A two-channel audio encryption method and apparatus

Abstract

The application relates to a double-channel audio encryption method and device, which adopts a stream cipher system based on a 1+1-dimensional nonlinear fractional-order pseudo-parabolic equation encryption and decryption model to design a double-channel audio data encryption algorithm. Operations on audio data include subtraction (addition), key matrix averaging, encryption and decryption model numerical calculation, numerical constraint (release), etc. In the application, the signal time domain characteristics and signal spectrum characteristics of the encrypted audio data can be effectively concealed, the encryption algorithm effectively changes the audio data, and the encryption algorithm can effectively resist peak signal-to-noise ratio statistical attacks.

Description

Technical Field

[0001] The present application belongs to the technical field of data encryption and decryption, and specifically relates to a dual-channel audio encryption method and device. Background Art

[0002] Cryptography is a widely used data security technology. It is a crucial measure for application security when data is threatened by various attacks. The core of encryption and decryption technology lies in the encryption and decryption algorithm. Traditional symmetric encryption algorithms include AES and DES, while traditional asymmetric encryption algorithms include RSA. Common voice and image encryption algorithms include chaotic encryption and permutation encryption. Chaotic encryption uses the operation of chaotic equations to generate keys. The uncertainty of a chaotic model entering a chaotic state is equivalent to its security. Its advantage is that the chaotic state is unpredictable and difficult to crack. However, its disadvantage is that it is extremely sensitive to initial values; even slight differences in initial values ​​can lead to significant errors in the result. Permutation algorithms work by altering the position of the original digital signal to achieve encryption. The key is the relative position before and after the alteration. Its advantage is low encryption and decryption cost and overhead, but its disadvantage is relatively low security. In summary, traditional encryption and decryption algorithms are characterized by high cost, high algorithmic complexity, and unstable security performance. In today's network environment with high traffic, numerous users, wide coverage, and high requirements for information authenticity, it is particularly important to develop encryption and decryption algorithms with reduced errors, greater reliability, and stability. Summary of the Invention

[0003] The present invention provides a dual-channel audio encryption and decryption method, which can achieve high-reliability encryption and maintain encryption stability.

[0004] The technical solution of this application is as follows:

[0005] A dual-channel audio encryption method comprises the following steps:

[0006] Step 1: Get the two-channel audio data matrix Audio , whose dimensions are L ×2, which means as follows:

[0007] ;

[0008] In the formula, the first column represents the left channel data from top to bottom, and the second column represents the right channel data from top to bottom;

[0009] Step 2: Audio Perform matrix transformation operation of Euclidean subtraction to obtain Audio 1, which means the following:

[0010] ;

[0011] Step three: build a key matrix with dimension L × 2 Rand 1, build Rand 2 by averaging the elements in corresponding positions of Audio 1 and Audio 1

[0012] Step four: group the elements in Audio 2 after unfolding by column to form Audio 3, each group contains 16 elements in sequence and the last group is padded with 0 when it is less than 16 elements Audio Audio The specific form of 3 is as follows:

[0013]

[0014] Step five: use the encryption model of 1+1 dimensional nonlinear fractional pseudo-parabolic equation to perform numerical calculation on the data in Audio 3, the encryption model is:

[0015]

[0016] wherein u and t are parameter variables; denotes the 2nd order partial derivative of with respect to and the 1st order partial derivative of ; denotes the 1st order partial derivative of with respect to ; is a function of t ; is a boundary value condition; f ( x , t ) is a given function; T is a constant; denotes the Caputo fractional order term with respect to x ;

[0017] During encryption, the direct linearization iterative format of the nonlinear fractional pseudo-parabolic equation is solved by calculating the initial time, and the encryption of the remaining time is completed, which includes the following steps:

[0018] Step one: solve the function value Audio 3 at the initial time , including:

[0019] Discretize the spatial variable x and the time t respectively: ​​

[0020] ;

[0021] Then the discrete space variable at the initial moment is x The nodes are:

[0022] ;

[0023] Then the boundary conditions The corresponding discrete nodes are:

[0024] ;

