram of the embodiment of the present application;

[0064] Figure 2 The system structure diagram of the embodiment of the present application; w 22 Lyapunov bifurcation diagram of fractional-order Hopfield neural network;

[0065] Figure 3 Embodiments of the present invention w 22 Lyapunov exponent plot of fractional Hopfield neural network;

[0066] Figure 4 This is an xz phase diagram of an embodiment of the present invention;

[0067] Figure 5 This is a schematic diagram of the encryption process according to an embodiment of the present invention;

[0068] Figure 6 This is a schematic diagram of the decryption process according to an embodiment of the present invention. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0071] Example 1:

[0072] In this embodiment, as Figure 1 As shown, a chaotic image encryption system based on discrete fractional neural networks using RNA dynamic transcription and DNA encoding includes: a model building module, a key generation module, and an image encryption module.

[0073] The model building module is used to construct fractional neural networks and, based on these networks, to put the encryption system into a hyperchaotic state.

[0074] In the model building module, the constructed fractional neural network is a four-dimensional fractional discrete-time Hopfield neural network containing locally active memristors. The process includes: defining the discrete fractional Caputo operator:

[0075] ,

[0076] in, C Indicates the identifier of a Caputo-type fractional operator. Represents the difference operation of fractional order. q Indicates the fractional order. p This represents the discrete time step parameter. Represents the neuron's state variables.Γ denotes the gamma function, m denotes q rounds up, n denotes a discrete time point, denotes a time shift operator, s denotes a state variable, denotes m integer order difference; a local active memristor model is introduced to simulate synaptic connections, and the local active memristor model is:

[0077] ,

[0078] wherein, i ( n ) denotes an output current, v ( n ) denotes an input voltage, W denotes a conductance of the memristor, α , β , γ denotes a regulation parameter; a four-dimensional neuron dynamics equation activation function is constructed tanh ( x ): a fractional order neural network is constructed based on a discrete fractional Caputo operator, a local active memristor model and a four-dimensional neuron dynamics equation activation function:

[0079] ,

[0080] ,

[0081] ,

[0082] ,

[0083] ,

[0084] wherein, y ( n ), z ( n ) and w ( n ) denote neuron state variables, m ( n ) denotes a state variable of the memristor, w denotes a synaptic weight, j denotes a history traversal index of discrete time, w 11 denotes the connection strength of the first neuron to the first neuron, w 12 denotes the connection strength of the first neuron to the second neuron, w13 represents the connection strength of the 1st neuron to the 3rd neuron, w 14 represents the connection strength of the 1st neuron to the 4th neuron, w 21 represents the connection strength of the 2nd neuron to the 1st neuron, w 22 represents the connection strength of the 2nd neuron to the 2nd neuron, w 23 represents the connection strength of the 2nd neuron to the 3rd neuron, w 24 represents the connection strength of the 2nd neuron to the 4th neuron, w 32 represents the connection strength of the 3rd neuron to the 2nd neuron, w 33 represents the connection strength of the 3rd neuron to the 3rd neuron, w 34 represents the connection strength of the 3rd neuron to the 4th neuron, w 41 represents the connection strength of the 4th neuron to the 1st neuron, w 42 represents the connection strength of the 4th neuron to the 2nd neuron, w 43 represents the connection strength of the 4th neuron to the 3rd neuron, w 44 represents the connection strength of the 4th neuron to the 4th neuron, k 1 represents the coupling strength of the local active memristor model, x , y and z represent the state of the neurons, a , b and c represent parameters that regulate the dynamics of the neurons.

[0085] In the present embodiment, the parameters of the network model are set as follows: w 11 = 1, w 12 = -3, w 13 = 2, w 14 = 1, w 21 = 2, w 22 = 2.2, w 23 = -1, w24 =0, w 32 =4, w 33 =1.5, w 34 =1, w 41 =0, w 42 =4, w 43 =-5, w 44 =2, a =0.1, b =0.1, c =0.1, k 1=2.75, q =0.6. By analyzing w 22 the bifurcation diagram combined w 22 with the Lyapunov exponent diagram (LE>0) and the x-z phase diagram, as shown in Figure 2 , Figure 3 , Figure 4 , it is verified that the system is in a hyperchaotic state.

