A method and system for encrypted communication based on selective traversal binary tree encryption

Abstract

The application discloses an encryption communication method and system based on selective traversal binary tree encryption, and comprises the following steps: generating four columns of chaotic sequences according to an initial key by using a hyperchaotic model; performing selective traversal binary tree encryption on an original bit stream by using two columns of chaotic sequences to obtain a first-level encrypted signal; performing SCMA encoding and constellation mapping processing on the first-level encrypted signal to obtain a 16QAM constellation diagram; performing selective traversal binary tree encryption on the 16QAM constellation diagram by using two columns of chaotic sequences to obtain a second-level encrypted signal; performing time extraction-fast Hadamard transformation on the second-level encrypted signal after inserting a pilot to obtain a time domain transmission signal; and sending the time domain transmission signal to a receiver by using a transmitter; and high-security transmission of a large amount of data is realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of encrypted communication, and particularly relates to an encrypted communication method and system based on selective traversal binary tree encryption. BACKGROUND

[0002] With the rapid development of mobile Internet, cloud computing, big data and Internet of Things, network services are facing a huge transformation; in order to further improve the spectrum efficiency, the existing mobile communication system begins to use sparse code division multiple access (SCMA) technology.

[0003] SCMA technology is not a simple superposition of mapping and modulation, but a high-dimensional sparse codebook is designed to achieve efficient use of spectrum through overloading communication; however, the search and matching of code words in high-dimensional space become more complex, increasing the complexity of signal processing. At the same time, with the development of 5G and future communication technology, the data transmission rate is significantly improved, which leads to more prominent information security problems. Under high data transmission rate, the confidentiality and integrity of information face greater challenges. SUMMARY

[0004] The application provides an encrypted communication method and system based on selective traversal binary tree encryption, which reduces the complexity of signal processing in SCMA technology and realizes high-security transmission of large data volume.

[0005] To achieve the above purpose, the technical scheme adopted by the application is:

[0006] The application provides an encrypted communication method and system based on selective traversal binary tree encryption, which reduces the complexity of signal processing in SCMA technology and realizes high-security transmission of large data volume.

[0007] The application generates chaotic sequences , chaotic sequences , chaotic sequences and chaotic sequences from the initial key according to the initial key by using a four-dimensional fractional-order Xu hyperchaotic model.

[0008] The application uses chaotic sequences and chaotic sequences to perform selective traversal binary tree encryption on the original bit stream to obtain a first-level encrypted signal; and performs SCMA encoding and constellation mapping processing on the first-level encrypted signal to obtain a 16QAM constellation diagram.

[0009] The application uses chaotic sequences and chaotic sequences The 16QAM constellation diagram is selected to perform binary tree encryption to obtain a second-level encrypted signal; a pilot is inserted into the second-level encrypted signal, and time-domain transmission signal is obtained by performing time decimation and fast Hartley transform; the time-domain transmission signal is sent to the receiver through the transmitter;

[0010] In response to the receiver receiving the time-domain transmission signal, the time-domain transmission signal is decoded according to the initial key to obtain the original bit stream.

[0011] Further, the four-dimensional fractional-order Xu hyperchaotic model is used to generate chaotic sequences , chaotic sequences , chaotic sequences and chaotic sequences according to the initial key, and the process includes:

[0012] The initial key is input into the four-dimensional fractional-order Xu hyperchaotic model to obtain state variables , state variables , state variables and state variables , and the process includes:

[0013]

[0014] In the formula, the first group of key initial values are the initial values of the state variables , state variables , state variables and state variables , , b, c, d, e and f are parameters of the four-dimensional fractional-order Xu hyperchaotic model; , , and represent the first-order derivatives of the state variables , state variables , state variables and state variables , is expressed as Caputo fractional derivative, and are the upper and lower limits of integration, is the order of the fractional order;

[0015] The four-dimensional fractional-order Xu hyperchaotic model is solved by the fourth-order Runge-Kutta algorithm to obtain state variables , state variables , state variables and state variables ; the state variables , state variables , state variables and state variables generating chaotic sequences chaotic sequences chaotic sequences and chaotic sequences .

