Image encryption method, system and device based on biased Fourier quantum walk and add-fork structure, medium and product

Abstract

The invention discloses an image encryption method, system, device, medium and product based on biased Fourier quantum walk and add-fork structure, and relates to the technical field of image encryption, the method comprises the following steps: obtaining an initial pseudo-random sequence based on a two-dimensional discrete biased Fourier quantum walk model; generating a first conversion pseudorandom sequence, a second conversion pseudorandom sequence and a third conversion pseudorandom sequence based on the initial pseudorandom sequence; converting the first converted pseudo-random sequence into a first security key, converting the second converted pseudo-random sequence into a second security key, and converting the third converted pseudo-random sequence into a third security key; adopting a preset image scrambling strategy to perform multiple image scrambling on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; and coding the target scrambled image based on the third security key by adopting a dynamic DNA shift coding method to obtain a target encrypted image. According to the invention, the robustness of the encrypted image is improved.

Description

Technical Field

[0001] The present application relates to the field of image encryption technology, and particularly to an image encryption method, system, device, medium and product based on biased Fourier quantum walk and addition-cross structure. Background Technique

[0002] Traditional encryption algorithms can provide certain robustness, but due to the easy prediction and cracking of pseudo-randomness, there are certain security risks. Attackers can break through the encryption defense line by analyzing the rules of pseudo-random sequences, thereby leaking confidential information. Compared with traditional algorithms, quantum computing has significant advantages in pseudo-randomness generation and encryption robustness. Quantum algorithms utilize characteristics such as quantum superposition and quantum entanglement to generate more random and diverse pseudo-random sequences, thereby greatly enhancing encryption robustness. In addition, the quantum no-cloning theorem and the quantum uncertainty principle endow encryption methods based on quantum computing with powerful anti-attack capabilities. Quantum walk has the characteristics of non-periodicity and high sensitivity to initial conditions, and has been applied to the generation of pseudo-random sequences to enhance encryption intensity. However, existing encryption schemes based on one-dimensional quantum walk models are relatively weak in chaotic characteristics and difficult to meet the requirements of high robustness.

[0003] Therefore, it is necessary to provide an image encryption scheme based on two-dimensional discrete biased Fourier quantum walk (2D-DBFQW) and addition-cross structure to solve the above problems. Summary of the Invention

[0004] The purpose of the present application is to provide an image encryption method, system, device, medium and product based on biased Fourier quantum walk and addition-cross structure, which improves the robustness of encrypted images.

[0005] To achieve the above purpose, the present application provides the following solutions:

[0006] In the first aspect, the present application provides an image encryption method based on biased Fourier quantum walk and addition-cross structure, and the image encryption method based on biased Fourier quantum walk and addition-cross structure includes:

[0007] Construct a two-dimensional discrete biased Fourier quantum walk model;

[0008] Based on the two-dimensional discrete biased Fourier quantum walk model, obtain an initial pseudo-random sequence; the initial pseudo-random sequence includes: a first initial pseudo-random subsequence and a second initial pseudo-random subsequence;

[0009] Generate a first transformed pseudo-random sequence, a second transformed pseudo-random sequence, and a third transformed pseudo-random sequence based on the initial pseudo-random sequence;

[0010] Convert the first transformed pseudo-random sequence into a first security key, convert the second transformed pseudo-random sequence into a second security key, and convert the third transformed pseudo-random sequence into a third security key;

[0011] Obtain a plaintext image, and adopt a preset image scrambling strategy to perform multiple image scramblings on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; the preset image scrambling strategy includes: an additive image scrambling strategy and a cross-shaped image scrambling strategy;

[0012] Adopt a dynamic DNA shift coding method to encode the target scrambled image based on the third security key to obtain a target encrypted image.

[0013] In a second aspect, the present application provides an image encryption system based on a biased Fourier quantum walk and a plus-cross structure. The image encryption system based on a biased Fourier quantum walk and a plus-cross structure is used to implement the image encryption method based on a biased Fourier quantum walk and a plus-cross structure. The image encryption system based on a biased Fourier quantum walk and a plus-cross structure includes:

[0014] A model construction unit for constructing a two-dimensional discrete biased Fourier quantum walk model;

[0015] An initial pseudo-random sequence determination unit for obtaining an initial pseudo-random sequence based on the two-dimensional discrete biased Fourier quantum walk model; the initial pseudo-random sequence includes: a first initial pseudo-random subsequence and a second initial pseudo-random subsequence;

[0016] A random sequence transformation unit for generating a first transformed pseudo-random sequence, a second transformed pseudo-random sequence, and a third transformed pseudo-random sequence based on the initial pseudo-random sequence;

[0017] A security key determination unit for converting the first transformed pseudo-random sequence into a first security key, converting the second transformed pseudo-random sequence into a second security key, and converting the third transformed pseudo-random sequence into a third security key;

[0018] A target scrambled image determination unit for obtaining a plaintext image, and adopting a preset image scrambling strategy to perform multiple image scramblings on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; the preset image scrambling strategy includes: an additive image scrambling strategy and a cross-shaped image scrambling strategy;

[0019] A target encryption image determination unit, which uses a dynamic DNA shift coding method to encode the target scrambled image based on the third security key to obtain a target encryption image.

[0020] In a third aspect, the present application provides a computer device, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, where the processor executes the computer program to implement the image encryption method based on a biased Fourier quantum walk and an addition-cross structure described in any one of the above.

[0021] In a fourth aspect, the present application provides a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the image encryption method based on a biased Fourier quantum walk and an addition-cross structure described in any one of the above.

[0022] In a fifth aspect, the present application provides a computer program product, including a computer program, and when the computer program is executed by a processor, it implements the image encryption method based on a biased Fourier quantum walk and an addition-cross structure described in any one of the above.

[0023] According to the specific embodiments provided by the present application, the present application has the following technical effects:

[0024] The present application discloses an image encryption method, system, device, medium, and product based on a biased Fourier quantum walk and an addition-cross structure. First, based on a two-dimensional discrete biased Fourier quantum walk model, an initial pseudo-random sequence is obtained; secondly, a first transformed pseudo-random sequence, a second transformed pseudo-random sequence, and a third transformed pseudo-random sequence are generated based on the initial pseudo-random sequence; then, the first transformed pseudo-random sequence is converted into a first security key, the second transformed pseudo-random sequence is converted into a second security key, and the third transformed pseudo-random sequence is converted into a third security key; again, using a preset image scrambling strategy, the plaintext image is scrambled multiple times based on the first security key and the second security key to obtain a target scrambled image; finally, using a dynamic DNA shift coding method, the target scrambled image is encoded based on the third security key to obtain a target encryption image. The present application uses a two-dimensional discrete biased Fourier quantum walk model, an addition-type image scrambling strategy, and a cross-type image scrambling strategy to scramble and encrypt the plaintext image, improving the robustness of the encrypted image. Description of the Drawings

