Video encryption method and device based on linear fractional order hyperbolic equation, and storage medium

Abstract

The invention relates to a video encryption method and device based on a linear fractional order hyperbolic equation and a storage medium, and the method comprises the following steps: S01) obtaining all image frames of a to-be-encrypted video, and carrying out the normalization processing of all image frames; s02) segmenting the image frames, and performing Arnold transformation and gray scale scrambling operation on data information of each group of image frames after segmentation; s03) encrypting the data information by using a linear fractional order hyperbolic equation encryption model; s04) performing an XOR operation based on a chaotic sequence on the encrypted data information to obtain ciphertext data; and S05) arranging the ciphertext data according to the initial arrangement order of the image frames.According to the method, the problem of low solving efficiency of an encryption model of a fractional order partial differential equation used for video encryption in the prior art is solved, and the stability of the video encryption and decryption process is greatly improved.

Description

Technical Field

[0001] The present application relates to the field of video encryption technology, and in particular to a video encryption method, device and storage medium based on a linear fractional-order hyperbolic equation. Background Art

[0002] Encryption technology is the core technology of information security. Classical encryption technology rarely involves analytical mathematics theory, but with the introduction of the heat flow coding system, analytical mathematics has gradually been applied to the data encryption process. The heat flow cryptographic system is based on pseudo-parabolic equations, which are integer partial differential equations. Unlike integer partial differential equations, fractional partial differential equations belong to fractional partial differential equations. Fractional derivatives are derived from the generalization of integer reciprocals. They are more complex than pseudo-parabolic equations, but can more accurately simulate dynamic systems and natural physical phenomena.

[0003] In recent years, video has been widely used on the Internet as a more vivid communication medium. In order to protect the security of video data, an encryption model based on fractional-order partial differential equations can be selected for encryption. However, the decryption methods in the prior art, such as the finite difference method, the reproducing kernel method, and the finite element method, have problems of low solution accuracy and complex calculations, which is not conducive to the promotion of this encryption method. Summary of the invention

[0004] In a first aspect, the present invention provides a video encryption method based on a linear fractional-order hyperbolic equation, which solves the problem of low efficiency in solving the encryption model of the fractional-order partial differential equation used for video encryption in the prior art.

[0005] A technical solution of a video encryption method based on linear fractional-order hyperbolic equation is as follows: A video encryption method based on a linear fractional order hyperbolic equation, characterized in that it comprises the following steps: S01) obtaining all image frames of the video to be encrypted, and performing normalization processing on all image frames; S02) dividing each image frame into a number of matrix blocks of the same size, and after the division, performing Arnold transformation and grayscale scrambling operations on the data information of each matrix block; S03) Encrypting the data information using a linear fractional-order hyperbolic equation encryption model; The encrypted model of linear fractional-order hyperbolic equation is defined as follows: ; ; In the formula, , For a given function, its common as a key; and is the boundary condition; is the Caputo fractional order term ( ); During the encryption process, the plaintext frame is used as the function value at the initial moment , use the barycentric interpolation collocation method to solve the numerical solution of the fractional differential equation and obtain the function value at the final moment As ciphertext; S04) performing an XOR operation based on a chaotic sequence on the encrypted data information to obtain ciphertext data; S05) Arranging the ciphertext data according to the initial arrangement order of the image frames.

[0006] Furthermore, in step S02), the Arnold transformation formula is as follows: ; In the formula, ( ) represents the pixel to be encrypted in the image frame, ( Represents the pixel after grayscale scrambling, Indicates the length or width of the image to be encrypted. A and B For the given data.

[0007] Furthermore, in step S02), the grayscale scrambling formula is as follows: ; In the formula, is the gray value matrix of the image frame to be processed, represents a random matrix with the same size as the image frame to be processed, Represents the matrix after grayscale scrambling.

[0008] Furthermore, in step S04), the mapping of the Logistic chaotic system is as follows: ; In the formula, is the key in the Logistic chaotic encryption system, is the Logistic parameter, when , the mapping enters a chaotic state.