[0016] Further, using chaotic sequences and chaotic sequences selectively traversing a binary tree to encrypt the original bit stream to obtain a first-level encrypted signal, the process including:

[0017] According to chaotic sequences and chaotic sequences calculating to obtain an encryption factor A and an encryption factor B, the expression formula being:

[0018]

[0019] In the formula, is a rounding function to negative infinity; is a remainder operation function;

[0020] According to the encryption factor A, selecting a traversal mode from the traversal rule table ; After deleting the traversal mode from the traversal rule table, according to the encryption factor B, selecting a traversal mode from the traversal rule table ;

[0021] According to the traversal mode adding bits in the original bit stream to nodes on a pre-constructed binary tree; according to the traversal mode reading the nodes on the binary tree to obtain a first-level encrypted signal.

[0022] Further, SCMA encoding and constellation mapping processing are performed on the first-level encrypted signal to obtain a 16QAM constellation diagram, the process including:

[0023] Mapping bit sequences in the first-level encrypted signal to high-dimensional code words through a sparse codebook; performing constellation mapping on the high-dimensional code words to obtain a 16QAM constellation diagram.

[0024] Further, using chaotic sequences and chaotic sequences selectively traversing a binary tree to encrypt the 16QAM constellation diagram to obtain a second-level encrypted signal, the process including:

[0025] According to chaotic sequences and chaotic sequences calculating to obtain an encryption factor C and an encryption factor D, the expression formula being:

[0026] Further, SCMA encoding and constellation mapping processing are performed on the first-level encrypted signal to obtain a 16QAM constellation diagram, the process including:

[0023] Mapping bit sequences in the first-level encrypted signal to high-dimensional code words through a sparse codebook; performing constellation mapping on the high-dimensional code words to obtain a 16QAM constellation diagram.

[0024] Further, using chaotic sequences and chaotic sequences selectively traversing a binary tree to encrypt the 16QAM constellation diagram to obtain a second-level encrypted signal, the process including:

[0025] According to chaotic sequences and chaotic sequences calculating to obtain an encryption factor C and an encryption factor D, the expression formula being:

[0026]

[0027] In the formula, is a rounding function to negative infinity; is a remainder operation function;

[0028] According to the encryption factor C, the selected traversal mode is selected from the traversal rule table ; After the traversal mode is deleted from the traversal rule table, according to the encryption factor D, the selected traversal mode is selected from the traversal rule table ;

[0029] According to the traversal mode , the bits in the original bit stream are added to the nodes of the pre-constructed binary tree; according to the traversal mode , the nodes on the binary tree are read to obtain the second-level encrypted signal.

[0030] Further, the traversal rule table includes a hierarchical traversal mode, a pre-order traversal mode, an in-order traversal mode, and a post-order traversal mode.

[0031] Further, after inserting the pilot into the second-level encrypted signal, the time-domain transmission signal is obtained by performing time decimation and fast Hartley transform, and the process includes:

[0032] The pilot is inserted into the second-level encrypted signal to obtain the frequency-domain transmission signal; according to the parity of the bit sequence number, the frequency-domain transmission signal is decomposed into a subsequence and a subsequence , and the expression formula is:

[0033]

[0034] In the formula, and are the frequency-domain transmission signals, is the bit sequence number; is the number of bits in the frequency-domain transmission signal;

[0035] The fast Hartley transform is performed on the subsequence and the subsequence to obtain the time-domain transmission signal, and the expression formula is:

[0036]

[0037]

[0038] In the formula, is the time-domain transmission signal, is the frequency-domain transmission signal, n is the bit sequence number, ; k is the bit sequence number, ; Pi is represented as a fast Hartley transform function; Pi is represented as a fast Hartley transform function; Pi is represented as a fast Hartley transform function; Pi is represented as a fast Hartley transform function; Pi is represented as a fast Hartley transform function; Pi is represented as a fast Hartley transform function.

[0039] Further, the time domain transmission signal is sent to the receiver by the transmitter, and the process comprises:

[0040] After the time domain transmission signal is increased by the transmitter, the serial transmission signal is obtained by performing serial-parallel conversion, and the transmission signal is obtained by performing up-conversion processing on the serial transmission signal; the transmission signal is sent to the receiver through the transmission channel;

[0041] The parallel reception signal is obtained by performing down-conversion processing and serial-parallel conversion on the transmission signal by the receiver, and the time domain transmission signal is obtained by removing the cyclic prefix from the parallel reception signal.

