Chaotic encryption and decryption method and system based on random weights
By introducing random weights and auxiliary ciphertext into the Lorentz chaotic system, the problem of insufficient key space in existing chaotic encryption and decryption algorithms is solved, achieving higher security and a more difficult-to-crack encryption effect.
Patent Information
- Authority / Receiving Office
- WO · WO
- Patent Type
- Applications
- Current Assignee / Owner
- INSPUR GENERSOFT CO LTD
- Filing Date
- 2025-07-18
- Publication Date
- 2026-07-30
AI Technical Summary
Existing chaotic encryption and decryption algorithms rely heavily on the internal characteristics of nonlinear functions, do not expand the key space, and offer limited improvement in key security, making them easy to crack.
A chaotic encryption and decryption method based on random weights is adopted. The original image is injected into different subsystems of the Lorentz chaotic system. Multiple initial ciphertexts are linearly combined by random weights, and a weight matrix and auxiliary ciphertext are generated in the decryption stage. The original image is solved by inverse system method.
By extending the key length and introducing auxiliary ciphertext, the security of image encryption is improved, making it more difficult for attackers to crack the original text and enhancing the security of the key.
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Figure CN2025109380_30072026_PF_FP_ABST
Abstract
Description
A Chaotic Encryption / Decryption Method and System Based on Random Weights
[0001] Cross-references to related applications
[0002] This application claims priority to Chinese Patent Application No. 202510096323.3, filed on January 22, 2025, entitled "A Chaotic Encryption and Decryption Method and System Based on Random Weights", the entire contents of which are incorporated herein by reference. Technical Field
[0003] This application relates to the field of information security technology, and in particular to a chaotic encryption and decryption method and system based on random weights. Background Technology
[0004] In recent years, an increasing amount of image data has been transmitted and stored on networks. In various industries, the privacy of information has become a crucial issue. Traditional encryption algorithms, such as DES, AES, and RSA, are only suitable for text-structured data and are not suitable for encrypting image data. To address the problem of image encryption, chaotic encryption algorithms have been proposed. The main advantages of chaotic encryption algorithms lie in expanding the key space from the integer space to the real number space and their extreme sensitivity to the initial value of the system. Therefore, chaotic encryption algorithms generally set the initial value of the system as the key.
[0005] Current chaotic encryption algorithms suffer from weaknesses such as weak chaotic mapping, poor resistance to certain types of attacks, insufficient sensitivity to plaintext and keys, and small key spaces. Although various chaotic encryption algorithms are constantly emerging and have some encryption effect, these encryption and decryption algorithms heavily rely on the internal characteristics of nonlinear functions and do not expand the key space, thus offering limited improvement in key security and making them vulnerable to cracking. Summary of the Invention
[0006] This application provides a chaotic encryption and decryption method and system based on random weights to solve the following technical problem: existing chaotic encryption and decryption algorithms rely heavily on the internal characteristics of nonlinear functions, do not expand the key space, have limited improvement on key security, and are easily cracked.
[0007] The embodiments of this application adopt the following technical solutions:
[0008] On the one hand, embodiments of this application provide a chaotic encryption and decryption method based on random weights, specifically including: in the encryption stage, injecting the original image into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts;
[0009] By using random weights, multiple initial ciphertexts are linearly combined to obtain the ciphertext data of the original image;
[0010] During the decryption phase, a weight matrix and auxiliary ciphertext are generated based on the number of subsystems.
[0011] Based on the weight matrix and auxiliary ciphertext, the encrypted image is decrypted to obtain the original image.
[0012] In one implementation, during the encryption phase, the original image is injected into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts, specifically including:
[0013] Obtain the state-space expression of the Lorentz chaotic system, and divide it into three different subsystems based on the multiple system states in the state-space expression;
[0014] During the encryption phase, the initial system state values of the three subsystems are used as the initial encryption keys to encrypt the original image, resulting in three corresponding initial ciphertexts.
[0015] In one implementation, multiple initial ciphertexts are linearly combined using random weights to obtain the ciphertext data of the original image, specifically including:
[0016] Random weights are generated for each initial ciphertext, and multiple initial ciphertexts are linearly combined according to c(t)=w1y1(t)+w2y2(t)+w3y3(t) to obtain the ciphertext data expression c(t);
[0017] Where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, and w1, w2, and w3 are the random weights corresponding to the three initial ciphertexts.
