A video encryption method and device based on a linear fractional-order hyperbolic equation and a storage medium

Abstract

The application 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) acquiring all image frames of a to-be-encrypted video, and performing normalization processing on the all image frames; S02) performing segmentation on the image frames, and performing Arnold transformation and gray scrambling operation on data information of each group of image frames after the segmentation; S03) performing encryption on the data information by using a linear fractional order hyperbolic equation encryption model; S04) performing an exclusive or operation on the encrypted data information based on a chaotic sequence to obtain ciphertext data; and S05) arranging the ciphertext data according to an initial arrangement order of the image frames. The application solves the problem that the solving efficiency of an encryption model of a fractional order partial differential equation used for video encryption in the prior art is low, and greatly increases the stability of the video encryption and decryption process.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of video encryption, and particularly relates to a video encryption method based on a linear fractional-order hyperbolic equation, a device and a storage medium. BACKGROUND

[0002] Encryption technology is the core technology of information security. Classical encryption technology rarely involves analytical mathematics theory, but with the proposal of the heat flow coding system, analytical mathematics is gradually applied to the data encryption process. The heat flow coding system is based on a pseudo-parabolic equation, and the pseudo-parabolic equation belongs to an integer partial differential equation. Unlike the integer partial differential equation, the fractional-order partial differential equation belongs to a fractional-order partial differential equation, and the fractional derivative is generalized from the integer-order derivative. The fractional-order partial differential equation is more complex than the pseudo-parabolic equation, but can more accurately simulate dynamic systems and natural physical phenomena.

[0003] In recent years, video is widely used as a more vivid communication medium on the Internet, and in order to protect the security of video data, an encryption model based on a fractional-order partial differential equation can be selected for encryption. However, the existing decryption methods, such as the finite difference method, the reproducing kernel method and the finite element method, have the problems of low solving precision and complex calculation, which are not conducive to the promotion of this encryption method. SUMMARY

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

[0005] A video encryption method based on a linear fractional-order hyperbolic equation has the following technical scheme:

[0006] A video encryption method based on a linear fractional-order hyperbolic equation comprises the following steps:

[0007] S01) obtaining all image frames of a video to be encrypted, and performing normalization processing on all the image frames;

[0008] S02) dividing each image frame into a plurality of matrix blocks of the same size, and performing Arnold transformation and gray scrambling operations on the data information of each matrix block after the division;

[0009] S03) encrypting the data information after the Arnold transformation and the gray scrambling operations using a linear fractional-order hyperbolic equation encryption model;

[0010] The linear fractional-order hyperbolic equation encryption model is defined as follows:

[0011] ;

[0012] ;

[0013] wherein, , is a given function, which is common to as the key; and are boundary conditions; is a Caputo fractional term ( );

[0014] In the encryption process, the data information after the Arnold transformation and the gray scale scrambling operation is taken as the function value at the initial time , and the numerical solution of the fractional differential equation is solved by using the barycentric interpolation collocation method to obtain the function value at the final time as the ciphertext;

[0015] S04) XOR operation based on the chaotic sequence is performed on the encrypted data information to obtain the ciphertext data;

[0016] S05) The ciphertext data is arranged according to the initial arrangement order of the image frame.

[0017] Further, in step S02), the Arnold transformation formula is as follows:

[0018] ;

[0019] wherein, ( ) represents the pixel point to be encrypted in the image frame, ( represents the pixel point after the gray scale scrambling, represents the length or width of the image to be encrypted, A and B are given data.

[0020] Further, in step S02), the gray scale scrambling formula is as follows:

[0021] ;

[0022] wherein, is the gray scale 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 the gray scale scrambling.

[0023] Further, in step S04), the mapping of the Logistic chaotic system is as follows:

[0024] ;

[0025] wherein, The key for the Logistic chaotic encryption system, When the parameter of Logistic is , the mapping enters a chaotic state.

