Encryption method based on switched inertial neural network with leakage time delay

Abstract

An encryption method based on a switching inertia neural network with leakage time lag relates to the field of audio encryption. It solves the problem that the existing encryption method that relies on neural networks adopts a fixed network structure and a static processing mechanism, resulting in the encryption effect being limited by the model performance. The switching inertia neural network with a mixed time-varying delay and leakage time lag constructed by the present invention is used as an audio encryption drive system; and an audio decryption response system is constructed based on the designed synchronization controller and the audio encryption drive system; the subsequent encryption and decryption process is realized under the condition of global exponential synchronization controlled by the synchronization controller. The existence of multiple time lags forms a mixed time-varying delay, and the dynamic behavior of the system is more difficult to predict. The introduction of the time lag inertia weight factor makes the encryption process more complicated, has stronger resistance to randomness and reversibility, and the design of the synchronization controller greatly increases the difficulty of cracking. It is mainly used for the encryption of audio data.

Description

Technical Field

[0001] The present invention relates to the field of audio encryption. Background Art

[0002] With the advent of the digital age, the demand for digital audio information storage and transmission is growing. However, the complexity of network environments and the insecurity of information transmission pose significant challenges to the protection of audio information. To protect the confidentiality, integrity, and availability of audio data during transmission and storage, audio encryption technology has emerged. The research and application of audio encryption technology continues to attract attention from both scientific research and industry. A diverse range of technical approaches has emerged, including traditional encryption methods using symmetric key algorithms (such as AES) and asymmetric key algorithms (such as RSA), as well as innovative methods using digital watermarking to hide audio information. Each method has its own unique advantages and applicable scenarios, meeting the diverse needs of different users for security, speed, and convenience. Furthermore, in terms of technical features and progress, audio encryption technology is developing towards higher security and reliability. Researchers are continuously exploring new encryption algorithms and key management mechanisms to improve the security and randomness of encryption technology. Although audio encryption technology plays an important role in ensuring the security of audio data, it still faces some technical challenges. With the continuous improvement of computing power, the security of existing encryption algorithms may be threatened. Therefore, continuous research and development of more secure encryption algorithms is necessary. Early audio encryption algorithms may have design flaws, resulting in deficiencies in attack resistance, randomness, and reversibility. This can make encrypted audio data vulnerable to complex attacks, making it impossible to guarantee data confidentiality.

[0003] Neural networks perform large numbers of calculations through parallel distributed processing, enabling efficient encryption and decryption of audio data. This processing capability not only increases encryption speed but also reduces computational costs, making audio encryption technology more suitable for scenarios requiring high real-time performance. Artificial neural networks are based on nonlinear functions and can handle complex nonlinear relationships. This capability enables audio encryption systems to better capture subtle changes and features in audio data, thereby providing more secure and reliable encryption protection. Traditional neural networks typically use fixed network structures, such as multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs). These networks consist of multiple layers of neurons, with each layer connected to the previous and next layers, forming a fixed connection pattern. In audio encryption applications, traditional neural networks learn the characteristics of audio data through training and use these features in the encryption and decryption processes. However, due to their fixed network structure and static processing mechanisms, the encryption effectiveness of traditional artificial neural networks is limited by the model's performance.

[0004] Therefore, it is necessary to invent a method with higher anti-attack, randomness and reversibility to improve the security and complexity of audio encryption technology. Summary of the Invention

[0005] The purpose of the present invention is to solve the problem that the existing encryption methods that rely on neural networks adopt a fixed network structure and a static processing mechanism, resulting in the encryption effect being limited by the model performance. The present invention provides an encryption method based on a switching inertia neural network with leakage lag.

[0006] An encryption method based on a switched inertial neural network with leakage lag, the method comprising the following steps:

[0007] (1) Initial setup phase:

[0008] A switching inertial neural network with hybrid time-varying delay and leakage delay is constructed as an audio encryption driving system.

[0009] Construct an audio decryption response system based on the designed synchronization controller and audio encryption drive system;

[0010] After calculating the synchronization controller gain parameters through the synchronization condition inequality, the synchronization controller is used to control the audio encryption drive system and the audio decryption response system to achieve global exponential synchronization;

[0011] (2) Encryption and decryption stage:

[0012] The encryption process includes: treating the original audio to be encrypted, at a sampling rate of F s Sampling and normalization are performed to obtain the normalized original audio data matrix

[0013] The set transfer parameter q is used as the input data of the audio encryption driving system, and the encrypted data matrix is ​​generated according to the system neuron state change rate of the audio encryption driving system. Where q = Y b +1000, Y b is the number of audio samples;

[0014] According to the maximum upper bound of the absolute value of the derivation feedback coefficient and the set consisting of the maximum upper bounds of the absolute values ​​of multiple time lags Construct the time-delay inertia weight factor ξ; and are the maximum upper bounds of the absolute values ​​of leakage delay, transmission delay and distribution delay respectively;

[0015] Using ξ Encrypt and obtain encryption key coefficient

[0016] according to and ξ Scaling to construct the key factor key matrix

[0017] use right Encrypt and obtain the encrypted audio data matrix

[0018] The specific decryption process includes: At the sampling rate F s Sampling and normalization are performed to obtain the normalized ciphertext matrix

[0019] The set transfer parameter q is used as the input data of the audio decryption response system, and the decryption data matrix is ​​generated according to the system neuron state change rate of the audio decryption response system. Where q = Y b +1000, Y b is the number of audio samples,

[0020] According to the maximum upper bound of the absolute value of the derivation feedback coefficient and the set consisting of the maximum upper bounds of the absolute values ​​of multiple time lags Construct the time-delay inertia weight factor ξ; and are the maximum upper bounds of the absolute values ​​of leakage delay, transmission delay and distribution delay respectively;

[0021] Using ξ Decrypt and obtain the decryption key coefficient

[0022] according to and ξ to construct the key factor decryption matrix

[0023] use right Decrypt and get the decrypted audio data matrix

[0024] Preferably,

[0025]

[0026]

[0027] for The element in row i and column j of Y b ×X dThe real matrix of is the original audio data matrix before normalization The element in row i and column j in Indicates a set of integers;

[0028] Encrypted data matrix The element in row i and column j′ in Indicates Y b ×(X d +1), is the state change rate of the j′th neuron in the audio encryption driving system, X d is the number of audio channels;

[0029] is the normalized ciphertext matrix The element in row i and column j in is the ciphertext matrix before normalization The element in row i and column j of ;

[0030] To decrypt the data matrix The element in row i and column j′ in The rate of change of the j′th neuron in the audio decryption response system; X d is the number of audio channels, =1×(X d +1).