[0086] The key generation module takes a seed sequence as a starting point and generates an RNA key stream through three rounds of dynamic transcription.

[0087] The workflow of the key generation module includes: taking a seed sequence as a starting point, performing three rounds of dynamic transcription and gene mutation to obtain RNA bases; mapping the RNA bases to 0-255 numerical values to obtain an RNA key stream with a length of 256.

[0088] In this embodiment, as shown in Figure 5 , a seed sequence (such as AUCGAUCGAUCGAUCG) is taken as a starting point, and a key is generated through three rounds of dynamic transcription, each round performing: transcription (A→U, U→A, C→G, G→C), gene mutation (A→C, U→G; insert / delete base A); finally, the RNA bases (A / U / C / G) are mapped to 0-255 numerical values to generate an RNA key stream with a length of 256. This series of operations utilizes the characteristics of RNA base pairing rules and the like to generate a key, so that the key has high complexity and randomness, increases the difficulty of cracking the key, and provides reliable security for the subsequent encryption process.

[0089] The image encryption module performs triple hybrid diffusion encryption on the image to be encrypted, and then performs further diffusion based on the RNA key stream to obtain an encrypted image.

[0090] The working process of the image encryption module includes: pre-processing and size adjustment of the image to be encrypted to obtain a processed image; based on the key stream, performing three mixed diffusion operations of chaotic XOR diffusion, chaotic modulo addition diffusion and DNA coding diffusion on the processed image to obtain a diffused image; performing a global cyclic shift operation on the diffused image to obtain an enhanced diffused image; after repeating the three mixed diffusion operations and the global cyclic shift operation for 16 rounds, performing RNA key diffusion based on the RNA key stream to obtain an encrypted image.

[0091] In the present embodiment, the image encryption module first pre-processes the image to be encrypted. Specifically, first, the original image "pn2.png" is read through the imread function. If a single-channel grayscale image is read, it is copied into a three-channel "pseudo-color image" through cat(3, original_img, original_img, original_img), and the channel format is unified to adapt to the subsequent encryption logic designed based on three channels. Then, it is checked whether the image height (M) and width (N) are integer multiples of the set block size (block_size = 16). If not, the new size (M_new = ceil(M / block_size)*block_size, N_new = ceil(N / block_size)*block_size) is calculated, and the image is scaled to the new size through the imresize function to ensure that the image can be completely divided into 16x16 sub-blocks, avoiding "residual blocks" when dividing blocks. The finally obtained pre-processed image is in three-channel format, and the height and width are both integer multiples of 16, maintaining the uint8 type (pixel value 0-255). Then, the pre-processed image is size-adjusted to make the image meet the specific requirements of the encryption algorithm on the image size, and the processed image is obtained as the input of the subsequent encryption steps such as scrambling, diffusion, and RNA key mixing.