[0018] In one implementation, during the decryption phase, a weight matrix and auxiliary ciphertext are generated based on the number of subsystems, specifically including:
[0019] During the decryption phase, a decryption request is sent to the encryption module, and two sets of auxiliary weights are generated in the encryption module; each set of auxiliary weights contains three auxiliary weights.
[0020] The two sets of auxiliary weights and the random weights to be solved are used to construct a weight matrix;
[0021] In the encryption module, the original image is encrypted using two sets of auxiliary weights to obtain two sets of auxiliary ciphertext.
[0022] In one implementation, the original image is encrypted using two sets of auxiliary weights to obtain two sets of auxiliary ciphertext, specifically including:
[0023] In the encryption module, the weight matrix is defined as: in, and Two sets of auxiliary weights;
[0024] By using two sets of auxiliary weights, the three initial ciphertexts of the original image are linearly combined to obtain the corresponding two sets of auxiliary ciphertexts: Where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, respectively.
[0025] In one implementation, the encrypted image is decrypted based on a weight matrix and auxiliary ciphertext to obtain the original image, specifically including:
[0026] Based on the ciphertext data of the original image and the auxiliary ciphertext, a ciphertext vector is defined;
[0027] Define an initial ciphertext vector based on the initial ciphertext output by each subsystem;
[0028] Based on the ciphertext vector, weight matrix, and initial ciphertext vector, construct a system of linear equations for the ciphertext, find the unique solution to the system of linear equations for the ciphertext, and obtain the inverse matrix of the weight matrix.
[0029] The encrypted image is parsed using the inverse matrix to obtain the original image.
[0030] In one implementation, a ciphertext vector is defined based on the ciphertext data of the original image and auxiliary ciphertext; an initial ciphertext vector is defined based on the initial ciphertext output by each subsystem, specifically including:
[0031] Define the ciphertext vector as C(t) = [c(t) c 1 (t) c 2 (t)] T Where c(t) is the ciphertext data of the original image, c1(t) is the first set of auxiliary ciphertext, and c2(t) is the second set of auxiliary ciphertext;
[0032] Define the initial ciphertext vector as Y(t) = [y1(t) y2(t) y3(t)] T ; where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, respectively.
[0033] In one implementation, based on the ciphertext vector, the weight matrix, and the initial ciphertext vector, a system of linear equations is constructed, and the unique solution to the system of linear equations is obtained to yield the inverse of the weight matrix. Specifically, this includes:
[0034] When t≥0, we obtain the ciphertext linear equation system C(t)=WY(t); where C(t) is the ciphertext vector, Y(t) is the initial ciphertext vector, and W is the weight matrix;
[0035] Let the rank(W) of the weight matrix W be 3. At this point, the weight matrix is non-singular, and the encrypted linear equation system has a unique solution. Solving this system yields the inverse of the weight matrix.
[0036] In one implementation, the encrypted image is parsed using an inverse matrix to obtain the original image, specifically including:
[0037] Based on the element values in the inverse matrix, the initial ciphertext is parsed to obtain three initial ciphertexts: y1(t)=a 11 c(t)+a 12 c 1 (t)+a 13 c 2 (t); y2(t)=a 21 c(t)+a 22 c 1 (t)+a 23 c 2 (t); y3(t)=a 31 c(t)+a 32 c 1 (t)+a 33 c 2 (t);
[0038] Choose any of the above initial ciphertexts, differentiate it, and substitute the initial key of the subsystem corresponding to the selected initial ciphertext into the differentiation formula to calculate the original data and obtain the original image.
[0039] On the other hand, embodiments of this application also provide a chaotic encryption / decryption system based on random weights, the system comprising:
[0040] The encryption module is used to inject the original image into different subsystems of the Lorentz chaotic system during the encryption phase to obtain multiple initial ciphertexts; and to linearly combine the multiple initial ciphertexts with random weights to obtain the ciphertext data of the original image.