[0009] 5. The video encryption method based on linear fractional order hyperbolic equation according to claim 4, characterized in that: In step S04), an XOR operation of the chaotic sequence is performed based on the Logistic chaotic system. The specific steps are as follows: S41) Given the parameters of the Logistic chaotic system and system initial value , A random value in the range of 0 to 1; S42) The sum of all pixel values ​​of the image frame encrypted using the linear fractional order hyperbolic equation is expressed as , and will Perform a modulo operation on 256, then divide the integer part by 255. The result of the operation is used as the auxiliary key. ; S43) Use auxiliary key The initial value of the correction is ; The corrected As the initial value of the chaotic system, a chaotic sequence is constructed by the Logistic chaotic system mapping formula ; S44) Chaos sequence Press Transform to obtain an improved chaotic sequence .

[0010] S45) sequentially takes each pixel point in the image frame to Indicates the sequence number of the point, based on Construct the encryption key: S46) for the first The gray level of the pixel value of each pixel point is subjected to a binary exclusive OR operation with the encryption key in step S45) to obtain an encrypted pixel value; S47) Repeat steps S45) to S46) until all pixels are encrypted to obtain ciphertext data.

[0011] In a second aspect, the present application provides a video encryption device based on linear fractional-order hyperbolic equations, comprising a processor and a memory storing program instructions, wherein the processor is configured to execute the aforementioned video encryption method based on linear fractional-order hyperbolic equations when running the program instructions.

[0012] In a third aspect, the present application provides a computer-readable storage medium having a computer program stored thereon, which implements the aforementioned method when executed by a processor.

[0013] Due to the adoption of the above technical solution, the beneficial effects of this application are as follows: 1. This application uses the barycentric interpolation collocation method to solve fractional-order hyperbolic equations. For the fractional-order part, The Caputo fractional order term is transformed into a Riemann integral, and the barycentric interpolation basis function is used to approximate the unknown function in the differential equation. The above method greatly increases the stability of the video encryption and decryption process.

[0014] 2. This application uses an encryption model of linear fractional-order hyperbolic equations for encryption, which can simulate dynamic systems more accurately, thereby having higher accuracy and stability, improving encryption effects, and effectively protecting privacy data. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings: Figure 1 A flow chart of a video encryption method based on linear fractional-order hyperbolic equation provided in this application; Figure 2 A process diagram of a video encryption method based on a linear fractional-order hyperbolic equation provided by the present application; Figure 3 are several image frames extracted in the embodiment of the present application; Figure 4 is an encrypted image frame in an embodiment of the present application; Figure 5 It is a decrypted graph of the image frame in the embodiment of the present application; Figure 6 It is a histogram of the original image and the encrypted image in the embodiment of the present application. DETAILED DESCRIPTION

[0016] Based on the background technology, the present application provides a video encryption method based on a linear fractional-order hyperbolic equation, comprising the following steps: S01) obtaining all image frames of the video to be encrypted, and performing normalization processing on all image frames; The normalization formula is as follows: ; In the formula, is the pixel value to be processed, and Represent the minimum and maximum pixel values ​​in the image, respectively. Represents the normalized pixel value; S02) dividing each image frame into a number of matrix blocks of the same size, and after the division, performing Arnold transformation and grayscale scrambling operations on the data information of each matrix block; The Arnold transformation formula is as follows: ; In the formula, ( ) represents the pixel to be encrypted in the image frame, ( Represents the pixel after grayscale scrambling, Indicates the length or width of the image to be encrypted.A and B For the given data.

[0017] A and B It can be selected in many ways. In this embodiment, mutually prime positive integers are selected to ensure the randomness and security of the scrambling.

[0018] The grayscale scrambling formula is as follows: ; In the formula, is the gray value matrix of the image frame to be processed, represents a random matrix with the same size as the image frame to be processed, Represents the matrix after grayscale scrambling.

[0019] S03) Encrypting the data information using a linear fractional-order hyperbolic equation encryption model; The encrypted model of linear fractional-order hyperbolic equation is defined as follows: ; ; In the formula, , For a given function, its common as a key; and is the boundary condition; is the Caputo fractional order term ( ); During the encryption process, the plaintext frame is used as the function value at the initial moment , use the barycentric interpolation collocation method to solve the numerical solution of the fractional differential equation and obtain the function value at the final moment As ciphertext.

