A chaotic encryption and decryption method and system based on random weight

Abstract

The present invention discloses a chaotic encryption and decryption method and system based on random weights, which belongs to the field of information security technology and is used to solve the technical problems that the existing chaotic encryption and decryption algorithms are heavily dependent on the internal characteristics of nonlinear functions, do not expand the key space, have limited improvement on the security of the key, and are easily cracked. The method includes: in the encryption stage, injecting the original image into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts; linearly combining the multiple initial ciphertexts through random weights to obtain the ciphertext data of the original image; in the decryption stage, based on the number of the subsystems, generating a weight matrix and auxiliary ciphertexts; based on the weight matrix and the auxiliary ciphertexts, decrypting the encrypted image to obtain the original image. This design method adds weights to the initial value key of the original scheme, increases the key length, and ensures security.

Description

Technical Field

[0001] The present invention 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 Art

[0002] In recent years, more and more image data has been transmitted and stored in the network. In all walks of life, the privacy of information has become a crucial issue. Traditional encryption algorithms, such as DES, AES, RSA and other algorithms, are only applicable to text structured data and are not suitable for encrypting image data. In order to solve the problem of image encryption, chaotic encryption algorithms have been proposed. The main advantages of chaotic encryption algorithms are that the secret key space is extended from integer space to real number space, and it is extremely sensitive to the initial value of the system. Therefore, chaotic encryption algorithms generally set the initial value of the system as the secret key.

[0003] The current chaos encryption algorithms have weaknesses such as weak chaos mapping, weak resistance to certain types of attacks, insufficient sensitivity to plaintext and secret keys, and small secret key space. Although various chaos encryption algorithms emerge in an endless stream and have certain encryption effects, these encryption and decryption algorithms rely heavily on the internal characteristics of nonlinear functions and do not expand the secret key space. The improvement of secret key security is relatively limited and they are easy to be cracked. Summary of the invention

[0004] The embodiment of the present invention provides a chaotic encryption and decryption method and system based on random weights, which are used to solve the following technical problems: the existing chaotic encryption and decryption algorithms are heavily dependent on the internal characteristics of nonlinear functions, do not expand the key space, have limited improvement on the security of the keys, and are easily cracked.

[0005] The embodiment of the present invention adopts the following technical solutions:

[0006] On the one hand, an embodiment of the present invention provides a chaotic encryption and decryption method based on random weights, which specifically includes: in the encryption stage, injecting the original image into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts;

[0007] By using random weights, linearly combining the multiple initial ciphertexts to obtain ciphertext data of the original image;

[0008] In the decryption phase, a weight matrix and an auxiliary ciphertext are generated based on the number of the subsystems;

[0009] Based on the weight matrix and the auxiliary ciphertext, the encrypted image is decrypted to obtain the original image.

[0010] In a feasible 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:

[0011] Obtaining a state space expression of the Lorenz chaotic system, and dividing it into three different subsystems according to a plurality of system states in the state space expression;

[0012] In the encryption stage, the initial values ​​of the system states of the three subsystems are respectively used as initial encryption keys to encrypt the original image to obtain three corresponding initial ciphertexts.

[0013] In a feasible implementation, the multiple initial ciphertexts are linearly combined by random weights to obtain the ciphertext data of the original image, specifically including:

[0014] Generate random weights for each initial ciphertext and , perform linear combination on the multiple initial ciphertexts to obtain the ciphertext data expression c ( t );

[0015] in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems, w 1. w 2. w 3 are the random weights corresponding to the three initial ciphertexts.

[0016] In a feasible implementation, in the decryption stage, based on the number of the subsystems, a weight matrix and an auxiliary ciphertext are generated, specifically including:

[0017] In the decryption phase, a decryption request is sent to the encryption module, and two sets of auxiliary weights are generated in the encryption module; wherein each set of auxiliary weights includes three auxiliary weights;

[0018] The two groups of auxiliary weights and the random weights to be solved are constructed into the weight matrix;

[0019] In the encryption module, the original image is auxiliary-encrypted respectively by using the two sets of auxiliary weights to obtain two corresponding sets of auxiliary ciphertexts.