[0025] Step 2: Discrete space variables at the initial moment x Node substitution function In the initial moment, we get the function value matrix , which is expressed as follows:

[0026] ;

[0027] Step 3: Construct one and Audio 3 calculation matrices with the same dimensions, and in the calculation matrices, wrapped with 0 Audio 3 is the non-zero initial function value; the calculation matrix is ​​in the following form:

[0028] ;

[0029] Step 4: Take Audio Each column of data in 3 is filled with the calculation matrix to obtain the encryption matrix at the initial moment:

[0030] ;

[0031] Where, the lower left corner subscript of the element means that the value of the i-th (i=2,3,4,5,6) order in the matrix is ​​calculated;

[0032] Step 5: Calculate the matrix form of the encryption model based on the direct linearization iterative format of the nonlinear fractional-order pseudo-parabolic equation T Function value matrix at time , which is expressed as follows:

[0033] ;

[0034] Based on the calculation matrix construction principle in step three and step four, we get T The encryption matrix at this moment:

[0035] ;

[0036] Step 6: Repeat step 5 toAudio 3. Each data in the encryption is encrypted. Audio The original data in 3 is arranged in order and encrypted to obtain the final encryption matrix Audio 4, expressed as:

[0037] ;

[0038] Step 6: Construct Dimensions and Audio 4 identical numerically labeled matrices G , the numerical label matrix G The initial value of the elements in are all 0;

[0039] Will Audio Remove the negative sign from the negative elements in 4. When you remove the negative sign of an element, that is, in the matrix G Add a value to the element position at the corresponding position; after all is completed, write Audio 4 for ;right The values ​​of the elements in the matrix are constrained. G Mark the value; after the constraint Expand to a column, delete some data at the end of the expanded column, the number of deleted data is the same as the number of 0s added in step 4; after the constraint operation is completed, the numerical label matrix is ​​recorded G is the key matrix;

[0040] The front of the expanded column data L Data and L The data are respectively used as the first and second columns to form a dual-channel ciphertext audio data matrix Audio 5.

[0041] Furthermore, in step five, the matrix form of the direct linearization iterative format encryption model of the nonlinear fractional-order pseudo-parabolic equation is:

[0042] ; ;

[0043] Where, R 1 represents the coefficient matrix, and They are x 、 t of p 1. p 2nd order differential matrix, is the integral matrix, is the gamma function, and They are m +1st level, l +1-order identity matrix;f For a given function.

[0044] Furthermore, in the matrix of the direct linearization iterative format encryption model of the nonlinear fractional-order pseudo-parabolic equation, the boundary conditions and initial adjustments are imposed by the permutation method, and the accuracy of the iterative calculation is set to e=10 -9 .

[0045] Furthermore, in step six, The values ​​of the elements in the matrix are constrained and G The method for numerical marking is:

[0046] When the element value is in the range [0,1), keep and matrix G Original data;

[0047] When the element value is in the interval [1,10), divide the element value by 10 in the matrix G The corresponding element position of plus 10;

[0048] When the element value is in the interval [10,20), divide the element value by 40 and add it to the matrix G The corresponding element position of plus 100;

[0049] When the element value is in the interval [20,40), divide the element value by 80 and add it to the matrix G The corresponding element position of plus 1000;

[0050] When the element value is in the interval [40,80), divide the element value by 160 and add it to the matrix G The corresponding element position is added by 10000;

[0051] When the element value is in the range [80,200), divide the element value by 400 and add it to the matrix G The corresponding element position is added by 100000;

[0052] When the element value is greater than or equal to 200, in the matrix G The corresponding element position of is reset to zero.

[0053] Furthermore, the processor is configured to execute the above-mentioned dual-channel audio encryption method when running the program instructions.

