CN115499557B - Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method - Google Patents

Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method Download PDF

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CN115499557B
CN115499557B CN202211114087.6A CN202211114087A CN115499557B CN 115499557 B CN115499557 B CN 115499557B CN 202211114087 A CN202211114087 A CN 202211114087A CN 115499557 B CN115499557 B CN 115499557B
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赵朝锋
杜庆辉
尹承伟
翟志波
张永新
沈家全
李德光
赵鹏
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Luoyang Normal University
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Abstract

The invention discloses a delayed chaotic image encryption method based on Arnold mapping and a multi-shift mapping function, which comprises the following steps of: s1: selecting proper parameters and initial values as secret keys, generating a chaotic sequence by a delay-induced hyper-chaotic system, and carrying out imaging processing on the chaotic sequence to obtain an imaging sequence; s2: carrying out multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image; s3: converting the scrambled image into a diffuse image through an imaging sequence; s4: and processing the diffusion image through the imaging sequence and the multi-shift mapping function to obtain a ciphertext image. The encryption method has infinite key space in theory, and greatly improves the sensitivity and the security of algorithm keys. In addition, the encryption method has a faster encryption speed and can effectively resist security attacks. The encryption method solves the problems that the existing encryption method is too small in key space, poor in robustness, low in efficiency, difficult to resist plaintext attack and the like.

Description

Arnold mapping and multi-shift mapping function-based delayed chaotic image encryption method
Technical Field
The invention relates to the field of image information protection, in particular to a delayed chaotic image encryption method based on Arnold mapping and a multi-shift mapping function.
Background
Some digital images contain a lot of information and privacy, which is often not desired to be accessed and obtained illegally by people, and thus protection of image information is a focus of attention. At the same time, personalized image protection techniques are also of interest.
As is well known, digital images have the characteristics of large data volume, high redundancy, strong correlation and the like, and the conventional encryption method is not suitable for encrypting the digital images. The chaos has dynamic characteristics such as sensitivity to initial values and parameters, unpredictability, pseudo-randomness, ergodic property and the like, and is very suitable for encrypting digital images.
Currently, as the demand for digital image protection increases, more personalized image information protection technologies are being proposed. Although chaotic image protection technology shows remarkable advantages, an image encryption method based on low-dimensional chaos has a safety defect, and the method is common. The image encryption technology based on high-dimensional chaos is challenged because the encryption process is simple and the key algorithm is too dependent on the security of the key stream. In addition, the chaotic image protection technology has various difficult problems at present, such as encryption and decryption of the first element are irrelevant to an algorithm; the multi-purpose nonlinear function is used as an encryption machine, so that the algorithm efficiency is low; the scrambling function has periodicity, so that a large potential safety hazard appears; high-dimensional chaos is difficult to realize and the like.
Disclosure of Invention
In order to overcome the defects in the background technology, the invention discloses a delayed chaotic image encryption method based on Arnold mapping and a multi-shift mapping function, which aims at: the method solves the problems that the prior encryption method has too small key space, poor robustness, low efficiency, difficulty in enabling the first element to be related to the algorithm, scrambling periodicity and the like, meets the protection requirement of users on image information, and meets the unique individual requirement of the users.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
a delayed chaotic image encryption method based on Arnold mapping and a multi-shift mapping function comprises the following steps:
s1: selecting proper parameters and initial values as secret keys, generating a chaotic sequence by a delay-induced hyper-chaotic system, and carrying out imaging processing on the chaotic sequence to obtain an imaging sequence;
s2: carrying out multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image;
s3: converting the scrambled image into a diffuse image through an imaging sequence;
s4: and processing the diffusion image through the imaging sequence and the multi-shift mapping function to obtain a ciphertext image.
In the further improved technical scheme, in S1, the hyperchaotic system is a hyperchaotic system with theoretical infinite dimension, and the chaotic sequence generated by the hyperchaotic system is a pseudo-random chaotic sequence.