[0026] In step S04, the XOR operation of the chaotic sequence is performed based on the Logistic chaotic system, and the specific steps are as follows:

[0027] S41) The parameter of the Logistic chaotic system is given and the system initial value , is a random value in the range of 0-1;

[0028] S42) The sum of all pixel values of the image frame encrypted using the linear fractional order hyperbolic equation is expressed as , and is taken modulo 256, and then the integer part is divided by 255, and the result of the operation is taken as the auxiliary key ;

[0029] S43) The initial value is corrected to using the auxiliary key ; the corrected is taken as the initial value of the chaotic system, and a chaotic sequence is constructed from the Logistic chaotic system mapping formula;

[0030] S44) The chaotic sequence is converted according to the formula to obtain an improved chaotic sequence .

[0031] S45) A pixel point in the image frame is sequentially taken, and the serial number of the point is represented by , and the encryption key is constructed based on :

[0032] S46) The gray level of the pixel value of the th pixel point in the image frame is XORed with the encryption key in step S45) in binary to obtain the encrypted pixel value;

[0033] S47) Repeat S45) to S46) until all pixel points are encrypted to obtain the ciphertext data.

[0034] In a second aspect, the application provides a video encryption device based on a linear fractional order hyperbolic equation, comprising a processor and a memory storing program instructions, wherein the processor is configured to execute the aforementioned video encryption method based on a linear fractional order hyperbolic equation when the program instructions are run.

[0035] Thirdly, this application provides a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the aforementioned method.

[0036] Due to the adoption of the above technical solution, the beneficial effects of this application are as follows:

[0037] 1. This application utilizes the centroid interpolation collocation method to solve fractional hyperbolic equations. For the fractional part, it will...

[0038] The Caputo fractional terms are transformed into Riemann integrals, and the unknown functions in the differential equations are approximated using barycentric interpolation basis functions. This method significantly increases the stability of the video encryption and decryption process.

[0039] 2. This application uses a encryption model based on linear fractional hyperbolic equations for encryption, which can more accurately simulate dynamic systems, thus achieving higher precision and stability, improving encryption effectiveness, and effectively protecting private data. Attached Figure Description

[0040] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0041] Figure 1 A flowchart of a video encryption method based on a linear fractional hyperbolic equation is provided in this application;

[0042] Figure 2 A process diagram of a video encryption method based on a linear fractional hyperbolic equation provided in this application;

[0043] Figure 3 These are several image frames extracted in the embodiments of this application;

[0044] Figure 4 This is an encrypted image of an image frame in an embodiment of this application;

[0045] Figure 5 This is a decrypted image frame from an embodiment of this application;

[0046] Figure 6 These are histograms of the original image and the encrypted image in the embodiments of this application. Detailed Implementation

[0047] Based on the background technology, this application provides a video encryption method based on a linear fractional hyperbolic equation, comprising the following steps:

[0048] S01) Obtain all image frames of the video to be encrypted and normalize all image frames;

[0049] The formula of the normalization processing is as follows:

[0050] ;

[0051] In the formula, is the pixel value to be processed, and respectively represent the minimum and maximum pixel values in the image, represents the normalized pixel value.

[0052] S02) Each image frame is divided into a plurality of matrix blocks of the same size, and the data information of each matrix block is subjected to Arnold transformation and gray scrambling operation after the division;

[0053] The Arnold transformation formula is as follows:

[0054] ;

[0055] In the formula, represents the pixel point to be encrypted in the image frame, represents the pixel point after gray scrambling, represents the length or width of the image to be encrypted, A and B are given data.

[0056] A and B can be selected in various ways, and in the present embodiment, coprime positive integers are selected to ensure the randomness and security of the scrambling.

[0057] The gray scrambling formula is as follows:

[0058] ;

[0059] In the formula, is the gray value matrix of the image frame to be processed, represents a random matrix of the same size as the image frame to be processed, represents the matrix after gray scrambling.