[0054] Due to the adoption of the above technical solution, the beneficial effects of this application are as follows:

[0055] This application utilizes a stream cipher, a non-traditional cryptographic encryption and decryption system centered around a class of differential equations. Key factors in this cryptographic system are numerical calculation methods and the choice of differential equations. This application designs an encryption algorithm for dual-channel audio data based on a (1+1)-dimensional nonlinear fractional-order pseudo-parabolic equation encryption and decryption model. Operations performed on the audio data include Euclidean addition (subtraction), key matrix averaging, encryption and decryption model numerical calculation, and numerical constraint (release). In this application, the signal time domain and signal spectrum characteristics of the encrypted audio data can be effectively masked. The histogram of the ciphertext audio data can differ significantly from that of the original plaintext audio data, indicating that the audio encryption algorithm effectively changes the frequency distribution range of the audio data. The correlation coefficients between the left and right channel data of the ciphertext audio and the original plaintext audio are both close to 0, indicating that the encryption algorithm effectively changes the audio data and can effectively resist peak signal-to-noise ratio statistical attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] 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:

[0057] Figure 1 A flow chart of a dual-channel audio encryption method provided by this application;

[0058] Figure 2 A flowchart of a decryption method corresponding to a dual-channel audio encryption method provided in this application;

[0059] Figure 3 A time domain comparison chart of the original audio, encrypted audio signal, and decrypted audio signal;

[0060] Figure 4 A comparison chart of the spectrograms of the original audio, the encrypted audio signal, and the decrypted audio signal;

[0061] Figure 5 is the distribution histogram of the original audio signal;

[0062] Figure 6 is the distribution histogram of the encrypted audio signal. DETAILED DESCRIPTION

[0063] Based on the background technology, as shown in the attached Figure 1 As shown, this application provides a dual-channel audio encryption method. The basic unit of audio data is the signal value. The audio can be a mono file or a dual-channel file. The principle is the same. This application is an encryption method for dual-channel audio, specifically including the following steps:

[0064] Step 1: Get the two-channel audio data matrixAudio , whose dimensions are L ×2, which means as follows:

[0065] ;

[0066] In the formula, the first column represents the left channel data from top to bottom, and the second column represents the right channel data from top to bottom.

[0067] exist Audio In the figure, the number in the lower right corner of the element indicates the number of data.

[0068] Step 2: Audio Perform matrix transformation operation of Euclidean subtraction to obtain Audio 1, which means the following:

[0069] .

[0070] The matrix transformation operation of Euclidean subtraction in step 2 is to first subtract the second column from the first column of the matrix to replace the first column of the original matrix, and then subtract the replaced first column from the second column data. That is:

[0071] .

[0072] Step 3: Create a dimension L ×2 key matrix Rand 1. Rand 1 and Audio The elements at the corresponding positions in 1 are averaged and then established Audio 2. That is:

[0073] .

[0074] Step 4: Audio The elements in 2 are grouped and expanded into columns Audio 3. In Audio In 3, each group contains 16 elements in sequence and when the last group has less than 16 elements, it is padded with 0; Audio The specific form of 3 is as follows:

[0075] .

[0076] Will Audio 2 data are expanded by column, there are 2 L There are 16 data in each group. If the last group is less than 16, it will be padded with 0, thus obtaining Group data.

[0077] Step 5: Use the encrypted model of 1+1 dimensional nonlinear fractional-order pseudo-parabolic equation to Audio3, the encryption model is:

[0078]

[0079] where, u and t are parameter variables; denotes the second-order partial derivative of with respect to and the first-order partial derivative of with respect to ; t denotes the first-order partial derivative of t with respect to f ; x , t are given functions; T is a constant; denotes the Caputo fractional order term with respect to x . is the boundary condition.

[0080] In encryption, the direct linearization iterative format of the nonlinear fractional pseudo-parabolic equation is solved by calculating the initial time, and the encryption of the remaining time is completed, which includes the following steps:

[0081] Step 1: Solve Audio 3corresponding to the function value at the initial time , including:

[0082] Discretize the spatial variable x and time t respectively:

[0083] ;

[0084] Then the nodes of the discrete spatial variable x at the initial time are respectively:

[0085] ;

[0086] The discrete nodes corresponding to the boundary condition are respectively:

[0087] ;

[0088] Step 2: Substitute the nodes of the discrete spatial variable x at the initial time into the function , get the function value matrix at the initial time , which is expressed as:

[0089] ​ ;

[0090] Step 3: Construct one and Audio 3 calculation matrices with the same dimensions, and in the calculation matrices, wrapped with 0 Audio 3 is the non-zero initial function value; the calculation matrix is ​​in the following form:

[0091] .