Further improving the technical scheme, S1 comprises the following sub-steps:
s1.1: the mathematical model of the hyper-chaotic system is as follows:
wherein a, b and c are parameters, x, y and z are state variables, k is linear feedback gain, and τ is delay time;
taking the last M.N values of the state sequences x, y and z to obtain three sequences X, Y, Z;
s1.2: converting sequence X, Y, Z by formula (2) to sequences X ', Y ', Z ' with values of [0, 255 ];
constructing an imaging sequence Z by means of (3) h Imaging sequence Z h For obfuscating operations;
Z h ＝mod(X′+Y′，256)。 (3)
the method has the beneficial effects that the random sequence generated by the delayed chaos is beneficial to deep fusion with the image, so that a potential encryption effect is achieved.
In a further improved technical scheme, S2, arnold mapping is performed on the original image P through the method (4) to obtain a scrambled image P 1 ；
Where (i, j) is the pixel position of the original image P before conversion, (i ', j ') is the pixel position of the original image P after conversion, a, b are conversion parameters, M is the length of the image, N is the width of the image, and mod () ' is the modulo operation.
The method has the beneficial effects that the periodicity of the scrambling function can be well avoided, and the scrambling effect of the algorithm is optimal.
Further improving the technical scheme, setting a=113 and b=97, and performing two-round Arnold mapping on the original image P through the formula (4) to obtain a scrambled image P 1 。
Further improving the technical scheme, the decryption map of the formula (4) is as follows:
further improving the technical scheme, S3 comprises the following sub-steps:
s3.1: will scramble the image P 1 Conversion to one-dimensional pixel array P 2 Converting the complex image structure into a simpler one-dimensional structure;
s3.2: calculating the initial value P of the intermediate sequence by the method (6) m (0) A random confusion mechanism is established, and the defect that the first element is irrelevant to an algorithm is overcome.
S3.3: generating sequence P by formula (7) m (ii)；
P m (ii)＝mod(P 2 (ii)+P m (ii-1)+Z h (ii)，256) (7)
Where ii=1, 2,3,4, …, m×n.
The method has the beneficial effects that the delay chaotic system, the scrambling function, the linear function and the diffusion operation are combined, so that a good encryption effect is achieved.
Further improving the technical scheme, S4 comprises the following sub-steps:
s4.1: reconstructing the piecewise function using a multi-shift mapping function;
wherein f is a linear piecewise function:
wherein, C is a ciphertext image, p is plaintext, k is a secret key, n is the iteration number, and l is a parameter;
s4.2: sequence P m And the sequence Z' are respectively used as plaintext and key of the formula (8) and the formula (9), and the corresponding sequence value C is obtained after 2 times of iteration 1 ；
S4.3: c is C 1 Reconstructing the matrix into an MXN matrix, and repeating the steps S1-S3 to obtain a new round of reconstructed matrix, and finally forming the ciphertext image C.
The method has the beneficial effects that the novel linear function is applied to the encryption machine, and the defect of low efficiency caused by the nonlinear function is avoided.
By adopting the technical scheme, compared with the background technology, the invention has the following beneficial effects:
according to the delayed chaotic image encryption method based on Arnold mapping and the improved multi-shift mapping function, firstly, a hyperchaotic sequence generated by delay induction is imaged, and a random sequence generated by delayed chaos is well fused with an image depth; then, the original image is scrambled according to the characteristics of Arnold mapping, so that the problem of periodic scrambling is solved. The problem that the first pixel of the plaintext is irrelevant to the algorithm is solved through diffusion operation. Finally, the linear function is well applied to the encryption machine through the imaging sequence and the improved multi-shift mapping function, so that the confusion and diffusion effects are improved, and the algorithm efficiency is greatly improved.
When the encryption method adopts the hyperchaotic system generated by delay induction to encrypt the image, the key space has infinite dimension theoretically, and can resist various forms of statistical attacks. By utilizing the characteristics of Arnold mapping and an improved multi-shift mapping function and combining with the imaging of the chaotic sequence, the image achieves a good encryption effect and improves encryption efficiency. The execution of the diffusion operation establishes the relationship between the first pixel of the image and the algorithm, and can more effectively resist the attack of known or selected plaintext.
The encryption method can provide a larger key space, improves the sensitivity of algorithm keys, has a faster encryption speed, and can effectively resist security attacks. The encryption method solves the problems of the existing encryption method that the key space is too small, the robustness is poor, the efficiency is low, the first element is difficult to be related to the algorithm, the scrambling periodicity is difficult, and the like.