[0025] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required for use in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0026] Figure 1 Schematic flowchart of an image encryption method based on biased Fourier quantum walk and addition-cross structure provided by an embodiment of the present application;

[0027] Figure 2 Schematic diagram of the positions of row indices and column indices of the addition-based image scrambling strategy in the plaintext image provided by an embodiment of the present application;

[0028] Figure 3 Schematic diagram of the positions of row indices and column indices of the cross-based image scrambling strategy in the plaintext image provided by an embodiment of the present application;

[0029] Figure 4 Schematic diagram of the process of the image scrambling strategy provided by an embodiment of the present application;

[0030] Figure 5 Schematic diagram of test images provided by another embodiment of the present application; where (a) is "Elaine", (b) is "mandrill", (c) is "pirate", and (d) is "bell pepper";

[0031] Figure 6 Histograms of test images and encrypted images provided by another embodiment of the present application; where (a) is the histogram of the original "Elaine" image; (b) is the histogram of the original "mandrill" image; (c) is the histogram of the original "pirate" image; (d) is the histogram of the original "bell pepper" image; (e) is the histogram of the encrypted "Elaine" image; (f) is the histogram of the encrypted "mandrill" image; (g) is the histogram of the encrypted "pirate" image; (h) is the histogram of the encrypted "bell pepper" image;

[0032] Figure 7 Schematic diagrams of the pixel distributions of the original images and encrypted images in three-dimensional space provided by another embodiment of the present application; where (a) is the schematic diagram of the pixel distribution of the original "Elaine" image; (b) is the schematic diagram of the pixel distribution of the original "mandrill" image; (c) is the schematic diagram of the pixel distribution of the original "pirate" image; (d) is the schematic diagram of the pixel distribution of the original "bell pepper" image; (e) is the schematic diagram of the pixel distribution of the encrypted "Elaine" image; (f) is the schematic diagram of the pixel distribution of the encrypted "mandrill" image; (g) is the schematic diagram of the pixel distribution of the encrypted "pirate" image; (h) is the schematic diagram of the pixel distribution of the encrypted "bell pepper" image;

[0033] Figure 8Scatter plots of the original image and the encrypted image in the horizontal, vertical and diagonal directions provided in another embodiment of the present application; wherein (a) is a scatter plot of the original "mandrill" image in the horizontal direction; (b) is a scatter plot of the encrypted "mandrill" image in the horizontal direction; (c) is a scatter plot of the original "sweet pepper" image in the horizontal direction; (d) is a scatter plot of the encrypted "sweet pepper" image in the horizontal direction; (e) is a scatter plot of the original "mandrill" image in the vertical direction; (f) (g) is the scatter plot of the encrypted “mandrill” image in the vertical direction; (h) is the scatter plot of the encrypted “sweet pepper” image in the vertical direction; (i) is the scatter plot of the original “mandrill” image in the diagonal direction; (j) is the scatter plot of the encrypted “mandrill” image in the diagonal direction; (k) is the scatter plot of the original “sweet pepper” image in the diagonal direction; (l) is the scatter plot of the encrypted “sweet pepper” image in the diagonal direction;

[0034] Figure 9 A schematic diagram of the difference between two encrypted images using different keys and two decrypted images using different keys provided in another embodiment of the present application; wherein (a) is the difference between two encrypted images using the key κ 1 and κ 2 Encrypted image; (b) is Figure 9 (a) and using the key κ 3 and κ 4 Schematic diagram of the difference between the generated encrypted images; (c) Figure 9 (b) is the histogram of the key κ. 5 and κ 6 Decryption Figure 9 Schematic diagram of the results of (a); (e) Figure 9 (d) in the example and using the key κ 7 and κ 8 Decryption Figure 9 Schematic diagram of the difference between (a) and (f) Figure 9 Histogram of (e) in ;

[0035] Figure 10 Schematic diagrams of cropping attacks of different degrees on an encrypted "pirate" image and corresponding decrypted images provided in another embodiment of the present application; wherein (a) is a schematic diagram of a cropping attack of the first degree on an encrypted "pirate" image; (b) is a schematic diagram of a cropping attack of the second degree on an encrypted "pirate" image; (c) is a schematic diagram of a cropping attack of the third degree on an encrypted "pirate" image; (d) is a schematic diagram of a cropping attack of the fourth degree on an encrypted "pirate" image; (e) is Figure 10 The decrypted image of (a) in (f) Figure 10 The decrypted image of (b) in (g) isFigure 10 The decrypted image of (c) in; (h) is Figure 10 The decrypted image of (d) in;

[0036] Figure 11 Schematic diagrams of the results of adding different degrees of salt-and-pepper noise and speckle noise to an encrypted "pirate" image and the corresponding decrypted images provided by another embodiment of the present application; among them, (a) is a schematic diagram of the result of attacking the encrypted "pirate" image with salt-and-pepper noise at a density of 0.01; (b) is a schematic diagram of the result of attacking the encrypted "pirate" image with salt-and-pepper noise at a density of 0.05; (c) is a schematic diagram of the result of attacking the encrypted "pirate" image with speckle noise at a density of 0.0001; (d) is a schematic diagram of the result of attacking the encrypted "pirate" image with speckle noise at a density of 0.001; (e) is Figure 11 The decrypted image of (a) in; (f) is Figure 11 The decrypted image of (b) in; (g) is Figure 11 The decrypted image of (c) in; (h) is Figure 11 The decrypted image of (d) in;

[0037] Figure 12 Schematic diagram of the structure of a computer device provided by an embodiment of the present application. Detailed implementation manners

[0038] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the protection scope of the present application.

[0039] To make the above objects, features, and advantages of the present application more obvious and understandable, the present application will be further described in detail below in conjunction with the drawings and specific implementation manners.

[0040] In an exemplary embodiment, as Figure 1 shown, an image encryption method based on biased Fourier quantum walk and add-x structure is provided, including the following steps. Among them:

[0041] Step S1, construct a two-dimensional discrete biased Fourier quantum walk model.