[0031] Preferably,

[0032] round(·) means rounding the value to the nearest integer.

[0033] Preferably,

[0034]

[0035]

[0036]

[0037] is the key factor key matrix The element in row i and column j′ of ;

[0038] bitget(·) means taking the first 10 bits from the lowest to the highest bit in the binary representation; round(·) means rounding the value to the nearest integer; k is the bit number in the binary representation;

[0039]

[0040] Encrypted data matrix The element in row i and column j′ in Indicates Y b ×(X d +1), is the state change rate of the j′th neuron in the audio encryption driving system, X d is the number of audio channels, Indicates a set of integers.

[0041] Preferably,

[0042]

[0043] β ij Encrypted audio data matrix The element in row i and column j in Y b ×X d The real matrix, X d is the number of audio channels;

[0044] for The element in row i and column j of is the key factor key matrix The element in row i and column j in is the key factor key matrix The i-th row and the X-th d +1 column of elements, Indicates Y b ×(X d +1).

[0045] Preferably,

[0046]

[0047]

[0048] To decrypt the data matrix The element in row i and column j′ in Indicates Y b ×(X d +1), bitget(·) means taking the first 10 bits from the low bit to the high bit in the binary representation, and round(·) means rounding the value to the nearest integer. It represents a set of integers, and k is the bit number in the binary representation.

[0049] Preferably,

[0050]

[0051] Decrypt the matrix for the key factor The element in row i and column j′ in X d is the number of audio channels, Indicates taking a set of integers, round(·) means rounding the value to the nearest integer. Indicates Y b ×(X d +1).

[0052] Preferably,

[0053]

[0054] The decrypted audio data matrix The element in row i and column j in is the normalized ciphertext matrix The element in row i and column j in Decrypt the matrix for the key factor The element in row i and column j in Decrypt the matrix for the key factor The element in row i and column j+1 in Indicates a set of integers; Y b ×X d The real matrix of Y b ×(X d +1), X d The number of audio channels.

[0055] Preferably,

[0056] The expression of the inertia term of each neuron in the audio encryption drive system is:

[0057]

[0058] The expression of the inertia term of each neuron in the audio decryption response system is:

[0059]

[0060] The expressions of each control component in the synchronous controller are:

[0061]

[0062] is the inertia term of the j′th neuron of the audio encryption drive system, is the state change rate of the j′th neuron in the audio encryption driving system, x j′ (t) is the state of the j′th neuron in the audio encryption driving system at time t, x j′ (td j′w (t)) is td j′w (t) The state of the j′th neuron in the audio encryption driving system, x j′ (t-δ j′ (t)) is t-δ j′ (t) The state of the j′th neuron in the audio encryption driving system, x j′ (θ) is the state of the j′th neuron of the audio encryption driving system, θ is the integral variable, t is the time, t∈[0,Y b +1000], <n>It is a set of integers consisting of 1, 2, 3...n, n = X d +1, X d Indicates the number of audio channels; τ j′w (t) is the wth distributed time lag of the audio encryption driving system or the j′th neuron of the audio encryption driving system;

[0063] is the derivation feedback coefficient of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), is the self-feedback coefficient of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), as well as is the wth component of the first to third connection weights of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), δ j′ (t) is the leakage lag of the audio encryption driving system or the j′th neuron of the audio encryption driving system, d j′w (t) is the wth transmission delay of the audio encryption driving system or the j′th neuron of the audio encryption driving system, as well as are the w-th summation components of the first to third activation functions respectively;

[0064] is the inertia term of the j′th neuron in the audio decryption response system, is the rate of change of the j′th neuron in the audio decryption response system, y j′ (t) is the state of the j′th neuron in the audio decryption response system at time t, y j′ (t-δ j′ (t)) is t-δ j′ (t) The state of the j′th neuron in the audio decryption response system, y j′ (td j′w (t)) is td j′w (t) The state of the j′th neuron in the audio decryption response system, y j′ (θ) is the state of the j′th integrated neuron in the audio decryption response system, u j′ (t) is the j′th control component of the synchronous controller;

[0065] For the αth k The j′th component of the derivation feedback coefficient in the switching state, α k is a variable, is a set of integers consisting of 1, 2, 3...P. For the αth k The j′th gain component of the first gain parameter of the synchronous controller in the switching state, For the αth k The j′th gain component of the second gain parameter of the synchronous controller in the switching state,

[0066] Preferably, the implementation of calculating the synchronization controller gain parameter by the synchronization condition inequality includes:

[0067] First, calculate the synchronization condition inequality to solve the unknown quantity and Among them, the synchronization condition inequality is:

[0068]

[0069] For the αth k The j′th component of the first unknown quantity in the switching state, For the αth k The j′th component of the second unknown quantity in the switching state, for and The first proportional relationship expression is: for and The second proportional relationship expression is: For the αth k The j′th self-feedback coefficient in the switching state, is the upper bound of the absolute value of the first-order derivative of the leakage delay, is the upper bound of the absolute value of the second-order derivative of the leakage lag, for The algebraic expression composed of and λ is is the upper bound of the absolute value of the j′th leakage delay, λ is the decay rate of global exponential synchronization, λ>0, for The algebraic expression composed of and λ is is the j′th neuron in the αth k The maximum upper bound of the absolute value of the wth component of the distributed delay in the switching state is, For the αth k A given parameter in a switching state; G w The wth summation term of the maximum upper bound of the absolute value of the derivative of the activation function that satisfies the Lipschitz condition, for and The algebraic expression composed of is the j′th neuron in the αth k The wth component of the first connection weight in the switching state, is the j′th neuron in the αth k The wth component of the second connection weight in the switching state, e (·) is an exponential function, is the j′th neuron in the αth k The maximum upper bound of the absolute value of the wth component of the transmission delay in the switching state is, is the j′th neuron in the αth k The wth component of the third connection weight in the switching state, <n>It is a set of integers consisting of 1, 2, 3...n, n = X d +1, X d Indicates the number of audio channels,< / n> It is a set of integers consisting of 1, 2, 3...P.