[0092] because Audio Each data set in 3 has 16 elements. Therefore, if the encrypted data is wrapped with 0, the dimension of the calculation matrix is ​​6 × 6. It should be noted that wrapping with 0 in this step means wrapping with a layer of 0.

[0093] In the calculation matrix, the number in the lower left corner of the element indicates the number of times this column of data is obtained in the numerical calculation in this matrix.

[0094] Step 4: Take Audio Each column of data in 3 is filled with the calculation matrix to obtain the encryption matrix at the initial moment:

[0095] .

[0096] Step 5: Calculate the matrix form of the encryption model based on the direct linearization iterative format of the nonlinear fractional-order pseudo-parabolic equation T Function value matrix at time , which is expressed as follows:

[0097] ;

[0098] Based on the calculation matrix construction principle in step three and step four, we get T The encryption matrix at this moment:

[0099] .

[0100] The calculation matrix is ​​in the form of:

[0101] .

[0102] The matrix form of the direct linearization iterative format encryption model for nonlinear fractional-order pseudo-parabolic equations is:

[0103] ; ;

[0104] Where, R 1 represents the coefficient matrix, and They are x 、t of p 1. p 2nd order differential matrix, is the integral matrix, is the gamma function, and They are m +1st level, l +1-order identity matrix. In the matrix of the direct linearization iterative format encryption model of the nonlinear fractional-order pseudo-parabolic equation, the permutation method is used to impose boundary conditions and initial adjustments, and the accuracy of the iterative calculation is set to e=10 -9 .

[0105] Step 6: Repeat step 5 to Audio 3. Each data in the encryption is encrypted. Audio The original data in 3 is arranged in order and encrypted to obtain the final encryption matrix Audio 4, expressed as:

[0106] ;

[0107] Step 6: Construct Dimensions and Audio 4 identical numerically labeled matrices G , the numerical label matrix G The initial values ​​of the elements in the matrix are all 0; G Expressed as:

[0108] .

[0109] Will Audio Remove the negative sign from the negative elements in 4. When you remove the negative sign of an element, that is, in the matrix G Add a value to the element position at the corresponding position; after all is completed, write Audio 4 for ;right The values ​​of the elements in the matrix are constrained. G Mark the value; after the constraint Expand to a column, delete some data at the end of the expanded column, the number of deleted data is the same as the number of 0s added in step 4; after the constraint operation is completed, the numerical label matrix is ​​recorded G is the key matrix; The values ​​of the elements in the matrix are constrained and G The method for numerical marking is:

[0110] When the element value is in the range [0,1), keep and matrix G Original data;

[0111] When the element value is in the interval [1,10), divide the element value by 10 in the matrix G The corresponding element position of plus 10;

[0112] When the element value is in the interval [10,20), divide the element value by 40 and add it to the matrix G The corresponding element position of plus 100;

[0113] When the element value is in the interval [20,40), divide the element value by 80 and add it to the matrix G The corresponding element position of plus 1000;

[0114] When the element value is in the interval [40,80), divide the element value by 160 and add it to the matrix G The corresponding element position is added by 10000;

[0115] When the element value is in the range [80,200), divide the element value by 400 and add it to the matrix G The corresponding element position is added by 100000;

[0116] When the element value is greater than or equal to 200, in the matrix G The corresponding element position of is reset to zero.

[0117] Finally, the front of the expanded column data L Data and L The data are respectively used as the first and second columns to form a dual-channel ciphertext audio data matrix Audio 5.

[0118] The decryption method of the above encryption method is the inverse operation of the algorithm.

[0119] As attached Figure 2 As shown, for the dual-channel ciphertext audio data matrix Audio 5, whose dimensions are L ×2, that is L Row 2 column, where Left 1 means the first data of the left channel (column 1), Right 1 represents the first data of the right channel (column 2), and so on.