[0041] The decryption module is used to generate a weight matrix and auxiliary ciphertext based on the number of subsystems during the decryption phase; and to decrypt the encrypted image based on the weight matrix and auxiliary ciphertext to obtain the original image.
[0042] Compared with the prior art, the chaotic encryption and decryption method and system based on random weights provided in this application have the following beneficial effects:
[0043] The proposed chaotic encryption / decryption algorithm based on random weights introduces a corresponding chaotic encryption subsystem by injecting the original text into different state channels of a Lorentz chaotic system. Weight values are then appended to these subsystems as part of the key. This design method adds weights to the initial key of the original scheme, increasing the key length and ensuring security.
[0044] During the decryption process, an application needs to be made to the encryption unit. The encryption module randomly sends two sets of ciphertext integrated by auxiliary random weights, allowing the decryption unit to solve for the key and thus use the system inverse to solve for the original text. This application utilizes the idea of auxiliary ciphertext to solve for the original text. Specifically, since the coefficient matrix of a linear equation system is not full-rank, the system solution will be infinite. Even if an attacker obtains the ciphertext, they cannot solve for the true weights and cannot crack the original text. To achieve successful decryption, this application introduces the idea of auxiliary ciphertext. By randomly generating auxiliary ciphertext and combining it with the unknown weights to be solved for, a full-rank coefficient matrix is formed. This allows the plaintext to be solved using the concept of system inverse, thus improving the security of image encryption. Attached Figure Description
[0045] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings:
[0046] Figure 1 is a flowchart of a chaotic encryption / decryption method based on random weights provided in an embodiment of this application;
[0047] Figure 2 is a schematic diagram of an encryption module encryption process provided in an embodiment of this application;
[0048] Figure 3 is a schematic diagram of a ciphertext parsing process based on system inversion provided in an embodiment of this application;
[0049] Figure 4 is a schematic diagram of a chaotic encryption and decryption system based on random weights provided in an embodiment of this application. Detailed Implementation
[0050] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this specification, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.
[0051] This application provides a chaotic encryption / decryption method based on random weights, as shown in Figure 1. The chaotic encryption / decryption method based on random weights specifically includes steps S101-S104:
[0052] S101. In the encryption stage, the original image is injected into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts.
[0053] Specifically, the state-space expression of the Lorentz chaotic system is obtained, and based on the multiple system states in the state-space expression, it is divided into three different subsystems.
[0054] Furthermore, during the encryption phase, the encryption module uses the initial system state values of the three subsystems as the initial encryption keys to encrypt the original image, resulting in three corresponding initial ciphertexts.
[0055] As one implementation method, the Lorentz nonlinear system is a typical chaotic system, and its specific state-space expression is as follows: y(t) = x1(t);
[0056] Here, x1(t), x2(t), and x3(t) are three different state channels of the system, and y(t) is the output of the system.
[0057] By injecting plaintext p(t) into different positions in the Lorentz chaotic system, three distinct subsystems Σ1, Σ2, and Σ3 were constructed: Σ1:y1(t)=x 1,1 (t); Σ2:y2(t)=x 2,1 (t); Σ3:y3(t)=x 3,1 (t).
[0058] The three subsystems Σ1, Σ2, and Σ3 initialize the state with the value x. 1,1 (0), x 1,2 (0), x 1,3 (0), x 2,1 (0), x 2,2 (0), x 2,3 (0), x 3,1 (0), x 3,2 (0), x 3,3 (0) are used as encryption keys to encrypt the original image, and the initial ciphertexts obtained are y1(t), y2(t) and y3(t).
[0059] S102. By using random weights, multiple initial ciphertexts are linearly combined to obtain the ciphertext data of the original image.
[0060] Specifically, the encryption module generates random weights for each initial ciphertext and performs a linear combination of multiple initial ciphertexts according to c(t) = w1y1(t) + w2y2(t) + w3y3(t) to obtain the ciphertext data expression c(t). Here, y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, and w1, w2, and w3 are the random weights corresponding to the three initial ciphertexts.
[0061] As one implementation method, Figure 2 is a schematic diagram of the encryption process of an encryption module provided in an embodiment of this application. As shown in Figure 2, the encryption module combines the randomly generated weight coefficients w1, w2, and w3 with the initial state value of each subsystem as the encryption key of the system. After introducing random weights, the ciphertext data is c(t) = w1y1(t) + w2y2(t) + w3y3(t), which increases the length of the key and expands the key space.