[0042] The second aspect of the application provides an encryption communication system based on selective traversal binary tree encryption, comprising:

[0043] The receiving unit receives the original bit stream and the initial key, and generates chaotic sequences , chaotic sequences , chaotic sequences and chaotic sequences using a four-dimensional fractional-order Xu hyperchaotic model according to the initial key.

[0044] The encryption unit uses chaotic sequences and chaotic sequences to encrypt the original bit stream to obtain a first-level encrypted signal by selective traversal binary tree encryption; the first-level encrypted signal is processed by SCMA encoding and constellation mapping to obtain a 16QAM constellation diagram; chaotic sequences and chaotic sequences are used to encrypt the 16QAM constellation diagram by selective traversal binary tree encryption to obtain a second-level encrypted signal.

[0045] The signal conversion unit inserts a pilot into the second-level encrypted signal and performs time decimation-fast Hartley transform to obtain a time domain transmission signal; the time domain transmission signal is sent to the receiver by the transmitter.

[0046] The decryption unit decodes the time domain transmission signal according to the initial key to obtain the original bit stream in response to the receiver receiving the time domain transmission signal.

[0047] The third aspect of the present application provides an electronic device, comprising a storage medium and a processor; the storage medium is used for storing instructions; the processor is used for operating according to the instructions to execute the encryption communication method of the first aspect.

[0048] Compared with the prior art, the present application has the following beneficial effects:

[0049] The present application uses a chaotic sequence and a chaotic sequence The original bit stream is subjected to selective traversal binary tree encryption to obtain a first-level encrypted signal; the first-level encrypted signal is subjected to SCMA encoding and constellation mapping processing to obtain a 16QAM constellation diagram; the chaotic sequence and the chaotic sequence The 16QAM constellation diagram is subjected to selective traversal binary tree encryption to obtain a second-level encrypted signal; the original bit stream is subjected to twice encryption by using the selective traversal binary tree encryption method, which significantly improves the security performance of information transmission, has less calculation amount in the encryption process, and can realize high-security transmission of large data.

[0050] In the present application, the time domain transmission signal is obtained by performing time decimation-quick Hartley transform on the second-level encrypted signal after inserting a pilot; the time domain transmission signal is sent to a receiver by a transmitter; complex number operation is avoided, and the forward and inverse transform forms are basically consistent, which reduces the complexity of the algorithm and improves the calculation efficiency. BRIEF DESCRIPTION OF DRAWINGS

[0051] Figure 1 is a flowchart of the encryption communication method based on selective traversal binary tree encryption provided by the embodiment 1 of the present application;

[0052] Figure 2 is a schematic diagram of SCMA encoding provided by the embodiment 1 of the present application;

[0053] Figure 3 is an attractor phase diagram of the four-dimensional fractional-order Xu hyperchaotic model provided by the embodiment 1 of the present application;

[0054] Figure 4 is a sensitivity diagram of the four-dimensional fractional-order Xu hyperchaotic model provided by the embodiment 1 of the present application;

[0055] Figure 5 is a basic structure diagram of a binary tree provided by the embodiment 1 of the present application;

[0056] Figure 6 is an example diagram of depth traversal of a binary tree provided by the embodiment 1 of the present application;

[0057] Figure 7 is an example diagram of selective traversal binary tree encryption provided by the embodiment 1 of the present application;

[0058] Figure 8 is a schematic diagram of constructing a binary tree provided by embodiment 1 of the present application;

[0059] Figure 9 is a schematic diagram of selecting and traversing a binary tree to encrypt a 16QAM constellation provided by embodiment 1 of the present application;

[0060] Figure 10 is a flowchart of time decimation-fast Hartley transform operation provided by embodiment 1 of the present application;

[0061] Figure 11 is an input diagram, an encryption diagram and a decryption diagram of the encryption communication method provided by embodiment 1 of the present application. DETAILED DESCRIPTION

[0062] The present application will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solutions of the present application, and cannot be used to limit the protection scope of the present application.

[0063] Embodiment 1

[0064] As shown in the figure, the present embodiment provides an encryption communication method based on selecting and traversing a binary tree to encrypt, comprising: Figure 1

[0065] Receiving an original bit stream and an initial key, generating chaotic sequences , , and according to the initial key by using a four-dimensional fractional-order Xu hyperchaotic model, the process comprising:

[0066] Inputting the initial key into the four-dimensional fractional-order Xu hyperchaotic model to obtain state variables , , and , the process comprising:

[0067]

[0068] In the formula, the first group of key initial values are the initial values of state variables , , and , , b, c, d, e and f are parameters of the four-dimensional fractional-order Xu hyperchaotic model; , , and represent state variables ​, state variables , state variables , state variables , first derivatives of state variables, expressed as Caputo fractional derivatives, and upper and lower limits of integration, order of fractional order.