[0042] Specifically, this application proposes a method for generating pseudo-random numbers based on 2D-DBFQW, which is used to generate highly random sequences. Among them, the 2D-DBFQW model adopts the Fourier coin operator and controls the walking direction of particles by introducing the characteristics of quantum superposition and interference. In this application, the 2D-DBFQW model involves a bias parameter that gives a direction preference, enabling it to evolve preferentially along a certain trajectory. Specifically, the 2D-DBFQW model consists of two quantum systems: the coin (H c ) and the walker (H p ), and these two quantum systems can be represented as the tensor product in the Hilbert space: Different from one-dimensional quantum walks, the 2D-DBFQW model has the ability to move in four different directions on a two-dimensional lattice. Assuming that the position of the walker after walking t steps on the two-dimensional lattice is (x, y), then the possible positions of the walker in the next step are (x + 1, y + 1), (x + 1, y - 1), (x - 1, y + 1), or (x - 1, y - 1), and the coins in the four different directions are represented as |i x , i y >, where i x , i y ∈ {0, 1}. It should be noted that the state ψ(t) of the 2D-DBFQW system on the lattice after t steps can be represented as:

[0043]

[0044] Among them, is the probability amplitude;

[0045] The evolution of the 2D-DBFQW model from step t to step t + 1 can be represented as:

[0046]

[0047] Among them, is represented as:

[0048]

[0049] Among them, represents the identity matrix, represents the conditional shift operator; represents the Fourier coin operator:

[0050]

[0051] Each element in

[0052]

[0053] where \(p,q\in\{0,1,2,\cdots,N - 1\}\), \(i\) is the imaginary unit, and \(N\) represents the size of the lattice. If and only if \(N = 4\), is expressed as:

[0054]

[0055] Assume that the walker preferentially moves to the upper left. Before the evolution starts, the amplitude located at the center of the lattice is defined as

[0056]

[0057] Finally, after the walker moves \(t\) steps, the probability of being at \((x,y)\) is expressed as

[0058]

[0059] Step S2, based on the two-dimensional discrete biased Fourier quantum walk model, obtain the initial pseudo-random sequence; the initial pseudo-random sequence includes: a first initial pseudo-random subsequence and a second initial pseudo-random subsequence.

[0060] Among them, probability values are obtained according to the 2D-DBFQW model, and subsequent operations are performed to generate the first initial pseudo-random subsequence \(\gamma\) 1 and the second initial pseudo-random subsequence \(\gamma\) 2 . For convenience of description, let \(X'\) 1 =\(\gamma\) 1 or \(\gamma\) 2 , where the specific principle process of generating \(X'\) 1 is as follows:

[0061] Step S21, initialize the parameters of the 2D-DBFQW model: \([r,N,(x\) 1 ,y\) 1 ,x\) 2 ,y\) 2 )], where \(r\) represents the number of steps of the walker, and \((x\) 1 ,y\) 1 ,x\) 2 ,y\) 2 ) are the initial position-related parameters. Finally, the probability distribution \(P\) generated by the model can be expressed as:

[0062] \(P = \{p\) 1 ,p\) 2 ,p\) 3 ,\cdots,p\) G-1 ,p\) G}\}(9)

[0063] where \(p\) g represents the \(g\)-th probability value in the probability distribution, and the value of \(g\) ranges from 1 to \(G\), where \(G\) is the total number of probability values in the probability distribution.

[0064] Step S22: Remove the zero elements from the array P obtained in step S21 to enhance its randomness. Then, construct a larger sequence through the following formula

[0065]

[0066] where concat[·] is a concatenation function.

[0067] Step S23: According to the principle that every 8 consecutive numerical values are regarded as a whole, is segmented to generate an array and denoted as symbol

[0068] Step S24: If the size of the array is less than the size δ of the pseudo-random number sequence expected to be generated, set the number of steps r of the 2D-DBFQW model to r + 2, and jump to step S21 to regenerate the probability distribution; otherwise, execute the next step.

[0069] Step S25: According to the above steps, obtain the pseudo-random sequence generated by the 2D-DBFQW model and denote it as Then, select the first δ elements from the array to obtain the pseudo-random sequence X of the expected size 1 :

[0070] X 1 = {x 1 , x 2 ,..., x δ-1 , x δ}(11)

[0071] Step S26: Calculate the hexadecimal hash value of the input image using the SHA-512 hash function, and then randomly select 8-bit hash values as the seed S 1 , and generate the seed random sequence Y 1 :

[0072] Y 1 = {y 1 , y 2 ,..., y δ-1 , y δ}(12)

[0073] Step S27: Use Y 1 to rearrange the elements in X 1 obtained in step S25 respectively (that is, the elements in Y 1 are non-repeating and disordered integers between 1 and δ, and by replacing the elements in the array Y 1 with the elements in the array X1 by using the subscript of the element variable to implement the original array X 1 in the element position exchange), to obtain the rearranged pseudo-random sequence X′ 1 :

[0074]

[0075] Step S28, according to formula (14), for X′ 1 in the elements are normalized so that their values are converted in the range of 0 to 1.

[0076]

[0077] where, x max and x min respectively represent the maximum and minimum values in X′ 1 . The sequence X′ 1 is a highly random and sensitive pseudo-random sequence generated based on the 2D-DBFQW model and can be used for subsequent encryption operations.

[0078] Step S3, based on the initial pseudo-random sequence, generate the first transformed pseudo-random sequence, the second transformed pseudo-random sequence, and the third transformed pseudo-random sequence.

[0079] As an alternative implementation, step S3 specifically includes:

[0080] Step S31, using the formula to convert the initial pseudo-random sequence into the first transformed pseudo-random sequence and convert the initial pseudo-random sequence into the second transformed pseudo-random sequence; where, γ 1 represents the first initial pseudo-random subsequence; γ 2 represents the second initial pseudo-random subsequence; χ 1 represents the first transformed pseudo-random sequence; χ 2 represents the second transformed pseudo-random sequence; e represents the bitwise multiplication operator. Through the above transformation, γ 1 and γ 2 are converted into more complex pseudo-random sequences.

[0081] Step S32, using the formula χ 3 =concat[(γ 1 ⊙γ 2 ),γ 1 ,γ 2 ,γ 1 +γ 2 , based on the initial pseudo-random sequence, obtain the third transformed pseudo-random sequence; where, χ 3Denote the third transformed pseudo-random sequence; concat[·] denotes the concatenation function. Through the above transformation, on the basis of γ 1 and γ 2 a larger pseudo-random sequence χ 3 is generated.

[0082] Step S4, convert the first transformed pseudo-random sequence into a first security key, convert the second transformed pseudo-random sequence into a second security key, and convert the third transformed pseudo-random sequence into a third security key.

[0083] As an alternative implementation, step S4 specifically includes:

[0084] Step S41, use the formula to convert the first transformed pseudo-random sequence into a first security key and convert the second transformed pseudo-random sequence into a second security key; where ζ 1 (i) represents the i-th symbol in the first security key; χ 1 (i) represents the i-th pseudo-random number in the first transformed pseudo-random sequence; ζ 2 (i) represents the i-th symbol in the second security key; χ 2 (i) represents the i-th pseudo-random number in the second transformed pseudo-random sequence; floor(·) is the floor function; mod represents the modulo operation; i = {1, 2,..., η - 1, η}, and η represents the size of χ 1 (i.e., m × n), where m and n represent the width and height of the plaintext image.

[0085] Step S42, use the formula ζ 3 (j) = floor(mod(χ 3 (j) × 10 14 ), 256) to convert the third transformed pseudo-random sequence into a third security key; where ζ 3 (j) represents the j-th symbol in the third security key; χ 2 (i) represents the i-th pseudo-random number in the second transformed pseudo-random sequence; is the size of χ 3 .

