CN113055545A - Image encryption system based on two-dimensional index-cosine chaotic system - Google Patents

Image encryption system based on two-dimensional index-cosine chaotic system Download PDF

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CN113055545A
CN113055545A CN202110356974.3A CN202110356974A CN113055545A CN 113055545 A CN113055545 A CN 113055545A CN 202110356974 A CN202110356974 A CN 202110356974A CN 113055545 A CN113055545 A CN 113055545A
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CN113055545B (en
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刘思聪
彭淑燕
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Jiangsu Institute of Economic and Trade Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
    • H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
    • H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
    • H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
    • H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
    • H04N1/32272—Encryption or ciphering
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/44—Secrecy systems
    • H04N1/448—Rendering the image unintelligible, e.g. scrambling
    • H04N1/4486—Rendering the image unintelligible, e.g. scrambling using digital data encryption

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Abstract

The invention discloses an image encryption system based on a two-dimensional index-cosine chaotic system, which relates to the technical field of information security and comprises a 2D-Ecs chaotic system and an image information chaotic encryption operation carried out by utilizing the 2D-Ecs chaotic system; the method for carrying out chaotic encryption operation on image information by using the 2D-Ecs chaotic system comprises the following steps: 1) firstly, RGB multi-channel extraction is carried out on image data; 2) carrying out chaotic encryption on the extracted single-channel image data by utilizing a 2D-ECs chaotic system; 3) and then rewriting the encrypted single-channel image data back to the image so as to complete the encryption of the image data. The image encryption method designed by the invention has the characteristics of large key space, good encryption effect, strong anti-jamming capability and the like. Simulation experiments show that the algorithm can effectively resist exhaustive attacks and differential attacks.

Description

Image encryption system based on two-dimensional index-cosine chaotic system
Technical Field
The invention relates to the technical field of information security, in particular to an image encryption system based on a two-dimensional index-cosine chaotic system.
Background
At present, as the world enters the post epidemic situation era, more and more interpersonal communication is migrated to be carried out on line due to the requirement of epidemic situation protection and the arrival of the 5G era. There is an increasing demand for image encryption for protection of personal privacy and information security.
However, the current image encryption algorithm generally has the defects of complex encryption process, long time consumption and the like. For some fields requiring real-time encryption transmission, the existing encryption algorithm cannot meet the requirements. While the chaos encryption algorithm attracts the attention of researchers after the chaos system is applied to the field of information encryption by Matthews and the like. Up to now, various one-dimensional chaotic systems have been applied to the field of information encryption. Most of the one-dimensional chaotic systems have the characteristics of high iteration speed, simple implementation method and the like. However, the system control parameters of the one-dimensional chaotic system are less, and the phase space orbit distribution is single, so that the system is very easy to be attacked by methods such as phase space reconstruction and the like, and the ciphertext is maliciously cracked. In order to overcome the disadvantages of the one-dimensional chaotic system, researchers propose a series of improvements, such as: researchers have coupled a plurality of control parameters of a one-dimensional chaotic system, so that the chaotic nature of the whole system becomes more complex. Researchers also integrate a plurality of one-dimensional chaotic maps into one system, and the switching or cascading operation is carried out among different chaotic systems in the whole encryption process. By the method, the one-dimensional chaotic system has better iteration efficiency and unpredictability. Meanwhile, researchers try to encrypt information by constructing a one-dimensional chaotic system in a complex field so as to obtain better chaotic characteristics and encryption effects. Although the information encryption strength of the one-dimensional chaotic system is improved by the improvement means at present, the information encryption strength is still to be improved by being limited by the characteristics of the structure and parameters of the one-dimensional chaotic system.
Disclosure of Invention
The purpose of the invention is as follows: the invention aims to construct a new two-dimensional exponent-Cosine chaotic system aiming at the defects of complicated encryption process, long time consumption and the like of the image encryption algorithm in the prior art and the problem of low image encryption intensity of the one-dimensional chaotic system, the dimensionality of the one-dimensional chaotic system is improved by introducing a nonlinear exponent term and a high-order power term into the one-dimensional Cosine chaotic mapping system, and the introduced nonlinear exponent term and the high-order power term are used as chaotic disturbance sources to disturb the iterative process of Cosine chaotic mapping. By researching the chaotic characteristic of the system, the system is found to have the characteristics of chaotic characteristic and complex phase space orbit distribution structure, and on the basis of the system, an image encryption system based on a two-dimensional index-cosine chaotic system is provided.