[0092] Then, based on the key stream, the processed image is subjected to triple mixing diffusion operations of chaotic XOR diffusion, chaotic modulo addition diffusion, and DNA encoding diffusion to obtain a diffused image. Specifically, the chaotic XOR diffusion generates a pseudo-random sequence through a four-dimensional chaotic system, which is mapped to a key stream of 0-255 through amplification, rounding, and modulo 256 operation, and is XORed with the image pixels bit by bit to break the correlation between adjacent pixels. The chaotic modulo addition diffusion also generates a key based on a chaotic sequence, but uses a modulo addition operation (pixel value plus key value modulo 256), uses a nonlinear transformation to achieve an avalanche effect, and adjusts the chaotic parameters at each iteration to enhance the cumulative effect. The DNA encoding diffusion combines the principles of bioinformatics, splits the pixel value into four 2-bit binary groups and maps them to DNA bases, performs base operations according to randomly selected encoding rules and DNA XOR tables, and then maps them back to pixel values through bioinformatics processing to enhance encryption complexity. These three diffusion methods are alternately applied at each layer (e.g., first XOR, then modulo addition, and then DNA encoding), so that the ciphertext image responds sensitively to small changes in the plaintext image, effectively resisting statistical analysis and differential attacks. By using multiple diffusion methods, the pixel values of the image are transformed and mixed in space, aiming to break the pixel distribution rule of the original image, increase the confusion between the plaintext image and the ciphertext image, and prevent attackers from cracking the encryption by analyzing the pixel statistical characteristics.

[0093] Next, a global cyclic shift operation is performed on the diffused image to obtain an enhanced diffused image. Specifically, the pixel spatial position relationship is disturbed through row / column cyclic shift to enhance diffusion: before encryption, row_shift and col_shift are randomly generated through randi([0, M-1], 1) and randi([0, N-1], 1) (M and N are the height and width of the image), and in the multi-layer encryption cycle, the displacement amount of each round is row_shift*round and col_shift*round. During the displacement operation, the circshift function is used to perform row cyclic right shift and column cyclic down shift on the RGB three channels of the image simultaneously, i.e., the original pixel I(x, y) becomes I((x+col_shift*round)mod M, (y+row_shift*round)mod N), which destroys the spatial correlation between pixels. This operation provides a complex initial state for the subsequent encryption steps through spatial domain confusion, cooperation with chaotic sequences, and parameter sensitivity enhancement. Further changing the position arrangement of the image pixels enhances the randomness and unpredictability of the encrypted image.

[0094] Repeat the above three mixed diffusion operation and global cyclic shift operation (single round encryption process) for 16 rounds, multiple rounds of encryption can continuously accumulate the effect of encryption operation, make the relationship between the encrypted image and the original image more complex and hidden, greatly improve the security of encryption algorithm, because the attacker needs to crack the comprehensive effect of multiple rounds of encryption to obtain the original image information, which is very difficult in calculation.

[0095] Final RNA key diffusion: Expand the RNA key stream to the same size matrix as the image (MxNxC) through the repmat function (expanded_rna_key), ensure that each pixel corresponds to a unique key value; Finally, perform the exclusive or operation (bitxor), the expanded key and the 16 rounds of encrypted image are XORed pixel by pixel to generate the final encrypted image. Further strengthen the encryption effect, make the key and the encrypted image closely combined, ensure that only with the correct key can accurately decrypt, so as to improve the key sensitivity and confidentiality of the encryption system.

[0096] Example two:

[0097] In this embodiment, as shown in Figure 6 The decryption process of the image will be introduced:

[0098] (1) Final RNA key inverse diffusion:

[0099] Performing exclusive or operation on the encrypted image, using the self-reflection of "(A⊕B)⊕B=A", completely eliminate the influence of RNA key stream diffusion, restore the 16 rounds of decrypted intermediate image. The security of this process lies in: the key generation depends on the strict secrecy of the encryption parameters, the complexity of biological simulation makes the key difficult to crack, and the accuracy of inverse diffusion ensures that the final result is consistent with the original image.