[0020] In a feasible implementation manner, the original image is auxiliary-encrypted by using the two sets of auxiliary weights to obtain two corresponding sets of auxiliary ciphertexts, specifically including:

[0021] In the encryption module, the weight matrix is ​​defined as: ;in, and are the two sets of auxiliary weights;

[0022] Through 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: ; ;in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems respectively.

[0023] In a feasible implementation manner, decrypting the encrypted image based on the weight matrix and the auxiliary ciphertext to obtain the original image specifically includes:

[0024] Defining a ciphertext vector based on the ciphertext data of the original image and the auxiliary ciphertext;

[0025] According to the initial ciphertext output by each subsystem, an initial ciphertext vector is defined;

[0026] Based on the ciphertext vector, the weight matrix and the initial ciphertext vector, construct a ciphertext linear equation system, solve the ciphertext linear equation system for a unique solution, and obtain an inverse matrix of the weight matrix;

[0027] The encrypted image is parsed using the inverse matrix to obtain the original image.

[0028] In a feasible implementation manner, a ciphertext vector is defined based on the ciphertext data of the original image and the auxiliary ciphertext; and an initial ciphertext vector is defined according to the initial ciphertext output by each subsystem, specifically including:

[0029] Define the ciphertext vector as ;in, c ( t ) is the ciphertext data of the original image, c 1 ( t ) is the first set of auxiliary ciphertext, c 2 ( t ) is the second set of auxiliary ciphertext;

[0030] Define the initial ciphertext vector as ;in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems respectively.

[0031] In a feasible implementation, based on the ciphertext vector, the weight matrix and the initial ciphertext vector, a ciphertext linear equation system is constructed, and a unique solution of the ciphertext linear equation system is solved to obtain an inverse matrix of the weight matrix, specifically including:

[0032] when t ≥0, the ciphertext linear equation system is obtained ;in, C ( t ) is the ciphertext vector, Y ( t ) is the initial ciphertext vector, W is the weight matrix;

[0033] Let the weight matrix W Rank rank ( W )=3, the weight matrix is ​​a non-singular matrix, the ciphertext linear equations have a unique solution, and the inverse matrix of the weight matrix is ​​obtained by solving .

[0034] In a feasible implementation manner, parsing the encrypted image by using the inverse matrix to obtain the original image specifically includes:

[0035] According to the element values ​​in the inverse matrix, the initial ciphertext is parsed to obtain three initial ciphertexts:

[0036] ;

[0037] ;

[0038] ;

[0039] Select any one of the above initial ciphertexts for derivation, substitute the initial secret key of the subsystem corresponding to the selected initial ciphertext into the derivation formula, calculate the original text data, and obtain the original image.

[0040] On the other hand, an embodiment of the present invention further provides a chaotic encryption and decryption system based on random weights, the system comprising:

[0041] The encryption module is used to inject the original image into different subsystems of the Lorentz chaotic system during the encryption phase to obtain a plurality of initial ciphertexts; and to perform linear combination of the plurality of initial ciphertexts through random weights to obtain the ciphertext data of the original image;

[0042] The decryption module is used to generate a weight matrix and an auxiliary ciphertext based on the number of the subsystems during the decryption phase; and decrypt the encrypted image based on the weight matrix and the auxiliary ciphertext to obtain the original image.

[0043] Compared with the prior art, the chaotic encryption and decryption method and system based on random weights provided by the embodiment of the present invention have the following beneficial effects:

[0044] The random weight-based chaotic encryption and decryption algorithm proposed in this invention injects the original text into different state channels of the Lorenz chaotic system, introduces the corresponding chaotic encryption subsystem, and adds a weight value to the subsystem as part of the secret key. This design method adds the weight to the initial value secret key of the original scheme, increases the secret key length, and ensures security.