[0062] S103. During the decryption phase, a weight matrix and auxiliary ciphertext are generated based on the number of subsystems.
[0063] Specifically, during the decryption phase, the decryption module sends a decryption request to the encryption module and generates two sets of auxiliary weights in the encryption module; each set of auxiliary weights contains three auxiliary weights.
[0064] Furthermore, the encryption module constructs a weight matrix from the two sets of auxiliary weights and the random weights to be solved. It then uses the two sets of auxiliary weights to perform auxiliary encryption on the original image, obtaining two corresponding sets of auxiliary ciphertext. Finally, both the weight matrix and the auxiliary ciphertext are sent to the decryption module.
[0065] As one implementation method, the original image is encrypted using two sets of auxiliary weights to obtain two sets of auxiliary ciphertext, specifically including:
[0066] In the encryption module, the weight matrix is defined as: in, and There are two sets of auxiliary weights.
[0067] Then, using two sets of auxiliary weights, the three initial ciphertexts of the original image are linearly combined to obtain the corresponding two sets of auxiliary ciphertexts: Where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, respectively.
[0068] S104. Based on the weight matrix and auxiliary ciphertext, the encrypted image is decrypted to obtain the original image.
[0069] Specifically, the decryption module defines a ciphertext vector based on the ciphertext data of the original image and auxiliary ciphertext. An initial ciphertext vector is defined based on the initial ciphertext output by each subsystem.
[0070] Furthermore, the decryption module constructs a system of linear equations based on the ciphertext vector, the weight matrix, and the initial ciphertext vector. It then finds the unique solution to this system of linear equations, obtaining the inverse of the weight matrix. This inverse matrix is then used to parse the encrypted image, yielding the original image.
[0071] As one implementation method, the decryption module defines the ciphertext vector as C(t)=[c(t) c 1 (t) c 2 (t)] T Where c(t) is the ciphertext data of the original image, c1(t) is the first set of auxiliary ciphertext, and c2(t) is the second set of auxiliary ciphertext.
[0072] Define the initial ciphertext vector as Y(t) = [y1(t) y2(t) y3(t)] T ; where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, respectively.
[0073] When t≥0, we obtain the ciphertext linear equation system C(t)=WY(t); where C(t) is the ciphertext vector, Y(t) is the initial ciphertext vector, and W is the weight matrix.
[0074] Furthermore, when the rank(W) of the weight matrix W is 3, the weight matrix is a non-singular matrix, and the encrypted linear equation system has a unique solution. Therefore, by setting rank(W) to 3, we can obtain the inverse of the weight matrix.
[0075] Furthermore, Figure 3 is a schematic diagram of a ciphertext parsing process based on system inverse provided in an embodiment of this application. As shown in Figure 3, the encrypted image is parsed using the inverse matrix to obtain the original image, specifically including:
[0076] Based on the element values in the inverse matrix, the initial ciphertext is parsed to obtain three initial ciphertexts: y1(t)=a 11 c(t)+a 12 c 1 (t)+a 13 c 2 (t); y2(t)=a 21 c(t)+a 22 c 1 (t)+a 23 c 2 (t); y3(t)=a 31 c(t)+a 32 c1 (t)+a 33 c 2 (t).
[0077] Then, choose any of the above initial ciphertexts, perform differentiation, and substitute the initial key of the subsystem corresponding to the selected initial ciphertext into the differentiation formula to calculate the original data and obtain the original image.
[0078] Suppose we choose to differentiate with respect to y1(t), we get Then, the known initial values of the subsystem Σ1 are x. 1,1 (0), x 1,1 Substituting (t) into the above equation, we obtain the decrypted original image data:
[0079] In addition, this application also provides a chaotic encryption and decryption system based on random weights, as shown in Figure 4. The chaotic encryption and decryption system 400 based on random weights specifically includes:
[0080] The encryption module 420 is used to inject the original image into different subsystems of the Lorentz chaotic system during the encryption stage to obtain multiple initial ciphertexts; and to linearly combine the multiple initial ciphertexts with random weights to obtain the ciphertext data of the original image.