[0100] (2) Single round decryption process:

[0101] Global cyclic inverse shift: The global cyclic inverse shift operation is a key step in the decryption process to restore the pixel spatial position. The core is to offset the shift impact in the encryption process by the inverse shift amount in the reverse order. The specific implementation is as follows: first, load the encryption parameter file to obtain the basic row shift amount (row_shift), the basic column shift amount (col_shift), and the total number of rounds (num_rounds) generated during encryption; since the row and column shift amounts of each round during encryption are row_shift*round and col_shift*round, and the decryption uses reverse iteration (from the num_rounds round to the 1st round), the inverse shift amount corresponding to each round needs to be set as -row_shift*round and -col_shift*round (the negative sign indicates that the shift direction is opposite); then call the circshift function to perform a cyclic shift on the image after the "inverse block permutation"; the row direction is shifted upward by -row_shift*round, and the column direction is shifted left by -col_shift*round (the channel dimension remains unchanged); through this operation, the pixels shifted right / down during encryption are shifted back to the original position in the opposite direction; after 16 rounds of reverse iteration, the positive shift impact of all rounds is completely offset, and the row / column position of the pixel is restored to the state before the block permutation, providing a correct pixel distribution basis for the subsequent inverse diffusion operation.

[0102] Triple mixed diffusion inverse operation: Perform triple mixed diffusion inverse operation, which corresponds to the mixed diffusion operation in the encryption process. Through the inverse operation, the chaotic factors added during encryption are removed, and the distribution of image pixels gradually returns to the original state. The inverse diffusion processes of chaotic XOR diffusion, chaotic modulo addition diffusion, and DNA encoding diffusion strictly follow the inverse logic of encryption diffusion, and need to be executed in the reverse order (DNA encoding inverse diffusion first, then chaotic modulo addition inverse diffusion, and finally chaotic XOR inverse diffusion), and reuse the same round keys and parameters as encryption. Among them, chaotic XOR inverse diffusion uses the self-reflection of XOR operation to perform bit XOR operation (bitxor) again on the ciphertext pixels and the key matrix generated during encryption to directly restore the pixel value before XOR; chaotic modulo addition inverse diffusion targets the "(pixel value + key value) mod 256" operation during encryption, and offsets the nonlinear transformation through the modulus subtraction operation "(ciphertext value - key value) mod 256"; reuse the modulo encryption key matrix and convert the result back to uint8 type to restore the original pixel distribution; DNA encoding inverse diffusion relies on the self-reflection of DNA XOR operation, uses the same key matrix, encoding rules generated by chaotic sequence, and XOR table to perform the complete process of DNA encoding -> base XOR -> decoding on the ciphertext pixels, thereby restoring the pixel value before DNA diffusion. Through this inverse diffusion process in reverse order, the diffusion impact during encryption can be offset layer by layer.

[0103] (3) 16 rounds of decryption cycles:

[0104] Through the above 16 rounds of inverse decryption operations, the confusion and diffusion effects of each round in the encryption process are gradually eliminated, and the original image is finally restored. Since each round of decryption relies on specific parameters during encryption, attackers need to crack the combined effect of 16 rounds of encryption, which has extremely high computational complexity, thus ensuring the security of the algorithm.

[0105] (4) Image preprocessing inverse process:

[0106] First, the size is restored, and the size of the decrypted image is adjusted from the "block_size integer multiple" (M_new x N_new) during preprocessing to the original image size (M x N) through the imresize function interpolation or cropping, ensuring consistency with the original image size; Then restore the channel format, if the original image is a single-channel grayscale image (copied as a three-channel "pseudo-color image" during preprocessing), extract one channel as a single-channel grayscale image by judging whether the three channels are completely consistent, and restore the original channel format; Finally, the type and range correction is performed, the decrypted image is converted to uint8 type, and the pixel value is ensured to be in the normal range of 0-255 through rounding, eliminating possible calculation errors.

[0107] (5) Original image recovery:

[0108] After the above decryption operations, the original image is finally restored.

[0109] The entire decryption process is a complex process that combines biological genetic mechanisms (such as RNA transcription, gene mutation), chaos theory, and traditional encryption and decryption techniques (such as XOR operation), through multiple rounds of cycles and various inverse operations, gradually removing the chaotic factors added during encryption, and finally accurately restoring the original image.