The technical scheme is as follows: an image encryption system based on a two-dimensional index-cosine chaotic system comprises a 2D-Ecs chaotic system and an image information chaotic encryption operation carried out by utilizing the 2D-Ecs chaotic system;
the iterative formula of the 2D-ECs chaotic system is shown as the following formula (1):
Figure BDA0003003736910000021
wherein, the control parameters a, b and c satisfy a ∈ [0.2,0.4 ]],b∈[0,1.75],c∈[0.65,0.85]Initial value x0,y0Satisfy x0∈[0,1]，y0∈[0,2]；
The method for carrying out chaotic encryption operation on image information by using the 2D-Ecs chaotic system comprises the following steps:
1) firstly, RGB multi-channel extraction is carried out on original image data;
2) carrying out chaotic encryption on the extracted single-channel image data by using a 2D-ECs chaotic system;
3) and then rewriting the encrypted single-channel image data back to the image so as to complete the encryption of the image data.
Furthermore, when the extracted single-channel image data is subjected to chaotic encryption, a scrambling-diffusing-scrambling encryption method is adopted, and the chaotic encryption comprises a first round of scrambling encryption, a diffusing encryption and a second round of scrambling encryption.
Further, the first round of scrambling encryption comprises the following steps:
step 1): when the extracted single-channel image data is subjected to scrambling operation, firstly, a 2D-ECs chaotic system is utilized to generate a discrete data sequence (x)n,yn) Setting an initial value (x)0,y0) (0.74,1.38), control parameters (a, b, c) are (0.4,1.75, 0.85); the iteration round is M x N +10000, wherein M and N are the width and height values of the original image data, and the data of the first 8000 points in the sequence is not used after iteration;
after the above operation is completed, the generated discrete data sequence (x) is generatedn,yn) Performing de-duplication treatment to remove the duplicate xnSequence as line coordinates for image scrambling, ynThe sequence is used as the column coordinate of image scrambling to perform spatial scrambling operation on single-channel image data, and the specific spatial scrambling operation is shown as formula (2):
p(xi,yj)＝p'(xni,ymj) (2)
step 2) after the above operation is completed, expanding the spatially scrambled image data p obtained in step 1) into one-dimensional sequence data in the column direction; the reuse is initialized by the following value (x)0,y0) Encrypting the spatially scrambled image data p by a discrete encryption sequence for the first round of encryption generated by a 2D-ECs chaotic system configured with (0.15,1.7) and (0.4,1.75,0.85) control parameters (a, b, c); discrete encryption sequence (x) generated by 2D-ECs chaotic systemn,yn) The length of the image data is M x N +10000, wherein M and N are width and height values of original image data, and the data of the first 8000 points in the sequence is not used after iteration;
step 3): firstly, carrying out coordinate scrambling on single-channel image data to obtain image data Q; then the discrete encryption sequence (x) obtained in the step 2) is processedn,yn) And carrying out double-helix encryption with the image data Q, wherein the specific double-helix encryption steps are shown as a formula (3):
Figure BDA0003003736910000031
wherein xn -1,yn -1By discrete encryption sequences (x)n,yn) The data are obtained by reverse order arrangement, and Q' is encrypted image ciphertext data;
through the steps, the first round of scrambling encryption operation can be completed, and the image ciphertext data Q' after the first round of scrambling encryption is obtained.