The encryption method utilizes the delay phenomenon to generate a plurality of hyperchaotic attractors with different topological structures in a stable dynamic system, the hyperchaotic system shows more complex dynamic characteristics, a brand new random generator source is provided for information security protection, and the idea is unique in the industry and has creativity.
Drawings
Fig. 1 is a flowchart of encryption of a chaotic image generated by delay induction in an embodiment of the present invention.
Fig. 2 is a diagram of a chaotic system generated by delay induction in an embodiment of the present invention.
Fig. 3 is a "cam man" encryption/decryption map and histogram of the encryption method in the embodiment of the present invention.
Fig. 4 is a key sensitivity test chart and a histogram of the encryption method in the embodiment of the present invention.
Fig. 5 is a correlation diagram of a method of encryption in an embodiment of the present invention.
Fig. 6 is a test chart of a "full black" image of the encryption method in the embodiment of the present invention.
Fig. 7 is a test chart of a "full white" image of an encryption method in an embodiment of the present invention.
FIG. 8 is a line drawing of the "NPCR" of the encryption method in an embodiment of the invention.
Fig. 9 is a line drawing of "UACI" of the encryption method in the embodiment of the present invention.
FIG. 10 is a diagram of anti-noise and shear attacks of the encryption method in an embodiment of the present invention.
FIG. 11 is a runtime share graph of a cryptographic method in an embodiment of the invention.
Detailed Description
The following describes preferred embodiments of the present invention with reference to the accompanying drawings, and effects of the present encryption method are described. It should be understood by those skilled in the art that these embodiments are merely for explaining the technical principles of the present invention, and are not intended to limit the scope of the present invention.
Referring to fig. 1, the method for encrypting the delayed chaotic image based on Arnold mapping and multi-shift mapping functions comprises the following steps:
s1: and selecting proper parameters and initial values as keys, generating a pseudo-random chaotic sequence by a delay-induced hyper-chaotic system, and carrying out imaging processing on the pseudo-random chaotic sequence to obtain an imaging sequence.
The hyperchaotic system has theoretical infinite dimension, proper parameters and initial values are selected as secret keys, and the hyperchaotic system can generate a chaotic attractor with theoretical infinite dimension as shown in figure 2 through delay induction, which shows that the chaotic system has simple and feasible generation mechanism, more complex dynamics characteristic and better potential to be applied to the field of information safety. The pseudo-random chaotic sequence of the chaotic attractor is subjected to imaging processing, so that the sequence X ', Y ', Z ' and an imaging sequence Zh can be obtained, and the depth fusion of the chaotic system and the image in the encryption method is shown. The encryption method can effectively expand the key space, achieves the infinite dimension in theory, and effectively resists the attack of statistics.
Specifically, S1 includes the following sub-steps:
s1.1: taking a Chen system as an example, the mathematical model of the hyper-chaotic system is as follows:
(1) Where a, b, c are parameters, x, y, z are state variables, k is a linear feedback gain, and τ is a delay time. When k=0, the system stabilizes.
As shown in fig. 2 (a), when a=35, b=3, c=18.5, and k=0, the hyperchaotic system is a normal stable Chen system (without delay characteristics). From some initial condition, convergence to one of two stable equilibrium points.
As shown in fig. 2 (b), when a=35, b=3, c=18.5, k=3.8, τ=0.3, the hyperchaotic system has a delay characteristic, and hyperchaotic is generated, and a composite multi-scroll hyperchaotic attractor is presented.
As shown in fig. 2 (c), when a=35, b=3, c=18.5, k=2.85, τ=0.3, the hyperchaotic system is still hyperchaotic, presenting a double scroll hyperchaotic attractor.
As shown in fig. 2 (d), when a=35, b=3, c=18.35978, k=2.85, τ=0.3, the system is still hyperchaotic, presenting a single scroll hyperchaotic attractor.
The parameters a=35, b=3, c=18.5, k=3.8, τ=0.3 of the hyperchaotic system generated by delay induction are determined, the initial values x (0) =0.1, y (0) =0.1, z (0) =0.1, the initial conditions on [ - τ, 0) are: z (t) =0, - τ.ltoreq.t < 0. To avoid transient effects, the value of the evolution of the delayed attractor system (1) over 0 < t < Tp (tp=50 in the present invention) is not employed. The system evolves to generate state sequences x, y, z of length M x N, forming three sequences X, Y, Z.