[0081] The decryption module 430 is used to generate a weight matrix and auxiliary ciphertext based on the number of subsystems during the decryption stage; and to decrypt the encrypted image based on the weight matrix and auxiliary ciphertext to obtain the original image.
[0082] As one implementation, the system also includes a chaotic system model library 410, which contains three subsystems of the Lorentz chaotic system.
[0083] The various embodiments in this application are described in a progressive manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the embodiments of apparatus, systems, and non-volatile computer storage media are basically similar to the method embodiments, so the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.
[0084] The foregoing has described specific embodiments of this application. Furthermore, the processes depicted in the accompanying drawings do not necessarily require a specific or sequential order to achieve the desired results. In some embodiments, multitasking and parallel processing are possible or may be advantageous.
[0085] The above are merely embodiments of this application and are not intended to limit this application. For those skilled in the art, the embodiments of this application can have various modifications and variations. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the embodiments of this application should be included within the protection scope of this application.
Claims
1. A chaotic encryption / decryption method based on random weights, characterized in that, The method includes: During the encryption phase, the original image is injected into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts; By using random weights, the multiple initial ciphertexts are linearly combined to obtain the ciphertext data of the original image; During the decryption phase, a weight matrix and auxiliary ciphertext are generated based on the number of the subsystems. Based on the weight matrix and auxiliary ciphertext, the encrypted image is decrypted to obtain the original image.
2. The chaotic encryption / decryption method based on random weights according to claim 1, characterized in that, During the encryption phase, the original image is injected into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts, specifically including: Obtain the state-space expression of the Lorentz chaotic system, and divide it into three different subsystems based on the multiple system states in the state-space expression; During the encryption phase, the initial system state values of the three subsystems are used as the initial encryption keys to encrypt the original image, resulting in three corresponding initial ciphertexts.
3. The chaotic encryption / decryption method based on random weights according to claim 1, characterized in that, The ciphertext data of the original image is obtained by linearly combining the multiple initial ciphertexts using random weights, specifically including: Random weights are generated for each initial ciphertext, and the multiple initial ciphertexts are linearly combined according to c(t)=w1y1(t)+w2y2(t)+w3y3(t) to obtain the ciphertext data expression c(t); Where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, and w1, w2, and w3 are the random weights corresponding to the three initial ciphertexts.
4. The chaotic encryption / decryption method based on random weights according to claim 1, characterized in that, During the decryption phase, a weight matrix and auxiliary ciphertext are generated based on the number of subsystems, specifically including: During the decryption phase, a decryption request is sent to the encryption module, and two sets of auxiliary weights are generated in the encryption module; each set of auxiliary weights contains three auxiliary weights. The two sets of auxiliary weights and the random weights to be solved are used to construct the weight matrix; In the encryption module, the original image is encrypted using the two sets of auxiliary weights to obtain two sets of auxiliary ciphertext.
5. The chaotic encryption / decryption method based on random weights according to claim 4, characterized in that, The original image is then encrypted using the two sets of auxiliary weights to obtain two sets of auxiliary ciphertext, specifically including: In the encryption module, the weight matrix is defined as: in, and These are the two sets of auxiliary weights; By using the two sets of auxiliary weights, the three initial ciphertexts of the original image are linearly combined to obtain the corresponding two sets of auxiliary ciphertexts: Where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, respectively.
6. The chaotic encryption / decryption method based on random weights according to claim 1, characterized in that, Based on the weight matrix and auxiliary ciphertext, the encrypted image is decrypted to obtain the original image, specifically including: Based on the ciphertext data of the original image and the auxiliary ciphertext, a ciphertext vector is defined; Define an initial ciphertext vector based on the initial ciphertext output by each subsystem; Based on the ciphertext vector, the weight matrix, and the initial ciphertext vector, a system of ciphertext linear equations is constructed, and the unique solution of the system of ciphertext linear equations is solved to obtain the inverse matrix of the weight matrix. The original image is obtained by parsing the encrypted image using the inverse matrix.