[0110] Example Three:

[0111] In this embodiment, the discrete fractional-order neural network chaotic image encryption method based on RNA dynamic transcription and DNA coding includes the following steps:

[0112] S1. Construct a fractional-order neural network and make the encryption system in a hyperchaotic state based on the fractional-order neural network.

[0113] The process of constructing a fractional-order neural network includes: defining a discrete fractional Caputo operator:

[0114] ,

[0115] wherein, C denotes the identity of the Caputo fractional-order operator, denotes a fractional order difference operation, q denotes a fractional order, p denotes a discrete time step parameter, denotes a neuron state variable, Γ denotes a gamma function, m denotes q rounding up, n denotes a discrete time point, denotes a time shift operator, s denotes a state variable; a local active memristor model is introduced to model the synaptic connection, the local active memristor model is:

[0116] ,

[0117] wherein, i ( n ) denotes an output current, v ( n ) denotes an input voltage, W denotes a conductance of the memristor, α , β , γ denotes a tuning parameter; a four-dimensional neuron dynamics equation activation function is constructed tanh ( x ): a fractional order neural network is constructed based on a discrete fractional Caputo operator, a local active memristor model and a four-dimensional neuron dynamics equation activation function:

[0118] ,

[0119] ,

[0120] ,

[0121] ,

[0122] ,

[0123] wherein, y ( n ), z ( n ) and w ( n ) denote a neuron state variable, m ( n ) denotes a state variable of the memristor, w denotes a synaptic weight, j denotes a discrete time history traversal index, w 11 denotes the connection strength of the first neuron to the first neuron,w 12 denotes the connection strength of the 1st neuron to the 2nd neuron, w 13 denotes the connection strength of the 1st neuron to the 3rd neuron, w 14 denotes the connection strength of the 1st neuron to the 4th neuron, w 21 denotes the connection strength of the 2nd neuron to the 1st neuron, w 22 denotes the connection strength of the 2nd neuron to the 2nd neuron, w 23 denotes the connection strength of the 2nd neuron to the 3rd neuron, w 24 denotes the connection strength of the 2nd neuron to the 4th neuron, w 32 denotes the connection strength of the 3rd neuron to the 2nd neuron, w 33 denotes the connection strength of the 3rd neuron to the 3rd neuron, w 34 denotes the connection strength of the 3rd neuron to the 4th neuron, w 41 denotes the connection strength of the 4th neuron to the 1st neuron, w 42 denotes the connection strength of the 4th neuron to the 2nd neuron, w 43 denotes the connection strength of the 4th neuron to the 3rd neuron, w 44 denotes the connection strength of the 4th neuron to the 4th neuron, k 1denotes the coupling strength of the local active memristor model, x 、 y and z denotes the state of the neuron, a 、 b and c denotes the parameter that regulates the dynamic properties of the neuron.

[0124] S2. Generating an RNA key stream through three rounds of dynamic transcription starting from a seed sequence.

[0125] The method for generating a key stream comprises: starting from a seed sequence, performing three rounds of dynamic transcription and gene mutation to obtain an RNA base; mapping the RNA base to a numerical value of 0-255 to obtain an RNA key stream with a length of 256.

[0126] S3. Triple hybrid diffusion encryption is performed on the image to be encrypted, and then RNA key stream-based diffusion is performed again to obtain an encrypted image.

[0127] The method for obtaining an encrypted image comprises: performing preprocessing and size adjustment on an image to be encrypted to obtain a processed image; performing triple hybrid diffusion operation of chaotic XOR diffusion, chaotic modulo addition diffusion and DNA encoding diffusion on the processed image based on a key stream to obtain a diffused image; performing a global cyclic shift operation on the diffused image to obtain an enhanced diffused image; and performing 16 rounds of triple hybrid diffusion operation and global cyclic shift operation, and then performing RNA key diffusion based on an RNA key stream to obtain an encrypted image.