[0045] During the decryption process, it is necessary to apply to the encryption unit, and the encryption module randomly sends two groups of ciphertexts integrated by auxiliary random weights. Only then can the decryption unit solve the secret key, thereby using the system inverse method to solve the original text. The present invention uses the idea of ​​auxiliary ciphertext to solve the original text. Specifically, since the coefficient matrix of the linear equations is not full rank, the system solutions will be infinite. Even if the attacker obtains the ciphertext, the real weight cannot be solved and the original text cannot be cracked. In order to successfully decrypt, the present invention introduces the idea of ​​auxiliary ciphertext. By randomly generating auxiliary ciphertext and forming a full-rank coefficient matrix with the unknown weights that need to be solved, the concept of system inverse is used to solve the plaintext, thereby improving the security of image encryption. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0047] Figure 1 A flow chart of a chaotic encryption and decryption method based on random weights provided by an embodiment of the present invention;

[0048] Figure 2 A schematic diagram of an encryption process of an encryption module provided in an embodiment of the present invention;

[0049] Figure 3 A schematic diagram of a ciphertext parsing process based on system inversion provided in an embodiment of the present invention;

[0050] Figure 4 A schematic diagram of the structure of a chaotic encryption and decryption system based on random weights provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0051] In order to enable those skilled in the art to better understand the technical solutions in the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of this specification, all other embodiments obtained by ordinary technicians in this field without creative work should fall within the scope of protection of the present invention.

[0052] The embodiment of the present invention provides a chaotic encryption and decryption method based on random weights, such as Figure 1 As shown, the chaotic encryption and decryption method based on random weights specifically includes steps S101-S104:

[0053] S101. In the encryption phase, the original image is injected into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts.

[0054] Specifically, a state space expression of the Lorenz chaotic system is obtained, and the system is divided into three different subsystems according to a plurality of system states in the state space expression.

[0055] Furthermore, in the encryption stage, the encryption module uses the initial values ​​of the system states of the three subsystems as initial encryption keys to encrypt the original image and obtain three corresponding initial ciphertexts.

[0056] As a feasible implementation method, the Lorentz nonlinear system is a typical chaotic system, and its specific state space expression is as follows:

[0057] ;

[0058] in, , , There are three different state channels of the system. is the output of the system.

[0059] By putting the plaintext Injected into different positions in the Lorenz chaotic system, three different subsystems were constructed , and :

[0060] : ;

[0061] : ;

[0062] : .

[0063] Three subsystems , , The initial value of the state , , , , , , , , As encryption keys, the original image is encrypted, and the initial ciphertexts are , and .

[0064] S102, performing linear combination on multiple initial ciphertexts by random weights to obtain ciphertext data of the original image.

[0065] Specifically, the encryption module generates a random weight for each initial ciphertext and , perform linear combination of multiple initial ciphertexts to obtain the ciphertext data expression c ( t ).in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems, w 1. w 2. w 3 are the random weights corresponding to the three initial ciphertexts.

[0066] As a feasible implementation method, Figure 2 A schematic diagram of an encryption process of an encryption module provided in an embodiment of the present invention, such as Figure 2 As shown, the encryption module will randomly generate the weight coefficient , , Combined with the initial state value of each subsystem as the secret key for system encryption, after introducing random weights, the ciphertext data is , increasing the length of the secret key and expanding the key space.

[0067] S103. In the decryption phase, a weight matrix and auxiliary ciphertext are generated based on the number of subsystems.

[0068] Specifically, in the decryption stage, the decryption module sends a decryption request to the encryption module, and generates two sets of auxiliary weights in the encryption module; wherein each set of auxiliary weights includes three auxiliary weights.

[0069] Furthermore, the encryption module constructs the two sets of auxiliary weights and the random weights to be solved into a weight matrix, and performs auxiliary encryption on the original image through the two sets of auxiliary weights to obtain the corresponding two sets of auxiliary ciphertexts, and then sends both the weight matrix and the auxiliary ciphertext to the decryption module.

[0070] As a feasible implementation method, the original image is auxiliary encrypted by two sets of auxiliary weights to obtain two corresponding sets of auxiliary ciphertexts, specifically including:

[0071] In the encryption module, the weight matrix is ​​defined as: ;in, and There are two sets of auxiliary weights.