[0086] Step S5, obtain the plaintext image, and adopt a preset image scrambling strategy to perform multiple image scramblings on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; the preset image scrambling strategy includes: an additive image scrambling strategy and a cross-shaped image scrambling strategy.

[0087] As an alternative implementation, in step S5, a preset image scrambling strategy is adopted to perform multiple image scramblings on the plaintext image based on the first security key and the second security key to obtain a target scrambled image, which specifically includes:

[0088] Step S51, ascendingly sort the first security key ζ 1 and the second security key ζ 2 respectively to obtain the ascendingly sorted first security key ζ′ 1 and the ascendingly sorted second security key ζ′ 2 . And initialize the iteration parameter ε to 1.

[0089] Step S52, adopt an additive image scrambling strategy and a cross-type image scrambling strategy to perform multiple additive image scramblings and multiple cross-type image scramblings on the plaintext image based on the ascendingly sorted first security key and the ascendingly sorted second security key to obtain the target scrambled image.

[0090] As an alternative implementation, step S52 specifically includes:

[0091] Step S521, based on the ascendingly sorted first security key, respectively determine the position of the row index of the additive image scrambling strategy in the plaintext image and the position of the column index in the plaintext image (i.e., the central pixel position of the addition).

[0092] Specifically, calculate the position μ 1 of the row index of the additive image scrambling strategy in the plaintext image and the position μ 2 of the column index in the plaintext image through formulas (15) and (16), as Figure 2 shown, Figure 2 the position where the pixel value is 164 in 1 is {μ 2}, where:

[0093]

[0094] μ 2 = ζ′ 1 (ε)-(μ 1 -1)×(m 1 -2)+1 (16)

[0095] where ceil(.) represents the ceiling function, m 1 represents the width of the plaintext image I 1 , and n 1 represents the height of the plaintext image I 1 .

[0096] Step S522: Determine the initial position of the additive scrambling region in the plaintext image based on the positions of the row index and column index of the additive image scrambling strategy in the plaintext image.

[0097] That is, use the central pixel position of the additive ({μ 1 , μ 2}) to determine the positions of other pixels in the additive scrambling region, and obtain the pixel positions of the additive (i.e., the initial position of the additive scrambling region in the plaintext image) as {μ 1 , μ 2}, {μ 1 , μ 2 - 1}, {μ 1 , μ 2 + 1}, {μ 1 - 1, μ 2} and {μ 1 + 1, μ 2}, as Figure 2 shown. Figure 2 The blue region in

[0098] is the initial position of the additive scrambling region in the plaintext image.

[0099] Step S523: Determine the number of circular shift operations for additive image scrambling based on the first security key; the circular shift operation for additive image scrambling includes: horizontal circular shift operation and vertical circular shift operation. 1 :

[0100] ρ 1 = floor(mod(ζ 1 (ε), 4)) + 1 (17)

[0101] Step S524: Based on the second security key sorted in ascending order, determine the position of the row index of the cross-shaped image scrambling strategy in the plaintext image and the position of the column index in the plaintext image (i.e., the central pixel position of the cross).

[0102] Among them, use formulas (18) and (19) to calculate the position v 1 of the row index of the cross-shaped image scrambling strategy in the plaintext image and the position v 2 of the column index in the plaintext image. As Figure 3 shown, Figure 3 the position with a pixel value of 94 in 1 is {v 2}, where:

[0103]

[0104] v1 = ζ' 2 (ε) - (v 2 -1) × (n 1 -2) + 1(19)

[0105] Step S525: Determine the initial position of the fork-shaped scrambling area in the plaintext image based on the position of the row index and the position of the column index of the fork-shaped image scrambling strategy in the plaintext image.

[0106] Specifically, the pixel positions of the fork (i.e., the initial position of the fork-shaped scrambling area in the plaintext image) are {v 1 , v 2}}, {v 1 -1, v 2 -1}, {v 1 +1, v 2 +1}, {v 1 -1, v 2 +1} and {v 1 +1, v 2 -1}, as Figure 3 shown, Figure 3 the green area in it is the initial position of the fork-shaped scrambling area in the plaintext image.

[0107] Step S526: Determine the number of circular shift operations for fork-shaped image scrambling based on the second security key; the circular shift operations for fork-shaped image scrambling include: left diagonal circular shift operation and right diagonal circular shift operation.

[0108] Calculate the circular shift number of the fork (i.e., the number of circular shift operations for fork-shaped image scrambling) ρ 2 :

[0109] ρ 2 = floor(mod(ζ 2 (ε), 4)) + 1 (20)

[0110] Step S527: Perform multiple additive image scramblings and multiple fork-shaped image scramblings on the plaintext image based on the number of circular shift operations of additive image scrambling and the number of circular shift operations of fork-shaped image scrambling to obtain the target scrambled image.

[0111] Specifically, Step S527 includes the following steps:

[0112] Step S5271: As Figure 4 shown, take the additive pixel values determined by μ 1 and μ 1 and μ 2 in the plaintext image I 1 and v 2Exchange the determined fork-shaped pixel values, and represent the image after the pixel value exchange as I′ 1 , and the exchange rule is as follows:

[0113]

[0114]

[0115] Among them, exchange I 1 (v 1 + 1, v 2 + 1) with I 1 (μ 1 , μ 2 + 1), exchange I 1 (v 1 , v 2 ) with I 1 (μ 1 , μ 2 ), exchange I 1 (v 1 - 1, v 2 - 1) with I 1 (μ 1 , μ 2 - 1), exchange I 1 (v 1 + 1, v 2 - 1) with I 1 (μ 1 + 1, μ 2 ), exchange I 1 (v 1 - 1, v 2 + 1) with I 1 (μ 1 - 1, μ 2 ).

[0116] Step S5272, as Figure 4 shown, perform an additive cyclic shift operation: Use formulas (23) and (24) to perform horizontal and vertical cyclic shift operations on I′ 1 repeated ρ 1 times to obtain I″ 1 .

[0117]

[0118] Step S5273, as Figure 4 shown, perform a fork-shaped cyclic shift operation: Use formulas (25) and (26) to perform left diagonal and right diagonal cyclic shift operations on I″ 1 repeated ρ 2 times.

[0119]

[0120] Step S5274, if ε is less than (m - 2)(n - 2), then increase ε by 1 and continue the iteration; otherwise, end the iteration (obtain the final scrambling times) and output the target scrambled image I 2 。

[0121] Step S6, adopt the dynamic DNA shift coding method to encode the target scrambled image based on the third security key to obtain the target encrypted image. Among them, in order to further improve the robustness of the target scrambled image, this application designs a diffusion technology based on dynamic DNA shift coding, aiming to modify the pixel values of the target scrambled image.

[0122] As an optional implementation manner, Step S6 specifically includes:

[0123] Step S61, convert the pixel value of each pixel point in the target scrambled image into a binary sequence to obtain the binary matrix of the target scrambled image.