[0120] .

[0121] Will Audio 5 data are expanded by column, with a total of 2 L There are 16 data in each group. If the last group is less than 16, it will be padded with 0, thus obtaining Group data. After writing into a matrix:

[0122] .

[0123] According to the matrix G and binding rules release .

[0124] The specific expression is:

[0125] .

[0126] 、 、 、 、 、 Represents the numerical label matrix G exist The units, tens, hundreds, thousands, ten thousand, and hundred thousand digits of the element value are released, and the data matrix after the values ​​are released is recorded as:

[0127] .

[0128] The data in the above matrix is ​​numerically calculated using the decryption model. The decryption model of the heat flow cipher system in this paper is:

[0129] ;

[0130] Assume the boundary condition is 0, the data matrix to be decrypted Corresponding to the function value at the final value moment Time variable x and spatial variables t are discretized into

[0131]

[0132] Discretized spatial variables at the terminal time x The nodes are:

[0133] ;

[0134] Boundary conditions The corresponding discrete nodes are:

[0135] ;

[0136] Substitute all interpolation nodes into the function In the figure, the function value matrix at the final value moment is :

[0137] .

[0138] Write the data to be decrypted into the middle 4 of the 6 final value interpolation nodes, and perform a numerical calculation to decrypt the 4 data. Each set of data has 16, and the following 6×6 dimension matrix is ​​designed:

[0139] ;

[0140] The data to be decrypted is written into the middle 16-bit non-zero element position. Each numerical calculation takes 1 column of data. The subscript in the lower left corner of the element means the number of times this column of data is taken in the numerical calculation in this matrix. Each set of data in fills the 6×6 dimensional matrix to obtain:

[0141]

[0142] One numerical calculation decrypts 16 data.

[0143] The matrix form of the direct linearization iterative format decryption model of the nonlinear fractional-order pseudo-parabolic equation is:

[0144]

[0145] Use the displacement method to impose boundary conditions and final value conditions, and set the accuracy of the iterative calculation to e=10 -9 , numerically calculate the function value matrix at the initial moment for:

[0146]

[0147] The 6×6 dimensional matrix corresponding to the function value at the final value moment has the following matrix form at the initial moment:

[0148]

[0149] The result at the initial moment corresponds to the decrypted matrix:

[0150] .

[0151] Will The 16 data in each column are numerically calculated according to this method, and then rearranged in order to obtain the data matrix decrypted by the equation decryption model. , the expression is

[0152]

[0153] Will Audio 3 Expand by column and take the first 2 L data, and discard the rest of the data. L The data is used as the left channel signal of the audio data. L The data is used as the right channel signal of the audio data and recombined into a dimension of The data matrix Audio 2, Audio 2 and key matrix Rand 1 Perform the following operations:

[0154]

[0155] Get the data matrix Audio 1. Assume Audio The expression for 1 is

[0156]

[0157] in and They represent the first signal data of the left channel and the first signal data of the right channel of the current audio data, respectively, and the rest are similar.

[0158] for Audio 1. Perform Euclidean addition on the two columns of the data matrix. The data in the second column plus the data in the first column replace the original data in the second column, and the data in the first column plus the replaced data in the second column replace the original data in the first column. The Euclidean addition process is equivalent to matrix transformation:

[0159]

[0160] Audio That is the decrypted audio data:

[0161]

[0162] in and They represent the first signal data of the left channel and the first signal data of the right channel of the current audio data, respectively, and the rest are similar.

[0163] In this embodiment, the feasibility and security of the audio encryption and decryption algorithm are verified by simulation experiments. ,The simulation software is MATLAB (R2020b), the processor is Intel Core i7-11800H, the 64-bit operating system is Windows 11, and the running memory is 16GB. ,The information of the encrypted and decrypted audio in the simulation ,experiment is shown in Table 1.