[0060] S03) The data information subjected to Arnold transformation and gray scrambling operation is encrypted using a linear fractional order hyperbolic equation encryption model;

[0061] The linear fractional order hyperbolic equation encryption model is defined as follows:

[0062] ;

[0063] ;

[0064] wherein, , is a given function, which is common to as the key; and are boundary conditions; is a Caputo fractional term ( );

[0065] In the encryption process, the data information after the Arnold transformation and the gray scrambling operation is taken as the function value at the initial time , the numerical solution of the fractional differential equation is solved by using the barycentric interpolation collocation method, and the function value at the final time is taken as the ciphertext.

[0066] S04) XOR operation based on the chaotic sequence is performed on the encrypted data information to obtain the ciphertext data;

[0067] This embodiment adopts a Logistic chaotic system, and the mapping of the Logistic chaotic system is as follows:

[0068] ;

[0069] wherein, is a key in the Logistic chaotic encryption system, is a Logistic parameter, when , the mapping enters a chaotic state. At this time, the behavior of the system may have shown sensitivity to the initial condition and some non-periodicity, but there may still be some periodic characteristics; when , the mapping completely enters a chaotic state. At this time, the dynamics of the system completely lose periodicity and exhibit completely chaotic characteristics. The system in a chaotic state has high unpredictability and extreme sensitivity to the initial condition.

[0070] The specific steps of the XOR operation of the chaotic sequence based on the Logistic chaotic system are as follows:

[0071] S41) Given the parameters and the system initial value , is a random value in the range of 0 to 1;

[0072] S42) the sum of all pixel values of the image frame encrypted by using the linear fractional hyperbolic equation is expressed as , and is taken modulo 256, and then the integer part is divided by 255, and the result after the operation is taken as the auxiliary key ;

[0073] S43)Use the auxiliary key Correct the initial value to ; the corrected is used as the initial value of the chaotic system, and a chaotic sequence is constructed by the Logistic chaotic system mapping formula ;

[0074] S44)Convert the chaotic sequence according to the formula to obtain an improved chaotic sequence .

[0075] S45)Sequentially take a pixel point in the image frame, denote the serial number of the point as , and construct an encryption key based on :

[0076] S46)Perform a binary XOR operation on the gray level of the pixel value of the th pixel point in the image frame and the encryption key in step S45) to obtain the encrypted pixel value;

[0077] S47)Repeat steps S45) to S46) until all pixel points are encrypted to obtain the ciphertext data.

[0078] S05)Arrange the ciphertext data according to the initial arrangement order of the image frame.

[0079] In this embodiment, two groups of videos are selected for encryption, as shown in the accompanying Figure 3 , the first group is a video containing parrots, flowers, and bananas, with a frame size of 256 256, a total of 50 frames; the second group is a video containing seashells, balloons, and lotus flowers, with a frame size of 128 128, a total of 150 frames.

[0080] In this embodiment, the size of each matrix block is 16 , and a chaotic sequence with a length of is constructed by the Logistic chaotic system mapping formula .

[0081] Take the (1+1)-dimensional encryption and decryption model as an example to encrypt the video, and the key function of the linear fractional order hyperbolic equation encryption model is selected as

[0082] .

[0083] As shown in the accompanying Figure 4 , the relevant information of the original image cannot be recognized at all in the encrypted image. As shown in the accompanying Figure 5In the middle, the decryption diagram again restores the pixel features before encryption. The histogram distribution of the original image and the encrypted image of the first frame of the video is shown in the attached Figure 6 The histogram distribution of the original image is large in height and has obvious rules. The histogram distribution of the encrypted image is uniform and has great difference from the plaintext, which can resist statistical attacks.

[0084] The embodiment of the disclosure also provides a video encryption device based on a linear fractional order hyperbolic equation, including a processor and a memory. Optionally, the device can also include a communication interface and a bus. Wherein, the processor, the communication interface and the memory can complete the communication among each other through the bus. The communication interface can be used for information transmission. The processor can call the logic instructions in the memory to execute the above-mentioned embodiment of a video encryption method based on a linear fractional order hyperbolic equation.

[0085] In addition, the above-mentioned logic instructions in the memory can be realized in the form of a software function unit and sold or used as an independent product, which can be stored in a computer readable storage medium.