[0128] The above-described embodiments are merely descriptions of the preferred modes of the present application and are not intended to limit the scope of the present application, and various modifications and improvements to the technical solutions of the present application made by those of ordinary skill in the art without departing from the design spirit of the present application shall fall within the protection scope of the present application as defined by the claims.

Claims

1. A chaotic image encryption system based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding, characterized in that, include: Model building module, key generation module, and image encryption module; The model building module is used to construct a fractional neural network and, based on the fractional neural network, to put the encryption system in a hyperchaotic state. The key generation module starts with a seed sequence and generates an RNA key stream through three rounds of dynamic transcription. The image encryption module performs triple hybrid diffusion encryption on the image to be encrypted, and then performs another diffusion based on the RNA key stream to obtain the encrypted image. The process of constructing the fractional-order neural network in the model construction module includes: Define the discrete fractional Caputo operator: ， in, C Indicates the identifier of a Caputo-type fractional operator. Represents the difference operation of fractional order. q Indicates the fractional order. p This represents the discrete time step parameter. Represents the neuron's state variables. Γ Represents the gamma function. m express q Round up. n Representing discrete time points, This represents the time shift operator. s Represents state variables, express m Integer-order difference; A locally active memristor model is introduced to simulate synaptic connections. The locally active memristor model is as follows: ， in, i ( n () indicates the output current. v ( n () indicates the input voltage. W Indicates the conductance of the memristor. α , β , γ Indicates the adjustment parameter; Constructing the activation function of the four-dimensional neuron dynamics equation tanh ( x ); The fractional neural network is constructed based on the discrete fractional Caputo operator, the locally active memristor model, and the activation function of the four-dimensional neuron dynamics equation: ， ， ， ， ， in, y ( n ), z ( n )and w ( n ) represents the neuron's state variable. m ( n ) represents the state variable of the memristor. w Indicates synaptic weight, j Represents a discrete-time history traversal index. w 11 This indicates the connection strength between the first neuron and the second neuron. w 12 This indicates the connection strength between the first neuron and the second neuron. w 13 This indicates the connection strength between the first neuron and the third neuron. w 14 This indicates the connection strength between the first neuron and the fourth neuron. w 21 This indicates the connection strength between the second neuron and the first neuron. w 22 This indicates the connection strength between the second neuron and the second neuron. w 23 This indicates the connection strength between the second neuron and the third neuron. w 24 This indicates the connection strength between the second neuron and the fourth neuron. w 32 This indicates the connection strength between the third neuron and the second neuron. w 33 This indicates the connection strength between the third neuron and the third neuron. w 34 This indicates the connection strength between the 3rd neuron and the 4th neuron. w 41 This indicates the connection strength between the 4th neuron and the 1st neuron. w 42 This indicates the connection strength between the 4th neuron and the 2nd neuron. w 43 This indicates the connection strength between the fourth neuron and the third neuron. w 44 This indicates the connection strength between the fourth neuron and the fourth neuron. k 1 represents the coupling strength of the locally active memristor model. x , y and z Indicates neuron state, a , b and c These are parameters that regulate the dynamic properties of neurons.

2. The chaotic image encryption system based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding according to claim 1, characterized in that, The workflow of the key generation module includes: Starting with the seed sequence, three rounds of dynamic transcription and gene mutation were performed to obtain RNA bases; The RNA bases are mapped to values ​​from 0 to 255 to obtain an RNA key stream of length 256.

3. The chaotic image encryption system based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding according to claim 1, characterized in that, The workflow of the image encryption module includes: The image to be encrypted is preprocessed and resized to obtain the processed image; The processed image is subjected to a triple hybrid diffusion operation of chaotic XOR diffusion, chaotic modulo diffusion, and DNA-encoded diffusion to obtain a diffused image; A global cyclic shift operation is performed on the diffused image to obtain an enhanced diffused image; After repeating the triple hybrid diffusion operation and the global cyclic shift operation 16 times, RNA key diffusion is performed based on the RNA key stream to obtain the encrypted image.