S1.2: the imaging operation is carried out by the formula (2) and the formula (3), and the sequence X, Y, Z is converted into the value of [0, 255]]The sequences X ', Y ', Z ' of (1) to obtain an imaging sequence Z h 。
Constructing an imaging sequence Z by means of (3) h Imaging sequence Z h For obfuscating operations.
Z h ＝mod(X′+Y′，256)。 (3)
The method has the beneficial effects that the random sequence generated by the delayed chaos is beneficial to deep fusion with the image, so that a potential encryption effect is achieved.
S2: and carrying out multi-round scrambling on the original image through Arnold mapping to obtain a scrambled image.
Specifically, in S2, let a=113 and b=97, and perform two rounds of Arnold mapping on the original image P by equation (4) to obtain the scrambled image P 1 。
Where (i, j) is the pixel position of the original image P before transformation, (i ', j') is the pixel position of the original image P after transformation, a, b are transformation parameters, M is the length of the image, N is the width of the image, and mod (·) is the modulo operation.
The method has the beneficial effects that the periodicity of the scrambling function can be well avoided, and the scrambling effect of the algorithm is optimal.
The inverse of the Arnold map is the decryption map, which is:
s3: converting the scrambled image into a diffuse image through an imaging sequence;
specifically, S3 includes the following sub-steps:
s3.1: will scramble the image P 1 Conversion to one-dimensional pixel array P 2 ；
S3.2: calculating the initial value P of the intermediate sequence by the method (6) m (0)；
S3.3: generating sequence P by formula (7) m (ii)；
P m (ii)＝mod(P 2 (ii)+P m (ii-1)+Z h (ii)，256) (7)
Where ii=1, 2,3,4, …, m×n.
The method has the beneficial effects that the scrambled image is converted into the diffusion image, and the relation between the first element and the algorithm is established, so that the attack of the selected or known plaintext can be well resisted. In addition, the delay chaotic system, the scrambling function, the linear function and the diffusion operation are combined, so that a good encryption effect is achieved.
S4: the diffusion image is processed through the imaging sequence and the multi-shift mapping function, and the linear function is applied to the encryption machine, so that the encryption efficiency is effectively improved, and the ciphertext image is quickly obtained. Specifically, according to the imaged sequences Z' and P m Substituting the modified multi-shift mapping function as the corresponding plaintext and key to obtain the final ciphertext image.
S4 comprises the following substeps:
s4.1: reconstructing the piecewise function using a multi-shift mapping function;
wherein f is a linear piecewise function:
wherein, C is a ciphertext image, p is plaintext, k is a secret key, n is the iteration number, and l is a parameter;
in this embodiment, l=128, n=2.
S4.2: sequence P m And the sequence Z' are respectively used as plaintext and key of the formula (8) and the formula (9), and the corresponding sequence value C is obtained after 2 times of iteration 1 ；
S4.3: c is C 1 Reconstructing the matrix into an MXN matrix, and repeating the steps S1-S3 to obtain a new round of reconstructed matrix, and finally forming the ciphertext image C.
The method has the beneficial effects that the novel linear function is applied to the encryption machine, and the defect of low efficiency caused by the nonlinear function is avoided.
The following is a performance test and analysis of the encryption method, which can well verify the advantages of the encryption method, and the performance test and analysis comprises the following parts:
(1) encryption and decryption effect analysis;
(2) key space analysis;
(3) key sensitivity analysis;
(4) correlation analysis;
(5) information entropy analysis;
(6) analysis against known or selected plaintext attacks;
(7) differential attack resistance analysis;
(8) data loss resistance and noise analysis;
(9) and (5) analyzing the operation efficiency.
To illustrate the versatility of the present invention, the test images were all selected from the USC-SIPI image library, with the computer configured as AMD Ryzen 53550H CPU and 8GB RAM, and corresponding tests were performed on the platform of MATLAB2016 a.
(1) And (3) encryption and decryption effect analysis:
as shown in fig. 3, a "camera" image (256×256) is selected for encryption and decryption tests, and the original image, the encrypted image, the decrypted image, and the corresponding histograms thereof are shown in fig. 3. The average fluctuation of the histogram is small like the noise image of the encrypted image, which means that the encryption method of the invention can effectively resist statistical attack in the pixel value distribution sense.