[0124] Specifically, convert the pixel value of each pixel point of I 2 into an 8-bit binary sequence in sequence to obtain the binary matrix I′ of the target scrambled image 2 。

[0125] Step S62, based on the third security key, perform a dynamic left shift on each element in the binary matrix to obtain the left-shifted binary matrix.

[0126] Specifically, in order to perform a dynamic left shift on each element in I′ 2 , calculate the shift number K according to formula (27) 1 :

[0127] K 1 (t) = floor(mod(ζ 3 (t), 7)) + 1 (27)

[0128] where t = {1, 2,..., τ - 1, τ}, τ = W × H, and W and H are the width and height of the target scrambled image I 2 respectively. Through K 1 , each element in I′ 2 is circularly left-shifted (if I′ 2 (1) = '10011011' and K 1 (1) = 2, then the left-shifted I′ 2 (1) = '01101110'), and the left-shifted binary matrix is denoted as I″ 2 。

[0129] Step S63: Convert each element in the left-shifted binary matrix into a 4-bit DNA code to obtain an initial dynamic DNA coding sequence.

[0130] Specifically, to implement dynamic DAN shift coding, this application defines a DNA coding sequence (i.e., Φ = 'ACGT'), where 'A', 'C', 'G', and 'T' respectively represent the four bases of DNA, namely adenine, cytosine, guanine, and thymine, and maps the binary values '00', '01', '10', and '11' to the bases 'A', 'C', 'G', and 'T' respectively to achieve the conversion of the correspondence between binary and bases. Among them, '00' corresponds to 'A', '01' corresponds to 'C', '10' corresponds to 'G', and '11' corresponds to 'T').

[0131] According to the mapping relationship between {'00', '01', '10', '11'} and {'A', 'C', 'G', 'T'}, convert each element in I″ 2 to obtain an initial dynamic DNA coding sequence.

[0132] Step S64: Calculate the dynamic shift number based on the third security key. Specifically, calculate the dynamic shift number K 2 :

[0133] K 2 (i) = mod(η - 1 + ζ3(i), 4) + 1 (28)

[0134] where 0 ≤ i ≤ ω, and ω is equal to τ × 4.

[0135] Step S65: Cyclically shift the initial dynamic DNA coding sequence according to the dynamic shift number K 2 to generate a target dynamic DNA coding sequence, and convert the target dynamic DNA coding sequence into a binary sequence to obtain a target binary sequence I 3 .

[0136] Map the bases 'A', 'C', 'G', and 'T' in the target dynamic DNA coding sequence to the binary values '00', '01', '10', and '11' respectively to achieve the conversion of the correspondence between bases and binary, so as to convert the newly generated DNA sequence (i.e., the target dynamic DNA coding sequence) into an 8-bit binary sequence and represent it as I 3 . For example, a DNA sequence "CAGT" can be converted into the corresponding binary sequence "01001011".

[0137] Step S66: Dynamically circularly right-shift each element in the target binary sequence to obtain the right-shifted target binary sequence.

[0138] Specifically, the principle involved in step S66 is as follows:

[0139] To further improve the robustness of this method, 3 perform a dynamic circular right-shift operation on each element in 3 :

[0140]

[0141] where r = {1, 2,..., τ - 1, τ}, denotes the size of ζ 3 .

[0142] Then, according to K 3 , perform a dynamic circular right-shift on the target binary sequence in 3 (if 3 I(1) = '11010010' and K 3 (1) = 3, then the right-shifted I 3 (1) = '01011010').

[0143] Step S67: Convert the right-shifted target binary sequence to decimal to obtain the target encrypted image.

[0144] Finally, convert the right-shifted target binary sequence to decimal to obtain the encrypted image, that is, the target encrypted image.

[0145] Furthermore, according to the above steps, the input plaintext image can be converted into a secure encrypted image (target encrypted image), thereby improving its robustness during network communication. It should be noted that image decryption is essentially the inverse process of image encryption. The keys ζ 1 , ζ 2 and ζ 3 used in the image encryption algorithm will be used in the image decryption process.

[0146] Specifically, first use the inverse image diffusion technique to decrypt the encrypted image into a scrambled image. During this process, the cyclic shift number is determined by formula (30) for dynamic DNA shift coding.

[0147] κ 2 (l) = mod(η - 1 - ζ 3 (l), 4) + 1 (30)

[0148] where l = {1, 2,..., ω - 1, ω}, and ω is equal to m × n × 4.

[0149] Finally, the scrambled image is decrypted using the inverse image permutation strategy to reconstruct the original image and obtain the input plaintext image.

[0150] The following presents a specific embodiment to verify the performance of the image encryption method based on biased Fourier quantum walk and add-X structure proposed in this application.

[0151] A series of simulation experiments and numerical analyses are carried out using grayscale images of different sizes. Histogram analysis, adjacent pixel correlation, and information entropy are used to evaluate the robustness of the encryption system. Meanwhile, differential attack, key sensitivity analysis, cropping, and noise attacks are adopted to systematically evaluate the robustness of the encryption mechanism.

[0152] As Figure 5 shown, this application selects the "mandrill" image with a size of 256×256 and the "bell pepper" image with a size of 512×512 as test images.

[0153] 1. Statistical analysis of pixel distribution histogram

[0154] A histogram is a tool for describing the brightness distribution of an image by showing the pixel frequencies of different gray levels in the image. In the evaluation of image encryption algorithms, histogram analysis is of great significance because it can reflect the randomness and uniformity of the encrypted image. As Figure 6 shown, this application presents the histograms of test images and encrypted images of different sizes. Among them, Figure 6 (a)-(d) in Figure 6 respectively represent the histograms of the original "Elaine", "mandrill", "pirate", and "bell pepper", while

[0155] (e)-(f) in Figure 7 respectively represent the histograms of the encrypted "Elaine", "mandrill", "pirate", and "bell pepper". According to the experimental results, it can be inferred that the histograms of the original images (i.e., test images) usually show a certain regularity and the pixel value distributions are uneven. On the contrary, for the encrypted images, their histograms show a uniform distribution. This indicates that the image encryption method based on biased Fourier quantum walk and add-X structure proposed in this application can effectively disrupt the pixel intensity distribution of the original image, making the encrypted image have no obvious structure or regularity visually, thus increasing the randomness and anti-attack ability of the encrypted image. Figure 7 (a)-(d) in Figure 7Among (e)-(h) are the schematic diagrams of the pixel distributions of the encrypted images of "Elaine", "Mandrill", "Pirate" and "Sweet Pepper". It can be clearly seen from the three-dimensional view that the pixels of the encrypted images are evenly distributed within the entire gray scale range of 0 to 255, which further indicates that the encrypted images have high randomness.