[0070] Secondly, according to and get

[0071] For the αth k The j′th gain component of the first gain parameter of the synchronous controller in the switching state, For the αth k The j′th gain component of the second gain parameter of the synchronous controller in the switching state,

[0072] Advantages of the present invention:

[0073] It can be seen from the encryption steps that the method proposed in the present invention for audio encryption using a switching inertia neural network with multiple time delays combined with a time delay inertia weight factor can better encrypt audio files; the inertia neural network has a more complex dynamic behavior and can better resist attacks from external attackers; at the same time, due to the introduction of the switching signal, a dynamic processing mechanism is formed, and the encryption drive system of the method of the present invention is more difficult to be intercepted by attackers; and due to the existence of multiple time delays (leakage delay, transmission delay and distribution delay), the dynamic behavior of the system is more difficult to predict, and in comparison, the present method has higher security; moreover, the design of the synchronization controller and the design of the synchronization condition inequality can not only achieve the synchronization of the drive-response system, but are also relatively complex, which greatly increases the difficulty of cracking; in addition, the introduction of the time delay inertia weight factor makes the encryption process of the present method more complex, and has stronger resistance to randomness and reversibility.

[0074] In addition to the above, the encryption process of this method also includes the design of a synchronous controller for the drive-response system. The designed controller also includes state feedback (i.e., the state of the j′th neuron of the audio decryption response system minus the state of the j′th neuron of the audio encryption drive system, i.e., y j′ (·)-x j′ (t)) and the derivation feedback (i.e., the rate of change of the j′th neuron in the audio decryption response system minus the rate of change of the state of the j′th neuron in the audio encryption drive system), that is: ), and the controller also contains the parameters of the inertial neural network. In the case of an unknown controller, it is extremely difficult to crack. In addition, the synchronization condition inequality for calculating the controller gain is the first of its kind in this method and is relatively complex. In the case of an unknown synchronization condition inequality, it is extremely difficult to crack.

[0075] The present invention has a large key space, high key sensitivity and high resistance to statistical analysis attacks. It can resist brute force attacks and even attacks by quantum computers, and can effectively ensure security, encryption effect and explainability. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 is a flow chart of an encryption method based on a switched inertial neural network with leakage time lag;

[0077] Figure 2 is a switching signal diagram of the inertial neural network switching of the present invention;

[0078] Figure 3 is the global exponential synchronization graph when j′∈{3}; Figure 3 a is the synchronous state response diagram of the error system, Figure 3 b is the synchronous state response diagram of the error system’s rate of change; Figure 4 The waveform of the original audio channel to be encrypted;

[0079] Figure 5 It is the waveform of the encrypted audio channel;

[0080] Figure 6 To decrypt the audio channel waveform;

[0081] Figure 7 This is the key sensitivity analysis effect diagram; among them, Figure 7 a is the first key sensitivity analysis effect diagram, Figure 7 b is the second key sensitivity analysis effect diagram, Figure 7 c is the third key sensitivity analysis effect diagram, Figure 7 d is the fourth key sensitivity analysis effect diagram,

[0082] Figure 8 For statistical analysis of audio histogram; Figure 8 a is the statistical analysis audio histogram of the left channel of the original audio, Figure 8 b is the audio histogram of the right channel statistical analysis of the original audio, Figure 8 c is the audio histogram of the left channel statistical analysis of the encrypted audio, Figure 8 d is the audio histogram of the right channel statistical analysis of the encrypted audio. DETAILED DESCRIPTION

[0083] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0084] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features therein may be combined with each other.

[0085] The present invention introduces a switching inertia neural network with a hybrid time-varying delay and leakage time lag as an audio encryption drive system; and constructs an audio decryption response system based on the designed synchronization controller and the audio encryption drive system; the audio decryption response system includes a partial neural network and a synchronization controller of the audio decryption response system corresponding to the switching inertia neural network in the audio encryption drive system, and the subsequent encryption and decryption process is realized under the condition of global exponential synchronization by controlling the audio encryption drive system and the audio decryption response system through the synchronization controller, and the audio encryption is combined with the time lag inertia weight factor during the encryption stage to better encrypt the audio file; an encryption method based on a switching inertia neural network with leakage time lag is proposed, and a method for audio encryption using a switching inertia neural network with multiple time lags combined with a time lag inertia weight factor is proposed to solve the problem that the encryption effect is limited by the model performance. The specific implementation method is as follows;

[0086] See also Figure 1 This embodiment describes an encryption method based on a switching inertial neural network with leakage lag, characterized in that the method comprises the following steps:

[0087] (1) Initial setup phase:

[0088] A switching inertial neural network with hybrid time-varying delay and leakage delay is constructed as an audio encryption driving system.

[0089] Construct an audio decryption response system based on the designed synchronization controller and audio encryption drive system;

[0090] After calculating the synchronization controller gain parameters through the synchronization condition inequality, the synchronization controller is used to control the audio encryption drive system and the audio decryption response system to achieve global exponential synchronization;

[0091] (2) Encryption and decryption stage:

[0092] The encryption process includes: treating the original audio to be encrypted, at a sampling rate of F s Sampling and normalization are performed to obtain the normalized original audio data matrix

[0093] The set transfer parameter q is used as the input data of the audio encryption driving system, and the encrypted data matrix is ​​generated according to the system neuron state change rate of the audio encryption driving system. Where q = Y b +1000, Y b is the number of audio samples;

[0094] According to the maximum upper bound of the absolute value of the derivation feedback coefficient and the set consisting of the maximum upper bounds of the absolute values ​​of multiple time lags Construct the time-delay inertia weight factor ξ; and are the maximum upper bounds of the absolute values ​​of leakage delay, transmission delay and distribution delay respectively;

[0095] Using ξ Encrypt and obtain encryption key coefficient

[0096] according to and ξ Scaling to construct the key factor key matrix

[0097] use right Encrypt and obtain the encrypted audio data matrix

[0098] The specific decryption process includes: At the sampling rate F s Sampling and normalization are performed to obtain the normalized ciphertext matrix

[0099] The set transfer parameter q is used as the input data of the audio decryption response system, and the decryption data matrix is ​​generated according to the system neuron state change rate of the audio decryption response system. Where q = Y b +1000, Y b is the number of audio samples,

[0100] According to the maximum upper bound of the absolute value of the derivation feedback coefficient and the set consisting of the maximum upper bounds of the absolute values ​​of multiple time lags Construct the time-delay inertia weight factor ξ; and are the maximum upper bounds of the absolute values ​​of leakage delay, transmission delay and distribution delay respectively;

[0101] Using ξ Decrypt and obtain the decryption key coefficient

[0102] according to and ξ to construct the key factor decryption matrix

[0103] use right Decrypt and get the decrypted audio data matrix

[0104] When applying specifically, round(·) means rounding the value to the nearest integer.