Further, the diffusion encryption, that is, performing the diffusion encryption on the image ciphertext data Q' after the first round of scrambling encryption, includes the following steps:
step 1): firstly, calculating an average pixel value M of single-channel image data, and then carrying out normalization operation on the average value to enable the average value to be in a value range of 0-1; then taking the normalized pixel mean value M' as x of the 2D-ECs chaotic system0Initial value, and setting Ky0The initial value is 1.5, and the control parameters (a, b, c) are (0.4,1.75, 0.85); after M × N +10000 iterations, M × N +10000, wherein M and N are the width and height values of the original image data, the first 8000 data points are discarded to obtain a diffusion sequence (Kx)n,Kyn)；
Step 2): expanding image ciphertext data Q' subjected to the first round of scrambling encryption into one-dimensional sequence data along the column direction; and then with the diffusion sequence (Kx) obtained in step 1)n,Kyn) Carrying out double-helix diffusion encryption operation; the specific double-helix diffusion encryption formula is shown as formula (4):
Figure BDA0003003736910000041
wherein xn -1,yn -1From diffusion sequences (Kx)n,Kyn) The image ciphertext data is obtained by reverse order arrangement, and G is the image ciphertext data after diffusion encryption;
through the steps, the diffusion operation of the scrambled and encrypted data in the first round is completed, and the image ciphertext data G after diffusion encryption is obtained.
Further, the second round of scrambling encryption, that is, scrambling operation is performed on the diffusion-encrypted image ciphertext data G, and the method includes the following steps:
when scrambling operation is carried out on the image ciphertext data G after diffusion encryption, firstly, a 2D-ECs chaotic system is utilized to generate a discrete data sequence (x)n,yn) Setting an initial value (x)0,y0) (0.74,1.38), control parameters (a, b, c) are equal(0.4,1.75, 0.85); the iteration turn is M × N +10000, wherein M and N are the width and height values of single-channel image data, and the data of the front 9000 points in the sequence is abandoned after iteration to generate a discrete data sequence (x)n,yn)；
After the above operation is completed, the generated discrete data sequence (x) is generatedn,yn) Performing de-duplication treatment to remove the duplicate xnSequence as line coordinates for image scrambling, ynThe sequence is used as a column coordinate for image scrambling to perform spatial scrambling operation on single-channel image data, and a specific scrambling operation formula is the formula (2);
through the steps, the second round of scrambling encryption operation can be completed.
Has the advantages that: the invention utilizes the 2D-Ecs chaotic system to carry out chaotic encryption operation on the image information, has the characteristics of large key space, good encryption effect, strong anti-jamming capability and the like, can effectively resist exhaustive attack and differential attack, can effectively eliminate the pixel correlation in a plaintext image, is extremely sensitive to tiny change among pixels in the plaintext, and can completely change the encrypted data due to tiny change.
Drawings
FIG. 1 is a schematic diagram of an algorithm flow of the encryption system of the present invention;
FIG. 2 is a phase trajectory diagram of a 2D-ECs chaotic system constructed by the invention;
FIG. 3 is a Lyapunov exponential curve of a 2D-ECs chaotic system constructed by the invention;
FIG. 4 is a schematic diagram of an encrypted image and histogram information of the 2D-ECs chaotic system of the present invention.
Detailed Description
The technical solution of the present invention is described in detail below with reference to the accompanying drawings, but the scope of the present invention is not limited to the embodiments.
An image encryption system based on a two-dimensional index-cosine chaotic system comprises a 2D-Ecs chaotic system and an image information chaotic encryption operation carried out by utilizing the 2D-Ecs chaotic system;
the iterative formula of the 2D-ECs chaotic system is shown in the following formula 1:
Figure BDA0003003736910000051
wherein, the control parameters a, b and c satisfy a ∈ [0.2,0.4 ]],b∈[0,1.75],c∈[0.65,0.85]Initial value x0,y0Satisfy x0∈[0,1]，y0∈[0,2]；
As shown in fig. 1, the method for performing chaotic encryption operation on image information by using a 2D-Ecs chaotic system is as follows:
1) firstly, RGB multi-channel extraction is carried out on original image data;
2) carrying out chaotic encryption on the extracted single-channel image data by using a 2D-ECs chaotic system;
3) and then rewriting the encrypted single-channel image data back to the image so as to complete the encryption of the image data.
Furthermore, when the extracted single-channel image data is subjected to chaotic encryption, a scrambling-diffusing-scrambling encryption method is adopted, and the chaotic encryption comprises a first round of scrambling encryption, a diffusing encryption and a second round of scrambling encryption.