[0156] 2. Adjacent Correlated Pixel Coefficient Analysis

[0157] The robustness of an image is closely related to the correlation between adjacent pixels. A lower correlation provides higher statistical randomness, preventing attackers from recovering the content of the plaintext image by analyzing the associations between pixels. Therefore, evaluating whether an encryption algorithm has successfully disrupted the correlation between adjacent pixels is an important indicator to measure its encryption strength. Specifically, the following formulas provide the calculation of the correlation coefficients for adjacent pixel pairs in the horizontal, vertical, and diagonal directions of an image:

[0158]

[0159] where Z is the number of pixel pairs in the image, A′ τ and B′ τ represent the pixel pair values in the horizontal, vertical, and diagonal directions respectively, and represent the average values of A′ and B′ respectively.

[0160] As shown in Table 1, this application presents the correlation coefficients of adjacent pixels of the original image and the encrypted image. Obviously, the correlation coefficients of the original image in different directions are very close to 1, especially in the plaintext images of "Elaine", "Pirate" and "Sweet Pepper", which indicates a high correlation between their adjacent pixels. While the correlation coefficients between adjacent pixels of the encrypted image are significantly close to 0. This shows that after encryption, there is almost no linear relationship between adjacent pixels of the encrypted image, and it has high randomness and unpredictability. This low correlation makes it impossible for attackers to recover or infer the content of the original image by analyzing adjacent pixels.

[0161] Table 1 Correlation Coefficient Table of Plaintext Images and Encrypted Images in Horizontal, Vertical and Diagonal Directions

[0162]

[0163] To further verify the correlation between adjacent pixels of the encrypted image, this application visualizes the correlation through the scatter plot of adjacent pixels.

[0164] As Figure 8 shows the correlation between adjacent pixels of the original image and the encrypted image. Among them, Figure 8(a)-(d), (e)-(h), and (i)-(l) in it respectively represent the scatter plots of the original image and the encrypted "mandrill" and "sweet pepper" images in the horizontal, vertical, and diagonal directions. According to the above experimental results, it can be seen that the pixel values in the scatter plot of the original image are mainly concentrated on the diagonal line, while the scatter plot of the encrypted image shows that the pixel points are evenly distributed throughout the graph without obvious concentrated areas. Therefore, there is almost no linear relationship between adjacent pixels of the encrypted image, and thus the encrypted image has high randomness.

[0165] 3. Information Entropy Analysis

[0166] Information Entropy (IE) is an index used to measure the uncertainty or randomness of pixel values in an image. Its main function is to evaluate the complexity or "chaos degree" of the image and reflect whether the pixel distribution of the image is uniform. Assuming that the pixel intensity is uniformly distributed at all possible pixel levels, the maximum potential IE value in an 8-bit grayscale image is close to 8. Specifically, the information entropy of an image can be calculated by the following formula:

[0167]

[0168] where ψ is the pixel set, and F(ψ k ) represents the probability that the pixel value ψ k appears.

[0169] Table 2 Information Entropy Table of Original and Encrypted Images

[0170]

[0171]

[0172] As shown in Table 2, the IE values of the original image and the encrypted image are calculated respectively. It can be seen from Table 2 that the IE value of the original image is significantly lower than the maximum ideal entropy value. The information entropy of the encrypted image is higher than that of the original image and close to the theoretical maximum value of 8, indicating that the encryption algorithm has successfully disrupted the pixel distribution of the original image, making it have good uncertainty and pixel distribution randomness. Therefore, the encryption scheme proposed in this application can effectively destroy the pixel distribution of the plaintext image, making it difficult to recover the original image, thus ensuring the confidentiality and robustness of privacy data.

[0173] 4. Differential Attack Analysis

[0174] Differential attack is a common cryptanalysis method that analyzes the differences between the original image and the encrypted image by modifying the pixel values in specific regions of the image. The number of pixels change rate (NPCR) is widely used to evaluate the sensitivity of encryption algorithms because it quantifies the degree of pixel change. In addition, the unified average changing intensity (UACI) can quantify the average intensity of pixel changes between two images. Therefore, this application uses NPCR and UACI to evaluate the robustness of the image encryption method based on biased Fourier quantum walk and add-X structure and its ability to resist differential attacks.

[0175] The NPCR values of two images are calculated as follows:

[0176]

[0177] where m×n represents the size of the image, and D(i,j) is calculated by the following formula:

[0178]

[0179] where c 1 (i,j) and c 2 (i,j) represent the encrypted images generated using the same security key for the original image and its version with one pixel value modified, respectively.

[0180] In addition, the UACI calculation formula for two images is as follows:

[0181]

[0182] As shown in Table 3, this application calculated the NPCR and UACI values of different encrypted images. Obviously, the NPCR values are all greater than 96%, indicating that the encryption algorithm is highly sensitive to the change of a single pixel. On the other hand, all UACI values are very close to the ideal values, indicating that there are significant differences between the encrypted images generated by different keys. Therefore, the encryption algorithm designed in this application can effectively defend against differential attacks, that is, it is difficult to infer the key and the plaintext image from the known encryption.

[0183] Table 3 Statistical table of NPCR values and UACI values of encrypted images

[0184] Test Image NPCR (%) UACI (%) Elaine 99.661255 33.422499 Mandrill 99.615479 33.443843 Pirate 99.622726 33.504072 Bell Pepper 99.612808 33.437442

[0185] 5. Key sensitivity analysis

[0186] Encrypting an image with a slightly modified key can produce an encrypted image that is significantly different from the previous one, and this phenomenon is called key sensitivity. Similarly, decrypting a given encrypted image with a slightly changed key may produce a different image. It should be noted that this application involves the use of two security keys (i.e., κ 1 and κ 2 ). To examine the key sensitivity of the proposed encryption scheme, each of the two keys was changed by one bit, and the corresponding encrypted and decrypted "Pirate" images were analyzed. As Figure 9 shows, this application presents the experimental results of the differences between two encrypted images using different keys and two decrypted images using different keys. Among them, Figure 9 (a) in represents the images encrypted using keys κ 1 and κ 2 ; Figure 9 (b) in represents the difference between Figure 9 (a) in and the encrypted images generated using keys κ 3 and κ 4 ; Figure 9 (c) in represents the histogram of Figure 9 (b) in; Figure 9 (d) in is the experimental result of decrypting 5 and κ 6 the Figure 9 (a) in; Figure 9 (e) in represents the difference between Figure 9 (d) in and decrypting 7 and κ 8 the Figure 9 (a) in; Figure 9 (f) in is the histogram of Figure 9 (e) in. According to the above experimental results, it can be clearly seen that modifying one bit of each key cannot recover the original image, and no valuable information can be extracted from it. Therefore, this encryption mechanism has strong key sensitivity and can effectively resist known plaintext attacks.

[0187] 6. Robustness Analysis

[0188] Encrypted images may be maliciously attacked during transmission. Therefore, it is crucial to enable the attacked encrypted image to still successfully recover the main features of the original image through the correct decryption algorithm and key. In this application, two common attack methods (i.e., cropping and noise attacks) are used to measure the robustness of the proposed encryption mechanism.