(2) Key space analysis:
if only 5 parameters (a, b, c, k, τ) and three initial values (x (0), y (0), z (0)) of the delay-induced hyper-chaotic system are used as keys, a key space of 2 is formed 256 (calculation accuracy is 2 -32 ). If the hyperchaotic system generated by delay induction is at [ -tau, 0]The initial condition on this is also used as a key, the key space will be expanded to the theoretically infinite dimension. Thus, the key space of the image encryption method of the present invention is resistant to any brute force attack.
(3) Key sensitivity analysis:
fig. 4 shows the results of the key sensitivity analysis. 4 (a) and (d) are histograms of the original image and its corresponding image, 4 (b) and (e) are histograms of the decrypted image and its image using the correct key (z (0) =0.1, the other key values are unchanged), and 4 (c) and (f) are histograms of the decrypted image and its image using the slightly different key (z (0) =0.1+10) -14 Other key values are unchanged) the image that decrypts the same encrypted image and its corresponding histogram. As can be seen from fig. 4, the reconstruction of the original image can only be done with the correct key, even if the slightly different key would result in a completely different decrypted image. This illustrates that the image encryption method of the present invention is very sensitive to keys in the encryption and decryption process.
(4) Correlation analysis:
fig. 5 shows the correlation of the original image "camera" (256×256) and the corresponding encrypted image in the horizontal direction, the vertical direction, and the diagonal direction. In addition, table 1 shows the quantitative results of the image neighboring pixel correlation test. This also shows that the image encryption method of the invention is subject to statistical attack, and an attacker cannot obtain any valuable information.
TABLE 1 Adjacent Pixel correlation analysis of original image and encrypted image
(5) Information entropy analysis:
the information entropy values of the original image and the corresponding encrypted image are given in table 2, which shows that the information leakage rate of the image encryption method of the invention is close to zero, meaning that the method has higher randomness in the information entropy sense.
TABLE 2 information entropy of encrypted image
(6) Analysis against known or selected plaintext attacks
An adversary will often select a particular original image, such as a full black image or a full white image (256 x 256), obtain a corresponding encrypted image to infer a key or reveal the relationship between the original image and the ciphertext image. In the confusion stage of the image encryption method, the confusion value is related to the scrambled image, so that a multi-shift mapping function is added, and the relation between the ciphertext and the plaintext is more complex. Therefore, the image encryption method can effectively resist the known or selected plaintext attack. As shown in fig. 6 and 7, the encrypted images are similar to noise, and have good encryption effect.
(7) Differential attack resistance analysis:
tables 3 and 4 show the NPCR and UACI values of the encrypted image, and fig. 9 and 10 show line diagrams of NPCR and UACI values. It can be seen that the NPCR and UACI values of the encryption method of the present invention are close to the expected values 99.6094% and 33.4635%. In fig. 9 and 10, the fold line of the encryption method of the present invention and the fold line of the expected value almost coincide at the key point, which illustrates that the differential attack resistance of the encryption method of the present invention is quite stable and does not change drastically with the change of the image.
TABLE 3 test results of NPCR (%)
Table 4 test results of UACI (%)
(8) Data loss and noise resistant analysis:
fig. 10 shows the result of using the image encryption method of the present invention to combat noise attacks and partial data loss in an image. As can be seen from fig. 10, although the encrypted image suffers from different types of noise pollution or different sizes of data loss, the identifiable original image can be restored after decryption by using the image encryption method of the present invention, which indicates that the image encryption method of the present invention has good robustness.
(9) And (3) analyzing the operation efficiency:
table 5 lists the average encryption time for 30 monte carlo tests using different images. The test was performed in a MATLAB environment with a computer (AMD) Ryzen 53550H CPU and 8gb RAM. Fig. 11 shows the time share of the whole encryption process, the chaotic evolution time (HCMACS-TD) is 29% of the total time, the Arnold mapping process is 16% of the total time, the diffusion process is 14% of the total time, and the multiple shift mapping function process is about 41% of the total time.