Further, the first round of scrambling encryption comprises the following steps:
step 1): when the extracted single-channel image data is subjected to scrambling operation, firstly, a 2D-ECs chaotic system is utilized to generate a discrete data sequence (x)n,yn) Setting an initial value (x)0,y0) (0.74,1.38), control parameters (a, b, c) are (0.4,1.75, 0.85); the iteration round is M x N +10000, wherein M and N are the width and height values of the original image data, and the data of the first 8000 points in the sequence is not used after iteration;
after the above operation is completed, the generated discrete data sequence (x) is generatedn,yn) Performing de-duplication treatment to remove the duplicate xnSequence as line coordinates for image scrambling, ynThe sequence is used as the column coordinate of image scrambling to perform spatial scrambling operation on single-channel image data, and the specific spatial scrambling operation is as a formula2, as shown in the figure:
p(xi,yj)＝p'(xni,ymj) (2)
step 2) after the above operation is completed, expanding the spatially scrambled image data p obtained in step 1) into one-dimensional sequence data in the column direction; the reuse is initialized by the following value (x)0,y0) Encrypting the spatially scrambled image data p by a discrete encryption sequence for the first round of encryption generated by a 2D-ECs chaotic system configured with (0.15,1.7) and (0.4,1.75,0.85) control parameters (a, b, c); discrete encryption sequence (x) generated by 2D-ECs chaotic systemn,yn) The length of the image data is M x N +10000, wherein M and N are width and height values of original image data, and the data of the first 8000 points in the sequence is not used after iteration;
step 3): firstly, carrying out coordinate scrambling on single-channel image data to obtain image data Q; then the discrete encryption sequence (x) obtained in the step 2) is processedn,yn) And carrying out double-helix encryption with the image data Q, wherein the specific double-helix encryption steps are shown as a formula (3):
Figure BDA0003003736910000061
wherein xn -1,yn -1By discrete encryption sequences (x)n,yn) The data are obtained by reverse order arrangement, and Q' is encrypted image ciphertext data;
through the steps, the first round of scrambling encryption operation can be completed, and the image ciphertext data Q' after the first round of scrambling encryption is obtained.
Further, the diffusion encryption, that is, performing the diffusion encryption on the image ciphertext data Q' after the first round of scrambling encryption, includes the following steps:
step 1): firstly, calculating an average pixel value M of single-channel image data, and then carrying out normalization operation on the average value to enable the average value to be in a value range of 0-1; then taking the normalized pixel mean value M' as x of the 2D-ECs chaotic system0Initial value, and setting Ky0Initial value is 1.5, and control parameter is in this caseThe number (a, b, c) is (0.4,1.75, 0.85); after M × N +10000 iterations, where M and N are the width and height values of the original image data, the first 8000 data points are discarded to obtain a diffusion sequence (Kx)n,Kyn)；
Step 2): expanding image ciphertext data Q' subjected to the first round of scrambling encryption into one-dimensional sequence data along the column direction; and then with the diffusion sequence (Kx) obtained in step 1)n,Kyn) Carrying out double-helix diffusion encryption operation; the specific double-helix diffusion encryption formula is shown in formula 4:
Figure BDA0003003736910000062
wherein xn -1,yn -1From diffusion sequences (Kx)n,Kyn) The image ciphertext data is obtained by reverse order arrangement, and G is the image ciphertext data after diffusion encryption;
through the steps, the diffusion operation of the scrambled and encrypted data in the first round is completed, and the image ciphertext data G after diffusion encryption is obtained.
Further, the second round of scrambling encryption, that is, scrambling operation is performed on the diffusion-encrypted image ciphertext data G, and the method includes the following steps:
when scrambling operation is carried out on the image ciphertext data G after diffusion encryption, firstly, a 2D-ECs chaotic system is utilized to generate a discrete data sequence (x)n,yn) Setting an initial value (x)0,y0) (0.74,1.38), control parameters (a, b, c) are (0.4,1.75, 0.85); the iteration turn is M × N +10000, wherein M and N are the width and height values of single-channel image data, and the data of the front 9000 points in the sequence is abandoned after iteration to generate a discrete data sequence (x)n,yn)；
After the above operation is completed, the generated discrete data sequence (x) is generatedn,yn) Performing de-duplication treatment to remove the duplicate xnSequence as line coordinates for image scrambling, ynThe sequence is used as a column coordinate for image scrambling to perform spatial scrambling operation on single-channel image data, wherein a specific scrambling operation formula is the formula 2;
through the steps, the second round of scrambling encryption operation can be completed.