[0105] In this embodiment, the inertial neural network can better resist attacks from external attackers due to its more complex dynamic behavior. Due to the existence of multiple time delays (leakage delay, transmission delay, and distribution delay), especially the mixed time-varying delay formed by the presence of leakage delay, the dynamic behavior of the system is more difficult to predict. In comparison, this method has higher security.

[0106] Moreover, the design of the synchronization controller and the design of the synchronization condition inequality can not only achieve the synchronization of the drive-response system, but also are relatively complex, which greatly increases the difficulty of cracking; in addition, due to the introduction of the time-delay inertia weight factor, the encryption process of this method is more complicated and has stronger resistance to randomness and reversibility.

[0107] The switching inertial neural network in the present invention introduces a switching signal and a leakage lag (time-varying lag, non-constant lag) into the existing inertial neural network to form a switching inertial neural network with leakage lag, forming a dynamic processing mechanism that makes the inertial neural network have more complex dynamic behavior, making the encryption drive system more difficult to be intercepted by attackers. Moreover, due to the existence of leakage lag, the behavior of the inertial neural network is more difficult to predict and more difficult to reverse analyze. In addition, the proposed encryption formula introduces a time lag inertia weight factor, making the encryption process more complex, with stronger anti-randomness ability and higher security.

[0108] Furthermore,

[0109]

[0110] for The element in row i and column j of Y b ×X d The real matrix of is the original audio data matrix before normalization The element in row i and column j in Indicates a set of integers;

[0111] Encrypted data matrix The element in row i and column j′ in Indicates Y b ×(X d +1), is the state change rate of the j′th neuron in the audio encryption driving system, X d is the number of audio channels;

[0112] is the normalized ciphertext matrix The element in row i and column j in is the ciphertext matrix before normalization The element in row i and column j of ;

[0113] To decrypt the data matrix The element in row i and column j′ in The rate of change of the j′th neuron in the audio decryption response system; X d is the number of audio channels, =1×(X d +1).

[0114] In this embodiment, a specific implementation of normalizing the original audio data matrix is ​​given, as well as the system neuron state change rate of the audio encryption driving system. Generate encrypted data matrix Decryption of the system's neuron state change rate based on the audio response system Generate decrypted data matrix The advantage is that the synchronized drive system and response system can realize audio encryption and decryption. Since the designed audio encryption drive system and audio decryption system are highly compatible, it is extremely difficult for attackers to crack the encrypted audio without knowing the system parameters and the design scheme of the controller. In addition, due to the switching mode and various time delays, especially the introduction of leakage time delay and the existence of inertia terms, the dynamic behavior of the neural network is quite complex, making it even more difficult for attackers to decipher. The generated encrypted data matrix and decrypted data matrix are extremely difficult to achieve reverse analysis.

[0115] Furthermore, the use of ξ to Encrypt and obtain encryption key coefficient and according to and ξ Scaling to construct the key factor key matrix The specific implementation method is as follows:

[0116]

[0117] is the key factor key matrix The element in row i and column j′ of ;

[0118] bitget(·) means taking the first 10 bits from the lowest to the highest bit in the binary representation; round(·) means rounding the value to the nearest integer; k is the bit number in the binary representation;

[0119]

[0120] Encrypted data matrix The element in row i and column j′ in Indicates Y b ×(X d +1), is the state change rate of the j′th neuron in the audio encryption driving system, X d is the number of audio channels, Indicates a set of integers.

[0121] In this preferred embodiment, the encryption key coefficient obtained It is not obtained by a simple algebraic expression, but by the time-delay inertia weight factor ξ on the encrypted data matrix Even if the attacker deciphers the system parameters, it is still impossible to perform reverse analysis without knowing the time-delay inertia weight factor ξ and the encryption coefficient calculation formula; the key factor key matrix The acquisition can encrypt the original audio matrix according to the matrix dimension, and the key factor key matrix The acquisition of the time lag inertia weight factor ξ and the encryption key coefficient The combined effect of the two makes the safety higher.

[0122] Furthermore, it provides the use of right Encrypt and obtain the encrypted audio data matrix The specific implementation method is as follows:

[0123]

[0124] β ij Encrypted audio data matrix The element in row i and column j in Y b ×X d The real matrix, X d is the number of audio channels;

[0125] for The element in row i and column j of is the key factor key matrix The element in row i and column j in is the key factor key matrix The i-th row and the X-th d +1 column of elements, Indicates Y b ×(X d +1).

[0126] In this preferred embodiment, using right Encrypt and obtain the encrypted audio data matrix The advantage is that due to the high matrix dimension brought by the high sampling frequency, the encrypted audio obtained under the double bit XOR operation is more difficult to crack, and the key sensitivity is higher, which can well resist the attack of statistical analysis method; in addition, due to the key factor key matrix The acquisition of data is relatively complex and extremely difficult to achieve reverse analysis, so it is highly secure.

[0127] Furthermore, the use of ξ to Decrypt and obtain the decryption key coefficient The specific implementation method is as follows:

[0128]

[0129] To decrypt the data matrix The element in row i and column j′ in Indicates Y b ×(X d +1), bitget(·) means taking the first 10 bits from the low bit to the high bit in the binary representation, and round(·) means rounding the value to the nearest integer. It represents a set of integers, and k is the bit number in the binary representation.