[0189] As Figure 10 (a)-(d) in shows, a series of cropping attacks with different degrees were carried out on the encrypted "Pirate" image. In addition, Figure 10(e)-(h) in it respectively represent the decrypted images of (a)-(d) in Figure 10 . Obviously, although some data is lost in the encrypted image, the decrypted image can still visually and effectively identify the main content of the original image.

[0190] On the other hand, this application adds different degrees of salt-and-pepper noise and speckle noise to the encrypted "pirate" image to test the noise resistance of the encrypted image. As Figure 11 (a)-(d) in it show the experimental results of adding salt-and-pepper noise and speckle noise to the encrypted image respectively. Among them, Figure 11 (a) and (b) in it respectively represent the results of attacks with salt-and-pepper noise of densities 0.01 and 0.05, while Figure 11 (c) and (d) in it respectively represent the results of attacks with speckle noise of densities 0.0001 and 0.001. As Figure 11 (e)-(h) in it show that this application gives Figure 11 the decrypted images of (a)-(d) in it. Obviously, after introducing noise into the encrypted image, the decrypted image can not only recover most of the content of the original image, but also show perceptual clarity and maintain visual fidelity. Therefore, based on the above experimental results and analysis, it can be inferred that the encryption mechanism proposed in this application has strong robustness and good anti-interference ability against cropping attacks and noise attacks.

[0191] Based on the same inventive concept, the embodiment of this application also provides an image encryption system based on biased Fourier quantum walk and add-cross structure for implementing the above-mentioned image encryption method based on biased Fourier quantum walk and add-cross structure. The implementation solutions provided by this system to solve problems are similar to the implementation solutions recorded in the above method. Therefore, the specific limitations in one or more embodiments of the image encryption system based on biased Fourier quantum walk and add-cross structure provided below can refer to the limitations on the image encryption method based on biased Fourier quantum walk and add-cross structure in the above text, and will not be elaborated here.

[0192] In an exemplary embodiment, an image encryption system based on biased Fourier quantum walk and add-cross structure is provided, including:

[0193] A model construction unit for constructing a two-dimensional discrete biased Fourier quantum walk model.

[0194] An initial pseudo-random sequence determination unit for obtaining an initial pseudo-random sequence based on the two-dimensional discrete biased Fourier quantum walk model; the initial pseudo-random sequence includes: a first initial pseudo-random subsequence and a second initial pseudo-random subsequence.

[0195] A random sequence conversion unit for generating a first converted pseudo-random sequence, a second converted pseudo-random sequence, and a third converted pseudo-random sequence based on the initial pseudo-random sequence.

[0196] A security key determination unit for converting the first converted pseudo-random sequence into a first security key, the second converted pseudo-random sequence into a second security key, and the third converted pseudo-random sequence into a third security key.

[0197] A target scrambled image determination unit for obtaining a plaintext image, and using a preset image scrambling strategy to perform multiple image scramblings on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; the preset image scrambling strategy includes: an additive image scrambling strategy and a cross-shaped image scrambling strategy.

[0198] A target encrypted image determination unit for encoding the target scrambled image based on the third security key by using a dynamic DNA shift coding method to obtain a target encrypted image.

[0199] In an exemplary embodiment, a computer device is provided, including: a memory, a processor, and a computer program stored on the memory and executable on the processor, and the processor executes the computer program to implement an image encryption method based on a biased Fourier quantum walk and an addition-cross structure.

[0200] In an exemplary embodiment, a computer-readable storage medium is provided, on which a computer program is stored, and when the computer program is executed by a processor, it implements an image encryption method based on a biased Fourier quantum walk and an addition-cross structure.

[0201] In an exemplary embodiment, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, it implements an image encryption method based on a biased Fourier quantum walk and an addition-cross structure.

[0202] In an exemplary embodiment, a computer device is provided, and the computer device can be a server or a terminal, and its internal structure diagram can be as Figure 12As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O), and a communication interface. Among them, the processor, the memory, and the input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. Among them, the processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program, and a database. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The input / output interface of the computer device is used to exchange information between the processor and external devices. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, it implements an image encryption method based on biased Fourier quantum walk and add-x structure.

[0203] Those skilled in the art can understand that Figure 12 the structure shown in is only a block diagram of some structures related to the solution of this application, and does not constitute a limitation on the computer device to which the solution of this application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine some components, or have different component arrangements.

[0204] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use, and processing of relevant data need to comply with relevant regulations.

[0205] Those of ordinary skill in the art can understand that all or part of the processes in the methods of the above embodiments can be completed by instructing relevant hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above methods. Among them, any reference to a memory, database, or other medium used in the embodiments provided in this application can include at least one of non-volatile and volatile memories. Non-volatile memories can include read-only memory (ROM), magnetic tapes, floppy disks, flash memories, optical memories, high-density embedded non-volatile memories, resistive random access memories (ReRAM), magnetoresistive random access memories (MRAM), ferroelectric random access memories (FRAM), phase change memories (PCM), graphene memories, etc. Volatile memories can include random access memory (RAM) or external cache memories, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0206] The databases involved in the embodiments provided in this application can include at least one of relational databases and non-relational databases. Non-relational databases can include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided in this application can be general-purpose processors, central processors, graphics processors, digital signal processors, programmable logics, data processing logics based on quantum computing, etc., without limitation.

[0207] The technical features of the above embodiments can be combined arbitrarily. For the sake of concise description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0208] Specific examples are used in this article to elaborate on the principles and implementation manners of this application. The descriptions of the above embodiments are only used to help understand the method and its core idea of this application; at the same time, for those of ordinary skill in the art, according to the idea of this application, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to this application.

Claims

1. An image encryption method based on biased Fourier quantum walk and plus-fork structure, characterized in that: The image encryption method based on biased Fourier quantum walk and plus-fork structure includes: Construct a two-dimensional discrete biased Fourier quantum walk model; Based on the two-dimensional discrete biased Fourier quantum walk model, an initial pseudo-random sequence is obtained; the initial pseudo-random sequence includes: a first initial pseudo-random subsequence and a second initial pseudo-random subsequence; generating a first conversion pseudo-random sequence, a second conversion pseudo-random sequence and a third conversion pseudo-random sequence based on the initial pseudo-random sequence; Convert the first converted pseudo-random sequence into a first security key, convert the second converted pseudo-random sequence into a second security key, and convert the third converted pseudo-random sequence into a third security key; Obtain a plaintext image, and use a preset image scrambling strategy to perform multiple image scrambling on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; the preset image scrambling strategy includes: an additive image scrambling strategy and a fork image scrambling strategy; The target scrambled image is encoded based on the third security key using a dynamic DNA shift encoding method to obtain a target encrypted image.