[0164] Table 1 Simulation experiment audio information

[0165]

[0166] As attached Figure 3As shown in the figure, the encryption algorithm of the present application effectively masks the time domain characteristics of the audio signal, and no valid audio signal information can be obtained from the figure. The time domain diagram of the decrypted plaintext audio signal shows that the time domain characteristics of the decrypted audio signal are highly consistent with the time domain characteristics of the original plaintext audio signal, that is, the decryption algorithm can effectively restore the audio data.

[0167] As attached Figure 4 As shown, the signal spectrum is the result of statistical analysis of speech signals with different frequency band amplitudes. The signal spectrum of the ciphertext audio data shows that the audio encryption algorithm of this application effectively masks the spectral characteristics of the audio signal. The frequency amplitude of the signal is concentrated at a few specific values: 0, 0.5, and 1.5, making it impossible to obtain valuable information based on the frequency distribution. The spectrum of the decrypted plaintext audio signal shows that the spectral characteristics of the decrypted audio signal are highly consistent with those of the original plaintext audio signal, indicating that the decryption algorithm can effectively restore the plaintext audio data.

[0168] As attached Figure 5 and attached Figure 6 As shown in the figure, a histogram is drawn based on the distribution of the audio signal to verify whether the encryption algorithm has effectively changed the signal distribution of the original plaintext audio data. The horizontal axis of the histogram represents the amplitude of the signal, and the vertical axis represents the proportion of the signal at this amplitude to the total number of signals. Figure 5 is the signal distribution histogram of the original plaintext two-channel data, which is generally normally distributed with the symmetry axis being x=0. Figure 6 The signal distribution histogram of the two channel data of the ciphertext shows that its amplitude range is 0~1, which is different from the interval symmetrical about x=0 of the original plaintext. Its frequency value and frequency statistical range have changed significantly, indicating that the encryption algorithm of this application has effectively changed the distribution law of the audio signal.

[0169] Table 2 Audio correlation data

[0170]

[0171] Table 3 Sample PSNR averages

[0172]

[0173] Table 2 and Table 3 respectively list the correlation degree of the left and right channel data before and after encryption from the perspective of audio data correlation angle, and the peak signal-to-noise ratio (PSNR) of the left and right channels before and after audio encryption to evaluate the encryption effect of the audio. As can be seen from Table 2 and Table 3, the correlation coefficients of the two channels of the audio before and after encryption are very close to 0, which shows that the audio encryption algorithm in this paper effectively changes the audio data; the PSNR values of the left and right channel data are small, which shows that the encrypted audio is quite different from the audio before encryption, effectively conceals the information in the audio data, and can better resist cracking attacks based on peak signal-to-noise ratio statistics.

[0174] The embodiments of the present disclosure also provide a dual-channel audio encryption device, 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 logical instructions in the memory to execute the dual-channel audio encryption method of the above-mentioned embodiments.

[0175] The places not mentioned in the present application can be realized by using or referring to the existing technology.

[0176] The above only describes the embodiments of the present application and is not used to limit the present application. The present application can have various changes and variations for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the scope of claims of the present application.