[0069] The state variables , state variables , state variables and state variables are obtained by solving the four-dimensional fractional Xu hyperchaotic model by the fourth-order Runge-Kutta algorithm , state variables , state variables and state variables ; and the chaotic sequences , chaotic sequences , chaotic sequences and chaotic sequences are generated from the state variables

[0070] The chaotic sequences generated by solving the four-dimensional fractional Xu hyperchaotic model in this embodiment using the fourth-order Runge-Kutta integration method have good randomness; as shown in Figure 3 , the hyperchaotic attractor under the initial condition (x, y, z, w)=(-1, 1, 1, -1). Due to the sensitivity of the four-dimensional fractional Xu hyperchaotic model to initial values, when the initial value of the key changes slightly, a completely different complex chaotic trajectory will be generated.

[0071] In order to quantify the security performance of the encryption communication method, the key space of the proposed encryption scheme is strictly calculated; as shown in Figure 4 , the key includes the initial value of the Xu hyperchaotic fractional multi-stable dynamic system and the control parameter, i.e. {x, y, z, w, a, b, c, d, e, f}. The step size is set to 0.001, and the key space can be calculated by experiment to be (1013×1014×1013×1014×1013×1012×1014×1013×1014×1013×103) = 10136. Since the key space is too large, it takes a long time to find the correct key, thereby effectively preventing the hijacker from obtaining the key.

[0072] The traversal rule table includes hierarchical traversal, pre-order traversal, in-order traversal and post-order traversal. As shown in Figure 5 , pre-order traversal: root node-left subtree-right subtree; in-order traversal: left subtree-root node-right subtree; post-order traversal: left subtree-right subtree-root node; hierarchical traversal only needs to be traversed by layer.

[0073] To better illustrate the various traversal methods, such as Figure 6 The binary tree diagram shown is an example. The data results read by various traversal methods are as follows: Level order traversal: [1 2 3 4 5 6 7 8]. Preorder traversal: [1 2 4 5 7 8 3 6]. Inorder traversal: [42 7 5 8 1 3 6]. Postorder traversal: [4 7 8 5 2 6 3 1].

[0074] like Figure 7 The binary tree encryption process involves encoding the bitstream using a binary tree. Different traversal methods result in entirely different bitstreams. For example, a bitstream [01101010111100001] can be encoded using a level-order traversal method. Changing the traversal method to one of the other three methods yields completely different bitstreams. Similarly, any traversal method can be replaced with any other traversal method to achieve encryption. Decryption only requires reversing the traversal rules to obtain the original bitstream.

[0075] like Figure 8 The above utilizes chaotic sequences and chaotic sequences The process of selecting and traversing a binary tree to encrypt the original bitstream to obtain the first-level encrypted signal includes:

[0076] According to the chaotic sequence and chaotic sequences The encryption factors A and B are calculated using the following formula:

[0077]

[0078] In the formula, This is a rounding function for negative infinity. This is the remainder operation function;

[0079] The traversal method is selected from the traversal rule table based on the encryption factor A. ; Traversal method After being deleted from the traversal rule table, the traversal method is selected from the traversal rule table based on the encryption factor B. ;

[0080] The first level has 10 branch nodes. A binary tree is built based on these 10 branch nodes, and the traversal method is then used to... Add bits from the original bitstream to nodes in the pre-constructed binary tree; follow the traversal method. The first-level encryption signal is obtained by reading the nodes on the binary tree.

[0081] The bit sequence in the first-level encrypted signal is mapped to a high-dimensional codeword using a sparse codebook; a constellation mapping is then performed on the high-dimensional codeword to obtain a 16QAM constellation diagram.