[0130] This preferred embodiment utilizes ξ Decrypt and obtain the decryption key coefficient It is not obtained by a simple algebraic expression, but by the time-delay inertia weight factor ξ to decrypt the data matrix Even if the attacker deciphers the system parameters, it is still impossible to decipher the system parameters without knowing the time-delay inertia weight factor and the decryption coefficient calculation formula.

[0131] Furthermore, the basis and ξ to construct the key factor decryption matrix The specific implementation method is as follows:

[0132]

[0133] Decrypt the matrix for the key factor The element in row i and column j′ in X d is the number of audio channels, Indicates taking a set of integers, round(·) means rounding the value to the nearest integer. Indicates Y b ×(X d +1).

[0134] In this preferred embodiment, the above-mentioned and ξ to construct the key factor decryption matrix Key Factor Decryption Matrix The encrypted audio matrix can be decrypted according to the matrix dimension, and the acquisition of the key factor decryption matrix requires the joint action of the time lag inertia weight factor and the decryption key coefficient. The introduction of the time lag inertia weight factor greatly improves the ability to resist randomness and has higher security.

[0135] Furthermore, the use of right Decrypt and get the decrypted audio data matrix The implementation method is as follows:

[0136] The decrypted audio data matrix The element in row i and column j in is the normalized ciphertext matrix The element in row i and column j in Decrypt the matrix for the key factor The element in row i and column j in Decrypt the matrix for the key factor The element in row i and column j+1 in Indicates a set of integers; Y b ×X d The real matrix of Y b ×(X d +1), X d The number of audio channels.

[0137] In this preferred embodiment, the key factor decryption matrix Split into the following form Using the Matrix The first X in d The matrix composed of column vectors and the column matrix composed of its last column vector Perform the relevant bitwise XOR operation to obtain the decrypted audio data matrix The advantages of the elements in the algorithm are that due to the high matrix dimension brought by the high sampling frequency, the decrypted audio obtained under the double bitwise XOR operation is closer to the original audio, and the key sensitivity is higher, which can effectively resist the attack of statistical analysis methods; in addition, since the acquisition of the key factor decryption matrix is ​​relatively complex, it is extremely difficult to crack and has high security.

[0138] Furthermore, a switching inertia neural network with a mixed time-varying delay and leakage delay is constructed as an implementation method of the audio encryption driving system. Specifically, the inertia term of each neuron in the audio encryption driving system is expressed as:

[0139]

[0140] In this preferred embodiment, the expression of the constructed audio encryption driving system is The existence of makes the dynamic behavior of the neural network more complicated. The existence of multiple time delays, especially the leakage delay δ j′ The existence of (t) makes the dynamic behavior of the neural network more difficult to predict, and due to the introduction of the switching mode (i.e., the switching signal σ(t)), the neural network can better resist various complex attacks.

[0141] Furthermore, a specific implementation method for constructing an audio decryption response system based on the designed synchronization controller and audio encryption drive system is provided. Specifically, the inertia term of each neuron in the audio decryption response system is expressed as:

[0142]

[0143] In this preferred embodiment, the expression of the constructed audio decryption response system is The existence of makes the dynamic behavior of the neural network more complicated. The existence of multiple time delays, especially the leakage delay δ j′ The existence of (t) makes the dynamic behavior of the neural network more difficult to predict, and the introduction of the switching mode (i.e., the switching signal σ(t)) makes the neural network more resistant to various complex attacks. The existence of the synchronous controller can not only synchronize the drive-response system to decrypt the encrypted audio, but also makes it extremely difficult for attackers to decrypt the encrypted audio when the controller design is unknown.

[0144] Furthermore, a specific implementation of the designed synchronous controller is provided. Specifically, the expressions of the control components in the synchronous controller are:

[0145]

[0146] In this preferred embodiment, the state feedback in the expression of the designed synchronous controller is: j′ (·)-x j′ (t) and derivation feedback: The coexistence of can make the drive-response system achieve synchronization faster, and the complex controller design makes this method safer.

[0147] is the inertia term of the j′th neuron of the audio encryption drive system, is the state change rate of the j′th neuron in the audio encryption driving system, x j′ (t) is the state of the j′th neuron in the audio encryption driving system at time t, x j′ (td j′w (t)) is td j′w (t) The state of the j′th neuron in the audio encryption driving system, x j′ (t-δ j′ (t)) is t-δ j′ (t) The state of the j′th neuron in the audio encryption driving system, x j′ (θ) is the state of the j′th neuron of the audio encryption driving system, θ is the integral variable, t is the time, t∈[0,Y b +1000], <n>It is a set of integers consisting of 1, 2, 3...n, n = X d +1, X d Indicates the number of audio channels; τ j′w (t) is the wth distributed time lag of the audio encryption driving system or the j′th neuron of the audio encryption driving system;

[0148] is the derivation feedback coefficient of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), is the self-feedback coefficient of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), as well as is the wth component of the first to third connection weights of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), δ j′ (t) is the leakage lag of the audio encryption driving system or the j′th neuron of the audio encryption driving system, d j′w (t) is the wth transmission delay of the audio encryption driving system or the j′th neuron of the audio encryption driving system, as well as are the w-th summation components of the first to third activation functions respectively;

[0149] is the inertia term of the j′th neuron in the audio decryption response system, is the rate of change of the j′th neuron in the audio decryption response system, y j′ (·) is the state of the j′th neuron in the audio decryption response system at time t, y j′ (t-δ j′ (t)) is t-δ j′ (t) The state of the j′th neuron in the audio decryption response system, y j′ (td j′w (t)) is td j′w (t) The state of the j′th neuron in the audio decryption response system, y j′ (θ) is the state of the j′th integrated neuron in the audio decryption response system, u j′ (t) is the j′th control component of the synchronous controller;

[0150] For the αth k The j′th component of the derivation feedback coefficient in the switching state, α k is a variable,< / n> is a set of integers consisting of 1, 2, 3...P. For the αth k The j′th gain component of the first gain parameter of the synchronous controller in the switching state, For the αth k The j′th gain component of the second gain parameter of the synchronous controller in the switching state,

[0151] Switching signal diagram of switching inertial neural network, see Figure 2 .