2. The image encryption method based on biased Fourier quantum walk and plus-fork structure according to claim 1 is characterized in that: Generating a first conversion pseudo-random sequence, a second conversion pseudo-random sequence, and a third conversion pseudo-random sequence based on the initial pseudo-random sequence specifically includes: Using the formula Converting an initial pseudo-random sequence into a first conversion pseudo-random sequence, and converting the initial pseudo-random sequence into a second conversion pseudo-random sequence; wherein γ1 represents the first initial pseudo-random subsequence; γ2 represents the second initial pseudo-random subsequence; χ1 represents the first conversion pseudo-random sequence; χ2 represents the second conversion pseudo-random sequence; and e represents a bitwise multiplication operator; The third converted pseudo-random sequence is obtained based on the initial pseudo-random sequence using the formula χ3=concat[(γ1⊙γ2),γ1,γ2,γ1+γ2]; wherein χ3 represents the third converted pseudo-random sequence; and concat[·] represents the concatenation function.

3. The image encryption method based on biased Fourier quantum walk and plus-fork structure according to claim 2 is characterized in that: Converting the first converted pseudo-random sequence into a first security key, converting the second converted pseudo-random sequence into a second security key, and converting the third converted pseudo-random sequence into a third security key specifically includes: Using the formula Convert the first converted pseudo-random sequence into a first security key, and convert the second converted pseudo-random sequence into a second security key; wherein ζ1(i) represents the i-th code element in the first security key; χ1(i) represents the i-th pseudo-random number in the first converted pseudo-random sequence; ζ2(i) represents the i-th code element in the second security key; χ2(i) represents the i-th pseudo-random number in the second converted pseudo-random sequence; floor(·) is a floor rounding function; mod represents a modulo operation; Using the formula ζ3(j)=floor(mod(χ3(j)×10 14 ),256), converting the third converted pseudo-random sequence into a third security key; wherein ζ3(j) represents the jth code element in the third security key; χ2(i) represents the i-th pseudo-random number in the second converted pseudo-random sequence.

4. The image encryption method based on biased Fourier quantum walk and plus-fork structure according to claim 1, characterized in that: Using a preset image scrambling strategy, performing multiple image scrambling on the plaintext image based on the first security key and the second security key to obtain a target scrambled image, specifically including: sorting the first security key and the second security key in ascending order respectively to obtain an ascending first security key and an ascending second security key; Adopting the additive image scrambling strategy and the fork image scrambling strategy, the plaintext image is subjected to multiple additive image scrambling and multiple fork image scrambling based on the ascending first security key and the ascending second security key to obtain the target scrambled image.

5. The image encryption method based on biased Fourier quantum walk and plus-fork structure according to claim 4 is characterized in that: Adopting an additive image scrambling strategy and a fork image scrambling strategy, performing multiple additive image scrambling and multiple fork image scrambling on the plaintext image based on the ascending first security key and the ascending second security key to obtain the target scrambled image, specifically including: Based on the first security key in ascending order, respectively determining the position of the row index of the additive image scrambling strategy in the plaintext image and the position of the column index in the plaintext image; Based on the positions of the row index and the column index of the additive image scrambling strategy in the plaintext image, determining the initial position of the additive scrambling region in the plaintext image; Based on the first security key, determining the number of cyclic shift operations of the addition type image scrambling; the cyclic shift operation of the addition type image scrambling includes: a horizontal cyclic shift operation and a vertical cyclic shift operation; Based on the second security key in ascending order, respectively determining the position of the row index of the fork-type image scrambling strategy in the plaintext image and the position of the column index in the plaintext image; Based on the position of the row index of the fork-type image scrambling strategy in the plaintext image and the position of the column index in the plaintext image, an initial position of the fork-type scrambling region in the plaintext image is determined; Based on the second security key, determining the number of cyclic shift operations of the fork-shaped image scrambling; the cyclic shift operations of the fork-shaped image scrambling include: a left diagonal cyclic shift operation and a right diagonal cyclic shift operation; Based on the number of cyclic shift operations of the addition-type image scrambling and the number of cyclic shift operations of the fork-type image scrambling, the plaintext image is subjected to multiple addition-type image scrambling and multiple fork-type image scrambling to obtain the target scrambled image.

6. The image encryption method based on biased Fourier quantum walk and plus-fork structure according to claim 5, characterized in that: The target scrambled image is encoded based on the second security key using a dynamic DNA shift encoding method to obtain a target encrypted image, specifically including: Convert the pixel value of each pixel in the target scrambled image into a binary sequence to obtain a binary matrix of the target scrambled image; Based on the third security key, dynamically left-shift each element in the binary matrix to obtain a left-shifted binary matrix; Convert each element in the left-shifted binary matrix into a 4-bit DNA code to obtain an initial dynamic DNA code sequence; Circularly shifting the initial dynamic DNA coding sequence according to the dynamic shift number to generate a target dynamic DNA coding sequence, and converting the target dynamic DNA coding sequence into a binary sequence to obtain a target binary sequence; Dynamically cyclically right-shift each element in the target binary sequence to obtain the right-shifted target binary sequence; Convert the right-shifted target binary sequence into decimal to obtain the target encrypted image.

7. An image encryption system based on biased Fourier quantum walk and plus-fork structure, characterized in that: The image encryption system based on biased Fourier quantum walk and plus-fork structure is used to implement the image encryption method based on biased Fourier quantum walk and plus-fork structure according to any one of claims 1 to 6, and the image encryption system based on biased Fourier quantum walk and plus-fork structure includes: A model building unit, used to build a two-dimensional discrete biased Fourier quantum walk model; An initial pseudo-random sequence determination unit is used to obtain an initial pseudo-random sequence based on the two-dimensional discrete biased Fourier quantum walk model; the initial pseudo-random sequence includes: a first initial pseudo-random subsequence and a second initial pseudo-random subsequence; A random sequence conversion unit, configured to generate a first conversion pseudo-random sequence, a second conversion pseudo-random sequence and a third conversion pseudo-random sequence based on the initial pseudo-random sequence; a security key determination unit, configured to convert the first converted pseudo-random sequence into a first security key, convert the second converted pseudo-random sequence into a second security key, and convert the third converted pseudo-random sequence into a third security key; a target scrambled image determination unit, configured to obtain a plaintext image, and adopt a preset image scrambling strategy to perform multiple image scrambling on the plaintext image based on the first security key and the second security key to obtain a target scrambled image; the preset image scrambling strategy includes: an additive image scrambling strategy and a fork image scrambling strategy; The target encrypted image determination unit is used to encode the target scrambled image based on the third security key using a dynamic DNA shift encoding method to obtain a target encrypted image.

8. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the image encryption method based on biased Fourier quantum walk and plus-fork structure as described in any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the image encryption method based on biased Fourier quantum walk and plus-fork structure described in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the image encryption method based on biased Fourier quantum walk and plus-fork structure described in any one of claims 1 to 6 is implemented.

Images