7. The chaotic encryption / decryption method based on random weights according to claim 6, characterized in that, Based on the ciphertext data of the original image and the auxiliary ciphertext, a ciphertext vector is defined; based on the initial ciphertext output by each subsystem, an initial ciphertext vector is defined, specifically including: Define the ciphertext vector as C(t) = [c(t) c 1 (t) c 2 (t)] T Wherein, c(t) is the ciphertext data of the original image, c1(t) is the first set of auxiliary ciphertext, and c2(t) is the second set of auxiliary ciphertext; Define the initial ciphertext vector as Y(t) = [y1(t) y2(t) y3(t)] T ; where y1(t), y2(t), and y3(t) are the initial ciphertexts output by the three subsystems, respectively.
8. The chaotic encryption / decryption method based on random weights according to claim 7, characterized in that, Based on the ciphertext vector, the weight matrix, and the initial ciphertext vector, a system of ciphertext linear equations is constructed. The unique solution to this system of equations is then obtained, yielding the inverse of the weight matrix. Specifically, this includes: In response to t≥0, the ciphertext linear equation system C(t)=WY(t) is obtained; where C(t) is the ciphertext vector, Y(t) is the initial ciphertext vector, and W is the weight matrix; Let the rank(W) of the weight matrix W be 3. At this point, the weight matrix is a non-singular matrix, and the encrypted linear equations have a unique solution. Solving this system yields the inverse of the weight matrix.
9. A chaotic encryption / decryption method based on random weights according to claim 8, characterized in that, The original image is obtained by parsing the encrypted image using the inverse matrix, specifically including: Based on the element values in the inverse matrix, the initial ciphertext is parsed to obtain three initial ciphertexts: y1(t)=a 11 c(t)+a 12 c 1 (t)+a 13 c 2 (t); y2(t)=a 21 c(t)+a 22 c 1 (t)+a 23 c 2 (t); y3(t)=a 31 c(t)+a 32 c 1 (t)+a 33 c 2 (t); Choose any of the above initial ciphertexts, differentiate it, and substitute the initial key of the subsystem corresponding to the selected initial ciphertext into the differentiation formula to calculate the original data and obtain the original image.
10. A chaotic encryption / decryption method based on random weights according to claim 2, characterized in that, The state-space expression of the Lorentz chaotic system is as follows: y(t)=x1(t) Here, x1(t), x2(t), and x3(t) are three different state channels of the system, and y(t) is the output of the system.
11. The chaotic encryption / decryption method based on random weights according to claim 10, characterized in that, The system is divided into three different subsystems based on multiple system states in the state-space expression, including: By injecting plaintext into different locations within the Lorentz chaotic system, three distinct subsystems are constructed.
12. The chaotic encryption / decryption method based on random weights according to claim 11, characterized in that, The three distinct subsystems Σ1, Σ2, and Σ3 are detailed below: Σ3:y3(t)=x 3,1 (t).
13. The chaotic encryption / decryption method based on random weights according to claim 11, characterized in that, In the encryption phase, the initial system states of the three subsystems are used as the initial encryption keys to encrypt the original image, resulting in three corresponding initial ciphertexts, including: The three subsystems Σ1, Σ2, and Σ3 initialize the state with the value x. 1,1 (0), x 1,2 (0), x 1,3 (0), x 2,1 (0), x 2,2 (0), x 2,3 (0), x 3,1 (0), x 3,2 (0), x 3,3 (0) are used as encryption keys to encrypt the original image, and the initial ciphertexts obtained are y1(t), y2(t) and y3(t).
14. The chaotic encryption / decryption method based on random weights according to claim 1, characterized in that, The Lorentz chaotic system is a nonlinear system.
15. The chaotic encryption / decryption method based on random weights according to claim 1, characterized in that, The length of the key after introducing random weights is greater than the length of the key before introducing random weights.
16. A chaotic encryption / decryption system based on random weights, characterized in that, The system includes: The encryption module is configured to inject the original image into different subsystems of the Lorentz chaotic system during the encryption phase to obtain multiple initial ciphertexts; and to linearly combine the multiple initial ciphertexts with random weights to obtain the ciphertext data of the original image. The decryption module is configured to generate a weight matrix and auxiliary ciphertext based on the number of the subsystems during the decryption phase. Based on the weight matrix and auxiliary ciphertext, the encrypted image is decrypted to obtain the original image.