[0152] Furthermore, a method for calculating the synchronization controller gain parameters through the synchronization condition inequality is provided, including:

[0153] First, calculate the synchronization condition inequality to solve the unknown quantity and Among them, the synchronization condition inequality is:

[0154]

[0155] For the αth k The j′th component of the first unknown quantity in the switching state, For the αth k The j′th component of the second unknown quantity in the switching state, for and The first proportional relationship expression is: for and The second proportional relationship expression is: For the αth k The j′th self-feedback coefficient in the switching state, is the upper bound of the absolute value of the first-order derivative of the leakage delay, is the upper bound of the absolute value of the second-order derivative of the leakage lag, for The algebraic expression composed of and λ is is the upper bound of the absolute value of the j′th leakage delay, λ is the decay rate of global exponential synchronization, λ>0, for The algebraic expression composed of and λ is is the j′th neuron in the αth k The maximum upper bound of the absolute value of the wth component of the distributed delay in the switching state is, For the αth k A given parameter in a switching state; G w The wth summation term of the maximum upper bound of the absolute value of the derivative of the activation function that satisfies the Lipschitz condition, for and The algebraic expression composed of is the j′th neuron in the αth k The wth component of the first connection weight in the switching state, is the j′th neuron in the αth k The wth component of the second connection weight in the switching state, e (·) is an exponential function, is the j′th neuron in the αth k The maximum upper bound of the absolute value of the wth component of the transmission delay in the switching state is, is the j′th neuron in the αth k The wth component of the third connection weight in the switching state, <n>It is a set of integers consisting of 1, 2, 3...n, n = X d +1, X d Indicates the number of audio channels,< / n> It is a set of integers consisting of 1, 2, 3...P.

[0156] Secondly, according to and get and

[0157] For the αth k The j′th gain component of the first gain parameter of the synchronous controller in the switching state, For the αth k The j′th gain component of the second gain parameter of the synchronous controller in the switching state,

[0158] In this preferred embodiment, a synchronization condition inequality is constructed, and the synchronization condition inequality is used to solve the gain parameter, and a specific implementation method for calculating the gain parameter of the synchronization controller is given. The designed synchronization condition inequality does not require solving a large number of linear matrix inequalities and is relatively easy to solve, which can save computer computing power and solution time, and facilitate key management when the key parameters are updated.

[0159] The synchronization condition inequality constructed by the present invention is a sufficient condition for the drive-response system to achieve global exponential synchronization. The synchronization effect diagram of the drive-response system is shown in FIG. Figure 3 As shown, Figure 3 The error system in a is the error between the driving system and the response system. Since j′∈{3}, error systems 1, 2, and 3 are formed, namely: j′ (t)-x j′ (t)(j′=1,2,3), and Figure 3 b) Error change rate of the drive system and the response system (error system change rate 1, 2, 3) (j′=1,2,3), the error system change rate 1 represents the state error between the change rate of the first neuron of the driving system and the change rate of the first neuron of the response system, the error system change rate 2 represents the state error between the change rate of the second neuron of the driving system and the change rate of the second neuron of the response system, and the error system change rate 3 represents the state error between the change rate of the third neuron of the driving system and the change rate of the third neuron of the response system; from Figure 3 a and Figure 3 As can be seen in b, the drive-response system can not only achieve synchronization in a short time, but also the synchronization state of the system is very stable after synchronization is achieved, which can be used to encrypt and decrypt the original audio.

[0160] Verification test:

[0161] The following experiments demonstrate the effectiveness of the encryption method based on the switched inertial neural network with leakage lag by using the method of the present invention to decrypt and decrypt, draw encrypted and decrypted vocal tract waveforms, and perform key space analysis, key sensitivity analysis, and analysis of the ability to resist statistical analysis attacks on the two vocal tract waveforms. Specifically:

[0162] A. Using MATLAB at sampling rate F s The output matrix of the original audio data before normalization is Among them, Y b and X d Refers to the number of audio samples and audio channels respectively, Then, using the formula Normalize the sampling matrix. The specific operation is as follows: Use the audioread function to normalize the sampling matrix at the sampling rate F s Read the audio file and get the dimensions of the audio data (the number of time samples and the number of channels, respectively) and output the audio matrix xr, using xr(:,1) to represent the first column of the matrix and xr(:,2) to represent the second column. These columns are multiplied by 10. 4 Scale and then round to the nearest integer using the round function;

[0163] The audioread function reads an audio file (.wav file) and obtains two main outputs: audio data (a two-dimensional array) and sampling frequency (F s ) and then obtain the number of time samples and the number of channels respectively, according to the sampling frequency and the length of the audio data t end =m / F s (m represents the number of arrays) Calculate the time value corresponding to each data point and create a time vector 0: (1 / F s ):(t end -(1 / F s )) , corresponding to the time point of the audio data, use MATLAB's plot function to draw a waveform graph (including left and right channels) with time as the horizontal axis and amplitude as the vertical axis, such as Figure 4 As shown, it is the channel waveform of the original audio to be encrypted.

[0164] B. Encrypt the audio data using the encryption method of the present invention and draw the encrypted sound channel waveform. The specific operations are as follows:

[0165] By formula The key matrix that will be used for encryption The left channel data and the right channel data are encrypted bit by bit and scaled by a suitable scaling factor (×10 -4 ), and get the matrix Used to store encrypted audio information, that is, use the bitxor function to convert the original data (xr1) and the key factor key matrix Perform bitwise XOR operation on each column vector of the bitwise XOR operation, and integrate the array after bitwise XOR operation into a matrix em, and multiply the matrix by 10 -4 (i.e. xr2=em / (10 4 )) is converted into 16-bit PCM format. The combined left and right channels are already encrypted integer data. The present invention can be directly written into a WAV file (the audio is in the range of -1 to 1);

[0166] With the time axis as the horizontal axis, according to the sampling frequency and the length of the audio data t end =m / F s (m represents the number of arrays) Calculate the time value corresponding to each data point and create a time vector 0: (1 / F s ):(t end -(1 / F s )) corresponds to the time point of the audio data, with amplitude as the ordinate: the value of the audio data (amplitude) will be used as the value of the ordinate, and MATLAB's plot function will be used to draw a waveform graph (including left and right channels) with time as the horizontal axis and amplitude as the vertical axis. MATLAB's graphics property setting function (such as xlabel, ylabel, title, etc.) will be used to add axis labels, titles, and legends to obtain a waveform graph of the encrypted audio channel (such as Figure 5 shown).