[0072] Then, through 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: ; ;in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems respectively.

[0073] S104: Decrypt the encrypted image based on the weight matrix and the auxiliary ciphertext to obtain the original image.

[0074] Specifically, the decryption module defines a ciphertext vector based on the ciphertext data of the original image and the auxiliary ciphertext, and defines an initial ciphertext vector according to the initial ciphertext output by each subsystem.

[0075] Furthermore, the decryption module constructs a ciphertext linear equation system based on the ciphertext vector, the weight matrix and the initial ciphertext vector, finds the unique solution of the decrypted linear equation system, and obtains the inverse matrix of the weight matrix. Then, the encrypted image is parsed by the inverse matrix to obtain the original image.

[0076] As a feasible implementation method, the decryption module defines the ciphertext vector as ;in, c ( t ) is the ciphertext data of the original image, c 1 ( t ) is the first set of auxiliary ciphertext, c 2 ( t ) is the second set of auxiliary ciphertext.

[0077] Define the initial ciphertext vector as ;in,y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems respectively.

[0078] when t ≥0, the ciphertext linear equation system is obtained ;in, C ( t ) is the ciphertext vector, Y ( t ) is the initial ciphertext vector, W is the weight matrix.

[0079] Furthermore, when the weight matrix W Rank rank ( W )=3, the weight matrix is ​​a non-singular matrix, and the ciphertext linear equations have a unique solution. rank ( W )=3, solve to get the inverse matrix of the weight matrix .

[0080] Further, Figure 3 A schematic diagram of a ciphertext parsing process based on system inversion provided by an embodiment of the present invention, such as Figure 3 As shown, the encrypted image is parsed through the inverse matrix to obtain the original image, which specifically includes:

[0081] According to the element values ​​in the inverse matrix, the initial ciphertext is parsed and the three initial ciphertexts are obtained as follows:

[0082] ;

[0083] ;

[0084] .

[0085] Then select any one of the above initial ciphertexts for derivation, substitute the initial secret key of the subsystem corresponding to the selected initial ciphertext into the derivation formula, calculate the original data, and obtain the original image.

[0086] Assume that the choice is Taking the derivative, we get , and then the known subsystem The system initial value , Substituting into the above formula, we get the decrypted original image data: .

[0087] In addition, the embodiment of the present invention also provides a chaotic encryption and decryption system based on random weights, such as Figure 4 As shown, the chaotic encryption and decryption system 400 based on random weights specifically includes:

[0088] The encryption module 420 is used to inject the original image into different subsystems of the Lorentz chaotic system during the encryption phase to obtain a plurality of initial ciphertexts; and to perform linear combination of the plurality of initial ciphertexts by random weights to obtain the ciphertext data of the original image;

[0089] The decryption module 430 is used to generate a weight matrix and an auxiliary ciphertext based on the number of the subsystems during the decryption phase; and decrypt the encrypted image based on the weight matrix and the auxiliary ciphertext to obtain the original image.

[0090] As a feasible implementation, the system further includes a chaotic system model library 410, which includes three subsystems of the Lorenz chaotic system.

[0091] Each embodiment of the present invention is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device, system, and non-volatile computer storage medium embodiments, since they are basically similar to the method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0092] The above describes specific embodiments of the present invention. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0093] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the embodiments of the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the embodiments of the present invention should be included in the protection scope of the present invention.