[0086] The memory as a computer readable storage medium can be used to store software programs, computer executable programs, such as program instructions / modules corresponding to the method in the embodiment of the disclosure. The processor executes the program instructions / modules stored in the memory, thereby executing function applications and data processing, that is, realizing the above-mentioned embodiment of a video encryption method based on a linear fractional order hyperbolic equation.

[0087] The memory can include a program storage area and a data storage area, wherein the program storage area can store an operating system and at least one application required by a function; the data storage area can store data created according to the use of the terminal device. In addition, the memory can include a high-speed random access memory and can also include a non-volatile memory.

[0088] The embodiment of the disclosure provides a computer readable storage medium, which stores computer executable instructions, and the computer executable instructions are set to execute a video encryption method based on a linear fractional order hyperbolic equation.

[0089] The above-mentioned computer readable storage medium can be a transitory computer readable storage medium or a non-transitory computer readable storage medium.

[0090] The technical solutions of the embodiments of the present disclosure can be embodied in the form of a software product. The computer software product is stored in a storage medium, and includes one or more instructions to make a computer device (which can be a personal computer, a server, or a network device, etc.) execute all or part of the steps of the method described in the embodiments of the present disclosure. The aforementioned storage medium can be a non-transitory storage medium, including: a U disk, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk, and various media that can store program codes, or can be a transitory storage medium.

[0091] The places not mentioned in the present application can be realized by using or referring to the existing technology.

[0092] The above only describes the embodiments of the present application and is not used to limit the present application. For those skilled in the art, the present application can have various changes and modifications. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the scope of claims of the present application.

Claims

1. A video encryption method based on linear fractional-order hyperbolic equation, characterized in that, The method comprises the following steps: S01) obtaining all image frames of a video to be encrypted, and performing normalization processing on all the image frames; S02) dividing each image frame into a plurality of matrix blocks of the same size, and performing Arnold transformation and grayscale scrambling operations on data information of each matrix block after the division; S03) encrypting the data information after the Arnold transformation and grayscale scrambling operations using a linear fractional order hyperbolic equation encryption model; The linear fractional order hyperbolic equation encryption model is defined as follows: ； ； wherein , is a given function whose common with as a key; and are boundary conditions; is a Caputo fractional term, ; In the encryption process, the data information after Arnold transformation and gray scrambling operation is taken as the function value at the initial moment The numerical solution of the fractional differential equation is solved by using the barycentric interpolation collocation method, and the function value at the final moment is obtained As ciphertext; S04) performing an XOR operation on the encrypted data information based on a chaotic sequence 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 a linear fractional order hyperbolic equation according to claim 1, characterized in that, In step S02), the Arnold transformation formula is as follows: ； In the formula, represents the pixel points to be encrypted in the image frame, represents the pixel points after the grayscale permutation, represents the length or width of the image to be encrypted, A and B are given data.

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

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

5. The video encryption method based on a linear fractional order hyperbolic equation according to claim 4, characterized in that, In step S04), the XOR operation of the chaotic sequence is performed based on the Logistic chaotic system, and the specific steps are as follows: S41) Parameters of the given Logistic chaotic system and system initial value , are random values in the range 0-1; S42) represents the sum of all pixel values of the encrypted image frame using the linear fractional-order hyperbolic equation as and mod 256, and then divides the integer part by 255, and the result of the operation is used as the auxiliary key ; S43) using the auxiliary key correcting the initial value to ; and correcting the initial value to as the initial value of the chaotic system, a chaotic sequence is constructed by a Logistic chaotic system mapping formula ; S44) converting the chaotic sequence to the form to obtain an improved chaotic sequence ; S45) sequentially taking one pixel point in the image frame, to represent the serial number of the point, based on constructing an encryption key: S46) For the first image frame The grayscale value of each pixel is XORed with the encryption key in step S45 to obtain the encrypted pixel value. S47) repeating steps S45) to S46) until all pixel points are encrypted to obtain the ciphertext data.

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

7. A computer-readable storage medium, characterized in that, A computer program is stored thereon, which is executed by a processor to implement the method according to any one of claims 1 to 5.

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