[0020] S04) performing an XOR operation based on a chaotic sequence on the encrypted data information to obtain ciphertext data; This embodiment adopts the Logistic chaotic system, and the mapping of the Logistic chaotic system is as follows: ; In the formula, is the key in the Logistic chaotic encryption system, is the Logistic parameter, when When , the mapping enters a chaotic state. At this point, the behavior of the system may have shown sensitivity to initial conditions and some non-periodicity, but may still have some periodic characteristics; when When the mapping is completely chaotic, the system's dynamics completely loses its periodicity and exhibits the characteristics of complete chaos. A system in a chaotic state is highly unpredictable and extremely sensitive to initial conditions.

[0021] The specific steps of XOR operation of chaotic sequence based on Logistic chaotic system are as follows: S41) Given the parameters of the Logistic chaotic system and system initial value , A random value in the range of 0 to 1; S42) The sum of all pixel values ​​of the image frame encrypted using the linear fractional order hyperbolic equation is expressed as , and will Perform a modulo operation on 256, then divide the integer part by 255. The result of the operation is used as the auxiliary key. ; S43) Use auxiliary key The initial value of the correction is ; The corrected As the initial value of the chaotic system, a chaotic sequence is constructed by the Logistic chaotic system mapping formula ; S44) Chaos sequence Press Transform to obtain an improved chaotic sequence .

[0022] S45) sequentially takes each pixel point in the image frame to Indicates the sequence number of the point, based on Construct the encryption key: S46) for the first The gray level of the pixel value of each pixel point is subjected to a binary exclusive OR operation with the encryption key in step S45) to obtain an encrypted pixel value; S47) Repeat steps S45) to S46) until all pixels are encrypted to obtain ciphertext data.

[0023] S05) Arranging the ciphertext data according to the initial arrangement order of the image frames.

[0024] In this embodiment, two groups of videos are selected for encryption, as shown in the attached Figure 3 As shown, the first group contains videos of parrots, flowers, and bananas, and its frame size is 256 256, a total of 50 frames; the second group contains videos of shells, balloons, and lotus flowers, with a frame size of 128 128, total 150 frames.

[0025] In this embodiment, the size of each matrix block during segmentation is 16 , a length of Chaotic sequence .

[0026] Taking the (1+1)-dimensional encryption and decryption model as an example, the video encryption experiment is carried out. The key function of the encryption model of the linear fractional-order hyperbolic equation is selected as: .

[0027] As attached Figure 4 As shown in the figure, the relevant information of the original image cannot be identified in the encrypted image. Figure 5 In the decrypted image, the pixel features before encryption are restored. Figure 6 The histogram distribution of the original image and the encrypted image of the first frame of the video. The histogram distribution of the original image has large fluctuations and has obvious regularity; the encrypted histogram is evenly distributed, which is very different from the plaintext and can resist statistical attacks.

[0028] The disclosed embodiment also provides a video encryption device based on a linear fractional-order hyperbolic equation, including a processor and a memory. Optionally, the device may also include a communication interface and a bus. The processor, the communication interface, and the memory may communicate with each other through the bus. The communication interface may be used for information transmission. The processor may call the logic instructions in the memory to execute a video encryption method based on a linear fractional-order hyperbolic equation of the above embodiment.

[0029] In addition, the logic instructions in the above-mentioned memory can be implemented in the form of software functional units and can be stored in a computer-readable storage medium when sold or used as an independent product.

[0030] The memory, as a computer-readable storage medium, can be used to store software programs and computer executable programs, such as program instructions / modules corresponding to the method in the embodiment of the present disclosure. The processor executes the function application and data processing by running the program instructions / modules stored in the memory, that is, implementing a video encryption method based on linear fractional-order hyperbolic equations in the above embodiment.

[0031] The memory may include a program storage area and a data storage area, wherein the program storage area may store an operating system and an application required for at least one function; the data storage area may store data created according to the use of the terminal device, etc. In addition, the memory may include a high-speed random access memory and may also include a non-volatile memory.

[0032] An embodiment of the present disclosure provides a computer-readable storage medium storing computer-executable instructions, wherein the computer-executable instructions are configured to execute a video encryption method based on a linear fractional-order hyperbolic equation.