Claims

1. A chaotic encryption and decryption method based on random weights, characterized in that: The method comprises: In the encryption stage, the original image is injected into different subsystems of the Lorentz chaotic system to obtain multiple initial ciphertexts, including: Obtaining a state space expression of the Lorenz chaotic system, and dividing it into three different subsystems according to a plurality of system states in the state space expression; In the encryption stage, the initial values ​​of the system states of the three subsystems are used as initial encryption keys to encrypt the original image, thereby obtaining three corresponding initial ciphertexts; The multiple initial ciphertexts are linearly combined by random weights to obtain the ciphertext data of the original image, specifically including: Generate random weights for each initial ciphertext and , perform linear combination on the multiple initial ciphertexts to obtain the ciphertext data expression c ( t ); in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems, w 1. w 2. w 3 are the random weights corresponding to the three initial ciphertexts; In the decryption phase, based on the number of subsystems, a weight matrix and auxiliary ciphertext are generated, specifically including: In the decryption phase, a decryption request is sent to the encryption module, and two sets of auxiliary weights are generated in the encryption module; wherein each set of auxiliary weights includes three auxiliary weights; The two groups of auxiliary weights and the random weights to be solved are constructed into the weight matrix; In the encryption module, the original image is auxiliary encrypted by using the two sets of auxiliary weights to obtain two corresponding sets of auxiliary ciphertexts, specifically including: In the encryption module, the weight matrix is ​​defined as: ;in, and are the two sets of auxiliary weights; Through 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: ; ;in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems respectively; Based on the weight matrix and the auxiliary ciphertext, the encrypted image is decrypted to obtain the original image.

2. The chaotic encryption and decryption method based on random weights according to claim 1 is characterized in that: Decrypting the encrypted image based on the weight matrix and the auxiliary ciphertext to obtain the original image specifically includes: Defining a ciphertext vector based on the ciphertext data of the original image and the auxiliary ciphertext; According to the initial ciphertext output by each subsystem, an initial ciphertext vector is defined; wherein the initial ciphertext vector is the quantity to be solved; Based on the ciphertext vector, the weight matrix and the initial ciphertext vector, construct a ciphertext linear equation system, solve the ciphertext linear equation system for a unique solution, and obtain an inverse matrix of the weight matrix; The encrypted image is parsed using the inverse matrix to obtain the original image.

3. The chaotic encryption and decryption method based on random weights according to claim 2 is characterized in that: Based on the ciphertext data of the original image and the auxiliary ciphertext, a ciphertext vector is defined; and according to the initial ciphertext output by each subsystem, an initial ciphertext vector is defined, specifically including: Define the ciphertext vector as ;in, c ( t ) is the ciphertext data of the original image, c 1 ( t ) is the first set of auxiliary ciphertext, c 2 ( t ) is the second set of auxiliary ciphertext; Define the initial ciphertext vector as ;in, y 1( t ), y 2( t ), y 3( t ) are the initial ciphertexts output by the three subsystems respectively.

4. The chaotic encryption and decryption method based on random weights according to claim 3 is characterized in that: Based on the ciphertext vector, the weight matrix and the initial ciphertext vector, a ciphertext linear equation system is constructed, and a unique solution of the ciphertext linear equation system is solved to obtain an inverse matrix of the weight matrix, specifically including: when t ≥0, the ciphertext linear equation system is obtained ;in, C ( t ) is the ciphertext vector, Y ( t ) is the initial ciphertext vector, W is the weight matrix; Let the weight matrix W Rank rank ( W )=3, the weight matrix is ​​a non-singular matrix, the ciphertext linear equations have a unique solution, and the inverse matrix of the weight matrix is ​​obtained by solving .

5. The chaotic encryption and decryption method based on random weights according to claim 4 is characterized in that: The encrypted image is parsed by using the inverse matrix to obtain the original image, which specifically includes: According to the element values ​​in the inverse matrix, the initial ciphertext is parsed to obtain three initial ciphertexts: ； ； ； Select any one of the above initial ciphertexts for derivation, substitute the initial secret key of the subsystem corresponding to the selected initial ciphertext into the derivation formula, calculate the original text data, and obtain the original image.

6. A chaotic encryption and decryption system based on random weights, characterized in that: For implementing a chaotic encryption and decryption method based on random weights as claimed in claim 1, the system comprises: The encryption module is used to inject the original image into different subsystems of the Lorentz chaotic system during the encryption phase to obtain a plurality of initial ciphertexts; and to perform linear combination of the plurality of initial ciphertexts through random weights to obtain the ciphertext data of the original image; The decryption module is used to generate a weight matrix and auxiliary ciphertext based on the number of the subsystems during the decryption phase; and decrypt the encrypted image based on the weight matrix and the auxiliary ciphertext to obtain the original image.

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