Table 5 algorithm average run time(s)
The basic principle and main technical features of the present invention are described above. When the image encryption method adopts the hyperchaotic system generated by delay induction to encrypt the image, the key space has infinite dimension theoretically. By utilizing the characteristics of Arnold mapping and an improved multi-shift mapping function and combining with the imaging of the chaotic sequence, the image achieves a good encryption effect. The relation between the first pixel of the image and the ciphertext is established by the execution of the diffusion operation, so that the known or selected plaintext attack can be more effectively resisted.
The method can provide larger key space, improves the sensitivity of algorithm keys, has higher encryption speed, and is more suitable for image information security protection.
The encryption method solves the problems that the existing encryption method is too small in key space, poor in robustness, low in efficiency, difficult to resist plaintext or select plaintext attack and the like.
The parts not described in detail are prior art. Although embodiments of the present invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made therein without departing from the spirit and scope of the invention as defined by the appended claims and their equivalents.

Claims (5)

1. A delayed chaotic image encryption method based on Arnold mapping and multiple shift mapping functions is characterized by comprising the following steps: the method comprises the following steps:
s1: selecting proper parameters and initial values as secret keys, generating a chaotic sequence by a delay-induced hyper-chaotic system, and carrying out imaging processing on the chaotic sequence to obtain an imaging sequence;
s1.1: the mathematical model of the hyper-chaotic system is as follows:
wherein a, b and c are parameters, x, y and z are state variables, k is linear feedback gain, and τ is delay time;
taking the last M.N values of the state sequences x, y and z to form three sequences X, Y, Z;
s1.2: converting sequence X, Y, Z by formula (2) to sequences X ', Y ', Z ' with values of [0, 255 ];
constructing an imaging sequence Z by means of (3) h Imaging sequence Z h For obfuscating operations;
Z h ＝mod(X′+Y′,256)； (3)
s2: arnold mapping is carried out on the original image P through the method (4) to obtain a scrambled image P 1 ；
Wherein (i, j) is the pixel position of the original image P before transformation, (i ', j') is the pixel position of the image after transformation, a, b are transformation parameters, M is the length of the image, N is the width of the image, and mod (·) is the modulo operation;
s3: scrambling an image P by an imaging sequence 1 Converting into a diffusion image;
s3.1: will scramble the image P 1 Conversion to one-dimensional pixel array P 2 ；
S3.2: calculating the initial value P of the intermediate sequence by the method (6) m (0)；
S3.3: generating sequence P by formula (7) m (ii)；
P m (ii)＝mod(P 2 (ii)+P m (ii-1)+Z h (ii),256) (7)
Wherein ii=1, 2,3,4, …, m×n;
s4: and processing the diffusion image through the imaging sequence and the multi-shift mapping function to obtain a ciphertext image.
2. The method for encrypting the delayed chaotic image based on Arnold mapping and multi-shift mapping functions as claimed in claim 1, wherein the method is characterized by comprising the following steps of: in S1, the hyperchaotic system is a hyperchaotic system with theoretical infinite dimension, and the chaotic sequence generated by the hyperchaotic system is a pseudo-random chaotic sequence.
3. The method for encrypting the delayed chaotic image based on Arnold mapping and multi-shift mapping functions as claimed in claim 1, wherein the method is characterized by comprising the following steps of: in S2, let a=113 and b=97, and perform two rounds of Arnold mapping on the original image P by equation (4) to obtain a scrambled image P 1 。
4. A delayed chaotic image encryption method based on Arnold mapping and multi-shift mapping functions as claimed in claim 1 or 3, wherein: in S2, the decryption map of equation (4) is:
5. the method for encrypting the delayed chaotic image based on Arnold mapping and multi-shift mapping functions as claimed in claim 1, wherein the method is characterized by comprising the following steps of: s4 comprises the following substeps:
s4.1: reconstructing the piecewise function using a multi-shift mapping function;
wherein f is a linear piecewise function:
wherein, C is a ciphertext image, p is plaintext, k is a secret key, n is the iteration number, and l is a parameter;
s4.2: sequence P m And the sequence Z' are respectively used as plaintext and key of the formula (8) and the formula (9), and the corresponding sequence value C is obtained after 2 times of iteration 1 ；
S4.3: c is C 1 Reconstructing the matrix into an MXN matrix, and repeating the steps S1-S3 to obtain a new round of reconstructed matrix, and finally forming the ciphertext image C.
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