4. A chaotic image encryption method based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding, wherein the encryption method is applied to the encryption system described in any one of claims 1-3, characterized in that, Includes the following steps: Construct a fractional-order neural network, and use the fractional-order neural network to put the encryption system into a hyperchaotic state; Starting with a seed sequence, an RNA key stream is generated through three rounds of dynamic transcription. The image to be encrypted is subjected to triple hybrid diffusion encryption, and then diffused again based on the RNA key stream to obtain the encrypted image.

5. The chaotic image encryption method based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding according to claim 4, characterized in that, The process of constructing the fractional neural network includes: Define the discrete fractional Caputo operator: ， in, C Indicates the identifier of a Caputo-type fractional operator. Represents the difference operation of fractional order. q Indicates the fractional order. p This represents the discrete time step parameter. Represents the neuron's state variables. Γ Represents the gamma function. m express q Round up. n Representing discrete time points, This represents the time shift operator. s Represents state variables, express m Integer-order difference; A locally active memristor model is introduced to simulate synaptic connections. The locally active memristor model is as follows: ， in, i ( n () indicates the output current. v ( n () indicates the input voltage. W Indicates the conductance of the memristor. α , β , γ Indicates the adjustment parameter; Constructing the activation function of the four-dimensional neuron dynamics equation tanh ( x ): The fractional neural network is constructed based on the discrete fractional Caputo operator, the locally active memristor model, and the activation function of the four-dimensional neuron dynamics equation: ， ， ， ， ， in, y ( n ), z ( n ) w ( n ) represents the neuron's state variable. m ( n ) represents the state variable of the memristor. w Indicates synaptic weight, j Represents a discrete-time history traversal index. w 11 This indicates the connection strength between the first neuron and the second neuron. w 12 This indicates the connection strength between the first neuron and the second neuron. w 13 This indicates the connection strength between the first neuron and the third neuron. w 14 This indicates the connection strength between the first neuron and the fourth neuron. w 21 This indicates the connection strength between the second neuron and the first neuron. w 22 This indicates the connection strength between the second neuron and the second neuron. w 23 This indicates the connection strength between the second neuron and the third neuron. w 24 This indicates the connection strength between the second neuron and the fourth neuron. w 32 This indicates the connection strength between the third neuron and the second neuron. w 33 This indicates the connection strength between the third neuron and the third neuron. w 34 This indicates the connection strength between the 3rd neuron and the 4th neuron. w 41 This indicates the connection strength between the 4th neuron and the 1st neuron. w 42 This indicates the connection strength between the 4th neuron and the 2nd neuron. w 43 This indicates the connection strength between the fourth neuron and the third neuron. w 44 This indicates the connection strength between the fourth neuron and the fourth neuron. k 1 represents the coupling strength of the locally active memristor model. x , y and z Indicates neuron state, a , b and c These are parameters that regulate the dynamic properties of neurons.

6. The chaotic image encryption method based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding according to claim 4, characterized in that, The method for generating the keystream includes: Starting with the seed sequence, three rounds of dynamic transcription and gene mutation were performed to obtain RNA bases; The RNA bases are mapped to values ​​from 0 to 255 to obtain an RNA key stream of length 256.

7. The chaotic image encryption method based on discrete fractional-order neural networks using RNA dynamic transcription and DNA encoding according to claim 4, characterized in that, The methods for obtaining the encrypted image include: The image to be encrypted is preprocessed and resized to obtain the processed image; Based on the key stream, a triple hybrid diffusion operation of chaotic XOR diffusion, chaotic modulo diffusion, and DNA-encoded diffusion is performed on the processed image to obtain the diffused image. A global cyclic shift operation is performed on the diffused image to obtain an enhanced diffused image; After repeating the triple hybrid diffusion operation and the global cyclic shift operation 16 times, RNA key diffusion is performed based on the RNA key stream to obtain the encrypted image.

Images