[0167] C. Use the method of the present invention to perform decryption operation and draw the decrypted vocal tract waveform diagram. The specific operations are as follows:

[0168] Construct a matrix To store the decrypted audio information, the operation is as follows: That is, use the bitxor function to decrypt the encrypted data (xr2) and the key factor calculated previously Perform bitwise XOR operation on each column vector and integrate the array after bitwise XOR operation into a matrix dm, multiply the matrix by 10 -4 After the storage operation is completed (ie xr3 = dm / (10 4 ));

[0169] With MATLAB's sampling rate F s Write xr3 into the decrypted audio file through the audiowrite function and draw the channel waveform of the decrypted audio through the plot function ( Figure 6 ).

[0170] Key space analysis: In the encryption method of the present invention, the key space can be expressed as in, For the αth k The j′th component of the derivation feedback coefficient in the switching state, For the αth k The j′th self-feedback coefficient in the switching state, is the j′th neuron in the αth k The wth component of the first connection weight in the switching state, is the j′th neuron in the αth k The wth component of the second connection weight in the switching state, is the j′th neuron in the αth k The wth component of the third connection weight in the switching state), for j′,w∈{3} and α k ∈{2}, when the calculation accuracy is 10 -10 When the key space is (10 10 ) 66 ≈2 2192 , which is sufficient to resist brute force attacks. In addition, due to the introduction of exchange technology, the key space of the proposed encryption method is larger than that of other methods.

[0171] Key sensitivity analysis: Key sensitivity refers to the difference between two ciphertext audio files obtained by encrypting the same audio when the key is slightly changed. Taking intermittent silent audio as an example, four sensitivities are demonstrated. ( is the third self-feedback coefficient in the second switching state, is the third component of the first connection weight of the third neuron in the second switching state, is the first self-feedback coefficient in the second switching state, is the first component of the first connection weight of the first neuron in the second switching state) and several parameters are added with 10 -10 , when the parameters are 10 -10 When adding, Figure 7 As shown, decryption cannot be successfully performed, indicating that the encryption algorithm proposed in the present invention is highly sensitive to the key.

[0172] Analysis of the ability to resist statistical analysis attacks: Use the audioread function to read the original audio file and the encrypted audio file, obtain the audio sample data and sampling frequency, and take the first column of all rows from the two-dimensional matrix and perform exponential scaling on it. At the same time, use the round function to round the scaled data to the nearest integer to quantize the data and convert it into an integer format. Then, use the hist function to draw a histogram, treat the audio data as a series of discrete values, and count the frequency of occurrence of each value. The histogram can reflect the statistical distribution characteristics of the original audio signal before and after encryption. It can be seen from the histogram of the original audio and encrypted audio in Figure 8 that the distribution of the histogram is relatively uniform, indicating that the encryption algorithm proposed in the present invention can well resist statistical analysis attacks.

[0173] Although the present invention is described herein with reference to specific embodiments, it should be understood that these embodiments are merely illustrative of the principles and applications of the invention. It should be understood that many modifications may be made to the illustrative embodiments, and that other arrangements may be devised, without departing from the spirit and scope of the invention as defined by the appended claims. It should be understood that the various dependent claims and features described herein may be combined in ways other than those described in the original claims. It should also be understood that features described in conjunction with individual embodiments may be employed in conjunction with other described embodiments. < / n>

Claims

1. An encryption method based on a switched inertial neural network with leakage lag, characterized in that The method comprises the following steps:

1. Initial setup phase: A hybrid time-varying time-delay switched inertial neural network with leakage time-delay is constructed as an audio encryption driving system. Construct an audio decryption response system based on the designed synchronization controller and audio encryption drive system; After calculating the synchronization controller gain parameters through the synchronization condition inequality, the audio encryption drive system and the audio decryption response system are controlled by the synchronization controller to achieve global exponential synchronization; (II) Encryption and decryption stage: The specific encryption process includes: treating the original audio to be encrypted, at a sampling rate of F s Sampling and normalization are performed to obtain the normalized original audio data matrix The set transfer parameter q is used as the input data of the audio encryption driving system, and the encrypted data matrix is ​​generated according to the system neuron state change rate of the audio encryption driving system. Where q = Y b +1000, Y b is the number of audio samples; According to the maximum upper bound of the absolute value of the derivation feedback coefficient and the set consisting of the maximum upper bounds of the absolute values ​​of multiple time lags Construct the time-delay inertia weight factor ξ; and are the maximum upper bounds of the absolute values ​​of leakage delay, transmission delay and distribution delay, respectively; Using ξ Encrypt and obtain the encryption key coefficient according to and ξ Scaling to construct the key factor key matrix use right Encrypt and get the encrypted audio data matrix The specific decryption process includes: At the sampling rate F s Sampling and normalization are performed to obtain the normalized ciphertext matrix The set transfer parameter q is used as the input data of the audio decryption response system, and the decryption data matrix is ​​generated according to the system neuron state change rate of the audio decryption response system. Where q = Y b +1000, Y b is the number of audio samples, According to the maximum upper bound of the absolute value of the derivation feedback coefficient and the set consisting of the maximum upper bounds of the absolute values ​​of multiple time lags Construct the time-delay inertia weight factor ξ; and are the maximum upper bounds of the absolute values ​​of leakage delay, transmission delay and distribution delay, respectively; Using ξ Decrypt and obtain the decryption key coefficient according to and ξ construct the key factor decryption matrix use right Decrypt and get the decrypted audio data matrix 2. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: for The element in the i-th row and j-th column of Y b ×X d A real matrix of is the original audio data matrix before normalization The element in row i and column j in Indicates taking a set of integers; Encrypted data matrix The element in the i-th row and j′th column of Represents Y b ×(X d +1), is the state change rate of the j′th neuron in the audio encryption driving system, X d is the number of audio channels; is the normalized ciphertext matrix The element in row i and column j in is the ciphertext matrix before normalization The element in row i and column j of ; To decrypt the data matrix The element in the i-th row and j′th column of The rate of change of the j′th neuron in the audio decryption response system; X d is the number of audio channels, =1×(X d +1).