Fig. 2 is a phase trajectory diagram of the 2D-ECs chaotic system constructed by the invention, and it can be seen from the diagram that the novel 2D-ECs chaotic system provided by the invention has a larger numerical search space.
FIG. 3 is a Lyapunov exponential curve of a 2D-ECs chaotic system constructed by the invention; as shown in fig. 3, the line a and the line B in the figure refer to Lyapnov exponential curves of the first dimension (x) and the second dimension (y) of the system along with the control variable a, and it can be found that the Lyapnov exponent of the one-dimensional curve (a) is greater than 0 in the range of the control variable a ∈ [0.26,0.4], which indicates that the system is in a chaotic state.
FIG. 4 is a schematic diagram of an encrypted image and histogram information of the 2D-ECs chaotic system of the present invention. As shown in fig. 4, it can be seen visually that after the original picture is encrypted by the encryption system of the present invention, the gray level histograms of the encrypted picture are uniformly distributed, and the effective information of all the images is annihilated in chaotic noise, thereby demonstrating that the encryption system of the present invention has a better encryption characteristic.
The invention utilizes the 2D-Ecs chaotic system to carry out chaotic encryption operation on the image information, has the characteristics of large key space, good encryption effect, strong anti-jamming capability and the like, can effectively resist exhaustive attack and differential attack, can effectively eliminate the pixel correlation in a plaintext image, is extremely sensitive to tiny change among pixels in the plaintext, and can completely change the encrypted data due to tiny change.
As noted above, while the present invention has been shown and described with reference to certain preferred embodiments, it is not to be construed as limited thereto. Various changes in form and detail may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.

Claims (5)

1. An image encryption system based on a two-dimensional index-cosine chaotic system is characterized by comprising a 2D-Ecs chaotic system and a chaotic encryption operation for image information by utilizing the 2D-Ecs chaotic system;
the iterative formula of the 2D-ECs chaotic system is shown as the following formula (1):
Figure FDA0003003736900000011
wherein, the control parameters a, b and c satisfy a ∈ [0.2,0.4 ]],b∈[0,1.75],c∈[0.65,0.85]Initial value x0,y0Satisfy x0∈[0,1]，y0∈[0,2]；
The method for carrying out chaotic encryption operation on image information by using the 2D-Ecs chaotic system comprises the following steps:
1) firstly, RGB multi-channel extraction is carried out on original image data;
2) carrying out chaotic encryption on the extracted single-channel image data by using a 2D-ECs chaotic system;
3) and then rewriting the encrypted single-channel image data back to the image so as to complete the encryption of the image data.
2. The image encryption system based on the two-dimensional exponential-cosine chaotic system as claimed in claim 1, wherein a scrambling-diffusion-scrambling encryption method is adopted when performing chaotic encryption on the extracted single-channel image data, and the chaotic encryption comprises a first round of scrambling encryption, a diffusion encryption and a second round of scrambling encryption.