[0033] The computer-readable storage medium mentioned above may be a transient computer-readable storage medium or a non-transitory computer-readable storage medium.

[0034] The technical solution of the embodiment of the present disclosure can be embodied in the form of a software product, which is stored in a storage medium and includes one or more instructions for enabling a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the method described in the embodiment of the present disclosure. The aforementioned storage medium may be a non-transient storage medium, including: a USB flash drive, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a disk or an optical disk, and other media that can store program codes, or a transient storage medium.

[0035] Anything not described in this application can be achieved by adopting or drawing on existing technologies. The above is only an embodiment of the present application and is not intended to limit the present application. For those skilled in the art, the present application may have various changes and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.

Claims

1. A video encryption method based on linear fractional-order hyperbolic equations, It is characterized in that The following steps are involved: S01) obtaining all image frames of the video to be encrypted, and performing normalization processing on all image frames; S02) dividing each image frame into a number of matrix blocks of the same size, and after the division, performing Arnold transformation and grayscale scrambling operations on the data information of each matrix block; S03) Encrypting the data information using a linear fractional-order hyperbolic equation encryption model; The encrypted model of linear fractional-order hyperbolic equation is defined as follows: ； ； In the formula, , For a given function, its common as a key; and is the boundary condition; is the Caputo fractional order term ( ); During the encryption process, the plaintext frame is used as the function value at the initial moment , use the barycentric interpolation collocation method to solve the numerical solution of the fractional differential equation and obtain the function value at the final moment As ciphertext; S04) performing an XOR operation based on a chaotic sequence on the encrypted data information to obtain ciphertext data; S05) Arranging the ciphertext data according to the initial arrangement order of the image frames.

2. The video encryption method based on linear fractional order hyperbolic equation according to claim 1, It is characterized in that In step S02), the Arnold transformation formula is as follows: ； In the formula, ( ) represents the pixel to be encrypted in the image frame, ( Represents the pixel after grayscale scrambling, Indicates the length or width of the image to be encrypted. A and B For the given data.

3. The video encryption method based on linear fractional order hyperbolic equation according to claim 1, It is characterized in that In step S02), the grayscale scrambling formula is as follows: ； In the formula, is the gray value matrix of the image frame to be processed, represents a random matrix with the same size as the image frame to be processed, Represents the matrix after grayscale scrambling.

4. The video encryption method based on linear fractional order hyperbolic equation according to claim 1, It is characterized in that In step S04), the mapping of the Logistic chaotic system is as follows: ； In the formula, is the key in the Logistic chaotic encryption system, is the Logistic parameter, when , the mapping enters a chaotic state.

5. The video encryption method based on linear fractional order hyperbolic equation according to claim 4, It is characterized in that In step S04), an XOR operation of the chaotic sequence is performed based on the Logistic chaotic system. The specific steps are as follows: S41) Given the parameters of the Logistic chaotic system and system initial value , A random value in the range of 0 to 1; S42) The sum of all pixel values ​​of the image frame encrypted using the linear fractional order hyperbolic equation is expressed as , and will Perform a modulo operation on 256, then divide the integer part by 255. The result of the operation is used as the auxiliary key. ; S43) Use auxiliary key The initial value of the correction is ; The corrected As the initial value of the chaotic system, a chaotic sequence is constructed by the Logistic chaotic system mapping formula ; S44) Chaos sequence Press Transform to obtain an improved chaotic sequence . S45) sequentially takes each pixel point in the image frame to Indicates the point number, based on Construct the encryption key: S46) for the first The gray level of the pixel value of each pixel point is subjected to a binary exclusive OR operation with the encryption key in step S45) to obtain an encrypted pixel value; S47) Repeat steps S45) to S46) until all pixels are encrypted to obtain ciphertext data.

6. A video encryption device based on a linear fractional order hyperbolic equation, comprising a processor and a memory storing program instructions, It is characterized in that The processor is configured to execute a video encryption method based on a linear fractional-order hyperbolic equation as described in any one of claims 1 to 5 when running the program instructions.

7. A computer-readable storage medium, It is characterized in that A computer program is stored thereon, and when the program is executed by a processor, the method described in any one of claims 1 to 5 is implemented.

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