3. The encryption method based on the switched inertial neural network with leakage lag according to claim 1, characterized in that: round(·) means rounding the value to the nearest integer.

4. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: is the key factor matrix The element in the i-th row and j′th column of ; bitget(·) means taking the first 10 bits from the lowest to the highest bit in the binary representation; round(·) means rounding the value to the nearest integer; k is the bit number in the binary representation; Encrypted data matrix The element in the i-th row and j′th column of Represents Y b ×(X d +1), is the state change rate of the j′th neuron in the audio encryption driving system, X d is the number of audio channels, Represents a set of integers.

5. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: β ij The encrypted audio data matrix The element in the i-th row and j-th column of Y b ×X d The real matrix, X d is the number of audio channels; for The element in the i-th row and j-th column of is the key factor matrix The element in the i-th row and j-th column of is the key factor matrix The i-th row and the X-th d +1 column elements, Represents Y b ×(X d +1).

6. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: To decrypt the data matrix The element in the i-th row and j′th column of Represents Y b ×(X d +1), bitget(·) means taking the first 10 bits from the low bit to the high bit in the binary representation, and round(·) means rounding the value to the nearest integer. It represents a set of integers, and k is the bit number in the binary representation.

7. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: Decryption matrix for key factors The element in the i-th row and j′th column of X d is the number of audio channels, Indicates taking a set of integers, round(·) means rounding the value to the nearest integer. Represents Y b ×(X d +1).

8. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: The decrypted audio data matrix The element in row i and column j in is the normalized ciphertext matrix The element in row i and column j in Decryption matrix for key factors The element in row i and column j in Decryption matrix for key factors The element in the i-th row and j+1-th column, Indicates taking a set of integers; Y b ×X d A real matrix of Y b ×(X d +1), X d The number of audio channels.

9. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: The expression of the inertia term of each neuron in the audio encryption drive system is: The expression of the inertia term of each neuron in the audio decryption response system is: The expressions of each control component in the synchronous controller are: is the inertia term of the j′th neuron of the audio encryption drive system, is the state change rate of the j′th neuron in the audio encryption driving system, x j′ (t) is the state of the j′th neuron in the audio encryption driving system at time t, x j′ (td j′w (t)) is td j′w (t) The state of the j′th neuron in the audio encryption driving system, x j′ (t-δ j′ (t)) is t-δ j′ (t) The state of the j′th neuron in the audio encryption driving system, x j′ (θ) is the state of the j′th neuron of the audio encryption driving system, θ is the integral variable, t is the time, t∈[0,Y b +1000], <n>is a set of integers consisting of 1, 2, 3, ... n, n = X d +1, X d Indicates the number of audio channels; τ j′w (t) is the wth distributed time lag of the audio encryption driving system or the j′th neuron of the audio encryption driving system;< / n> is the derivation feedback coefficient of the audio encryption drive system or the j′th neuron of the audio encryption drive system under the action of the switching signal σ(t), is the self-feedback coefficient of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), as well as is the wth component of the first to third connection weights of the audio encryption driving system or the j′th neuron of the audio encryption driving system under the action of the switching signal σ(t), δ j′ (t) is the leakage lag of the audio encryption driving system or the j′th neuron of the audio encryption driving system, d j′w (t) is the wth transmission delay of the audio encryption drive system or the j′th neuron of the audio encryption drive system, as well as are the w-th summation components of the first to third activation functions respectively; is the inertia term of the j′th neuron in the audio decryption response system, is the rate of change of the j′th neuron in the audio decryption response system, y j′ (t) is the state of the j′th neuron in the audio decryption response system at time t, y j′ (t-δ j′ (t)) is t-δ j′ (t) The state of the j′th neuron in the audio decryption response system, y j′ (td j′w (t)) is td j′w (t) The state of the j′th neuron in the audio decryption response system, y j′ (θ) is the state of the j′th integrated neuron in the audio decryption response system, u j′ (t) is the j′th control component of the synchronous controller; For the αth k The j′th component of the derivation feedback coefficient in the switching state, α k is a variable, is a set of integers consisting of 1, 2, 3, ... P. For the αth k The j′th gain component of the first gain parameter of the synchronous controller in the switching state, For the αth k The j′th gain component of the second gain parameter of the synchronous controller in the switching state, 10. The encryption method based on a switched inertial neural network with leakage lag according to claim 1, characterized in that: The implementation methods of calculating the synchronous controller gain parameters through the synchronization condition inequality include: First, calculate the synchronization condition inequality to solve the unknown quantity and Among them, the synchronization condition inequality is: For the αth k The j′th component of the first unknown quantity in the switching state, For the αth k The j′th component of the second unknown quantity in the switching state, for and The first proportional relationship expression is: for and The second proportional relationship expression is: For the αth k The j′th self-feedback coefficient in the switching state, is the upper bound of the absolute value of the first-order derivative of the leakage delay, is the upper bound of the absolute value of the second-order derivative of the leakage lag, for The algebraic expression composed of and λ is is the upper bound of the absolute value of the j′th leakage delay, λ is the decay rate of global exponential synchronization, λ>0, for The algebraic expression composed of and λ is is the j′th neuron in the αth k The maximum upper bound of the absolute value of the wth component of the distributed delay in the switching state is, For the αth k A given parameter in a switching state; G w The wth summation term of the maximum upper bound of the absolute value of the derivative of the activation function that satisfies the Lipschitz condition, for and The algebraic expression composed of is the j′th neuron in the αth k The wth component of the first connection weight in the switching state, is the j′th neuron in the αth k The wth component of the second connection weight in the switching state, e (·) is an exponential function, is the j′th neuron in the αth k The maximum upper bound of the absolute value of the wth component of the transmission delay in the switching state is, is the j′th neuron in the αth k The wth component of the third connection weight in the switching state, <n>is a set of integers consisting of 1, 2, 3, ... n, n = X d +1, X d Indicates the number of audio channels. It is a set of integers consisting of 1, 2, 3, ... P; < / n> Secondly, according to and get and For the αth k The j′th gain component of the first gain parameter of the synchronous controller in the switching state, For the αth k The j′th gain component of the second gain parameter of the synchronous controller in the switching state,

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