3. The image encryption system based on the two-dimensional exponential-cosine chaotic system as claimed in claim 1, wherein the first round of scrambling encryption comprises the following steps:
step 1): when the extracted single-channel image data is subjected to scrambling operation, firstly, a 2D-ECs chaotic system is utilized to generate a discrete data sequence (x)n,yn) Setting an initial value (x)0,y0) (0.74,1.38), control parameters (a, b, c) are (0.4,1.75, 0.85); the iteration turn is M × N +10000, wherein M and N are the width and height values of the original image data, and the sequence is processed after iterationThe data of the medium and former 8000 points are not used for abandonment;
after the above operation is completed, the generated discrete data sequence (x) is generatedn,yn) Performing de-duplication treatment to remove the duplicate xnSequence as line coordinates for image scrambling, ynThe sequence is used as the column coordinate of image scrambling to perform spatial scrambling operation on single-channel data, and the specific spatial scrambling operation is shown as formula (2):
p(xi,yj)＝p'(xni,ymj) (2)
step 2) after the above operation is completed, expanding the spatially scrambled image data p obtained in step 1) into one-dimensional sequence data in the column direction; the reuse is initialized by the following value (x)0,y0) Encrypting the spatially scrambled image data p by a discrete encryption sequence for the first round of encryption generated by a 2D-ECs chaotic system configured with (0.15,1.7) and (0.4,1.75,0.85) control parameters (a, b, c); discrete encryption sequence (x) generated by 2D-ECs chaotic systemn,yn) The length of the image data is M x N +10000, wherein M and N are width and height values of original image data, and the data of the first 8000 points in the sequence is not used after iteration;
step 3): firstly, carrying out coordinate scrambling on single-channel image data to obtain image data Q; then the discrete encryption sequence (x) obtained in the step 2) is processedn,yn) And carrying out double-helix encryption with the image data Q, wherein the specific double-helix encryption steps are shown as a formula (3):
Figure FDA0003003736900000021
wherein xn -1,yn -1By discrete encryption sequences (x)n,yn) The data are obtained by reverse order arrangement, and Q' is encrypted image ciphertext data;
through the steps, the first round of scrambling encryption operation can be completed, and the image ciphertext data Q' after the first round of scrambling encryption is obtained.
4. The image encryption system based on the two-dimensional exponential-cosine chaotic system as claimed in claim 3, wherein the diffusion encryption, that is, the diffusion encryption of the image ciphertext data Q' after the first round of scrambling encryption, comprises the following steps:
step 1): firstly, calculating an average pixel value M of single-channel image data, and then carrying out normalization operation on the average value to enable the average value to be in a value range of 0-1; then taking the normalized pixel mean value M' as x of the 2D-ECs chaotic system0Initial value, and setting Ky0The initial value is 1.5, and the control parameters (a, b, c) are (0.4,1.75, 0.85); after M × N +10000 iterations, M × N +10000, wherein M and N are the width and height values of the original image data, the first 8000 data points are discarded to obtain a diffusion sequence (Kx)n,Kyn)；
Step 2): expanding image ciphertext data Q' subjected to the first round of scrambling encryption into one-dimensional sequence data along the column direction; and then with the diffusion sequence (Kx) obtained in step 1)n,Kyn) Carrying out double-helix diffusion encryption operation; the specific double-helix diffusion encryption formula is shown as formula (4):
Figure FDA0003003736900000022
wherein xn -1,yn -1From diffusion sequences (Kx)n,Kyn) The image ciphertext data is obtained by reverse order arrangement, and G is the image ciphertext data after diffusion encryption;
through the steps, the diffusion operation of the scrambled and encrypted data in the first round is completed, and the image ciphertext data G after diffusion encryption is obtained.
5. The image encryption system based on the two-dimensional exponential-cosine chaotic system as claimed in claim 4, wherein the second round of scrambling encryption, namely scrambling operation is performed on the diffusion encrypted image ciphertext data G, comprising the following steps:
when scrambling operation is carried out on the image ciphertext data G after diffusion encryption, firstly, a 2D-ECs chaotic system is utilized to generate a discrete numberAccording to the sequence (x)n,yn) Setting an initial value (x)0,y0) (0.74,1.38), control parameters (a, b, c) are (0.4,1.75, 0.85); the iteration turn is M × N +10000, wherein M and N are the width and height values of single-channel image data, and the data of the front 9000 points in the sequence is abandoned after iteration to generate a discrete data sequence (x)n,yn)；
After the above operation is completed, the generated discrete data sequence (x) is generatedn,yn) Performing de-duplication treatment to remove the duplicate xnSequence as line coordinates for image scrambling, ynThe sequence is used as a column coordinate for image scrambling to perform spatial scrambling operation on single-channel image data, and a specific scrambling operation formula is the formula (2);
through the steps, the second round of scrambling encryption operation can be completed.
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