Claims

1. A dual-channel audio encryption method, characterized in that: The following steps are involved: Step 1: Get the two-channel audio data matrix Audio , whose dimensions are L ×2, which means as follows: ； In the formula, the first column represents the left channel data from top to bottom, and the second column represents the right channel data from top to bottom; Step 2: Audio Perform matrix transformation operation of Euclidean subtraction to obtain Audio 1, which means the following: ； Step 3: Create a dimension L ×2 key matrix Rand 1. Rand 1 and Audio The elements at the corresponding positions in 1 are averaged and then established Audio 2; Step 4: Audio The elements in 2 are grouped and expanded into columns Audio 3. In Audio In 3, each group contains 16 elements in sequence and when the last group has less than 16 elements, it is padded with 0; Audio The specific form of 3 is as follows: ； Step 5: Use the encrypted model of 1+1 dimensional nonlinear fractional-order pseudo-parabolic equation to Audio 3. The encryption model is as follows: ； Where, u and t is a parameter variable; express right Find the second-order partial derivatives of Find the first-order partial derivative; express right Find the first-order partial derivative; for t is the function at time zero; is the boundary condition; f ( x , t ) is a given function; T is a constant; Indicates about x Caputo fractional terms; During encryption, the initial moment is calculated and the direct linearized iterative format of the nonlinear fractional-order pseudoparabolic equation is solved to complete the encryption of the remaining moments. The specific steps include the following: Step 1: Solve Audio 3 corresponds to the function value at the initial moment ,include: The spatial variable x and time t Discrete into: ； Then the discrete space variable at the initial moment is x The nodes are: ； Then the boundary conditions The corresponding discrete nodes are: ； Step 2: Discrete space variables at the initial moment x Node substitution function In the initial moment, we get the function value matrix , which is expressed as follows: ； Step 3: Construct one and Audio 3 calculation matrices with the same dimensions, and in the calculation matrices, wrapped with 0 Audio 3 is the non-zero initial function value; the calculation matrix is ​​in the following form: ； Step 4: Take Audio Each column of data in 3 is filled with the calculation matrix to obtain the encryption matrix at the initial moment: ； In the formula, the lower left corner subscript of the element means the first i ( i =2,3,4,5,6) times are calculated; Step 5: Calculate the matrix form of the encryption model based on the direct linearization iterative format of the nonlinear fractional-order pseudo-parabolic equation T Function value matrix at time , which is expressed as follows: ； Based on the calculation matrix construction principle in step three and step four, we get T The encryption matrix at this moment: ； Step 6: Repeat step 5 to Audio 3. Each data in the encryption is encrypted. Audio The original data in 3 is arranged in order and encrypted to obtain the final encryption matrix Audio 4, expressed as: ； Step 6: Construct Dimensions and Audio 4 identical numerically labeled matrices G , the numerical label matrix G The initial value of the elements in are all 0; Will Audio Remove the negative sign from the negative elements in 4. When you remove the negative sign of an element, that is, in the matrix G Add a value to the element position at the corresponding position; after all is completed, write Audio 4 for ;right The values ​​of the elements in the matrix are constrained. G Mark the value; after the constraint Expand to a column, delete some data at the end of the expanded column, the number of deleted data is the same as the number of 0s added in step 4; after the constraint operation is completed, the numerical label matrix is ​​recorded G is the key matrix; The front of the expanded column data L Data and L The data are respectively used as the first and second columns to form a dual-channel ciphertext audio data matrix Audio 5.

2. A dual-channel audio encryption method according to claim 1, characterized in that: In step 5, the matrix form of the direct linearization iterative format encryption model of the nonlinear fractional-order pseudo-parabolic equation is: ； ； Where, R 1 represents the coefficient matrix, and They are x 、 t of p 1. p 2nd order differential matrix, is the integral matrix, is the gamma function, and They are m +1st level, l +1-order identity matrix; f For a given function.

3. A dual-channel audio encryption method according to claim 2, characterized in that: In the matrix of the direct linearization iterative format encryption model of the nonlinear fractional-order pseudo-parabolic equation, the boundary conditions and initial adjustments are imposed by the permutation method, and the accuracy of the iterative calculation is set to e=10 -9 .

4. A dual-channel audio encryption method according to claim 3, characterized in that: In step six, The values ​​of the elements in the matrix are constrained and G The method for numerical marking is: When the element value is in the range [0,1), keep and matrix G Original data; When the element value is in the interval [1,10), divide the element value by 10 in the matrix G The corresponding element position of plus 10; When the element value is in the interval [10,20), divide the element value by 40 and add it to the matrix G The corresponding element position of plus 100; When the element value is in the interval [20,40), divide the element value by 80 and add it to the matrix G The corresponding element position of plus 1000; When the element value is in the interval [40,80), divide the element value by 160 and add it to the matrix G The corresponding element position is added by 10000; When the element value is in the range [80,200), divide the element value by 400 and add it to the matrix G The corresponding element position is added by 100000; When the element value is greater than or equal to 200, in the matrix G The corresponding element position of is reset to zero.

5. A dual-channel audio encryption device, comprising a processor and a memory storing program instructions, characterized in that: The processor is configured to execute a dual-channel audio encryption method according to any one of claims 1 to 4 when running the program instructions.

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