[0082] like Figure 2 As shown, using chaotic sequences and chaotic sequences The process of selecting and traversing a binary tree to encrypt the 16QAM constellation graph to obtain the second-level encrypted signal includes:

[0083] like Figure 9 As shown, based on the chaotic sequence and chaotic sequences The encryption factors C and D are calculated using the following formulas:

[0084]

[0085] In the formula, This is a rounding function for negative infinity; This is the remainder operation function;

[0086] The traversal method is selected from the traversal rule table based on the encryption factor C. ; Traversal method After being deleted from the traversal rule table, the traversal method is selected from the traversal rule table based on the encryption factor D. ;

[0087] Based on the traversal method Add bits from the original bitstream to nodes in the pre-constructed binary tree; follow the traversal method. The second-level encryption signal is obtained by reading the nodes on the binary tree.

[0088] like Figure 10 As shown, after inserting pilot signals into the second-level encryption signal, a time-decimation-fast Hartley transform is performed to obtain the time-domain transmission signal. The process includes:

[0089] A pilot signal is inserted into the second-level encryption signal to obtain the frequency domain transmission signal; the frequency domain transmission signal is decomposed into sub-sequences according to the parity of the bit numbers. and subsequences The formula is as follows:

[0090]

[0091] In the formula, and For transmitting signals in the frequency domain, Bit sequence number; This refers to the number of bits in the frequency domain transmitted signal.

[0092] subsequence and subsequences The time-domain transmission signal is obtained by performing a fast Hadamard transform, and is expressed by the following formula:

[0093]

[0094]

[0095]

[0096] The derivation is as follows:

[0097]

[0098] In the formula, is the time-domain transmission signal, is the frequency-domain transmission signal, n is the bit sequence number, ; k is the bit sequence number, ; is the circular constant; is expressed as a fast Hadamard transform function; is an input variable; is a set trigonometric function; is a cosine function; is a sine function.

[0099] The time-domain transmission signal is sent to the receiver by the transmitter, and the process includes:

[0100] After the time-domain transmission signal is increased by the transmitter, a cyclic prefix is performed, and a serial transmission signal is obtained by serial-parallel conversion; the serial transmission signal is up-converted to obtain a transmission signal, and the transmission signal is sent to the receiver through a transmission channel;

[0101] The transmission signal is down-converted and converted by the receiver to obtain a parallel reception signal, and the cyclic prefix is removed to obtain a time-domain transmission signal.

[0102] In response to the receiver receiving the time-domain transmission signal, the time-domain transmission signal is decoded according to the initial key to obtain the original bit stream.

[0103] As shown in Figure 11 , the school badge is used as the initial information transmission in the embodiment, the values of the RGB three primary colors of each pixel point of the school badge are extracted to obtain a three-dimensional RGB primary color brightness value matrix, the value range of which is 0~255, each value is converted into an eight-bit binary sequence to obtain an initial bit stream, and the selected traversal binary tree encryption algorithm is used for encryption. The encrypted pattern completely loses any information of the pattern before encryption, and can achieve efficient information security protection.

[0104] Embodiment 2

[0105] The embodiment provides an encrypted communication system based on selective traversal binary tree encryption.

[0106] The receiving unit receives the original bit stream and the initial key, and generates chaotic sequences respectively according to the initial key by using a four-dimensional fractional-order Xu hyperchaos model , chaotic sequence , chaotic sequence and chaotic sequence .

[0107] The encryption unit performs selective traversal binary tree encryption on the original bit stream by using chaotic sequences and chaotic sequence to obtain a first-level encrypted signal; performs SCMA encoding and constellation mapping processing on the first-level encrypted signal to obtain a 16QAM constellation diagram; and performs selective traversal binary tree encryption on the 16QAM constellation diagram by using chaotic sequences and chaotic sequence to obtain a second-level encrypted signal.

[0108] The signal conversion unit inserts a pilot into the second-level encrypted signal and performs time decimation-quick Hartley transform to obtain a time-domain transmission signal; and the time-domain transmission signal is sent to a receiver through a transmitter.

[0109] The decryption unit decodes the time-domain transmission signal according to the initial key to obtain the original bit stream in response to the receiver receiving the time-domain transmission signal.

[0110] The selective traversal binary tree encryption method is used twice to encrypt the original bit stream in the embodiment, which significantly improves the security performance of information transmission, has less calculation amount in the encryption process, and can realize high-security transmission of large data amount. The time decimation-quick Hartley transform avoids complex number operation, and the forward and inverse transform forms are basically consistent, which reduces the complexity of the algorithm and improves the calculation efficiency.

[0111] Embodiment 3

[0112] The embodiment provides an electronic device, which comprises a storage medium and a processor; the storage medium is used for storing instructions; and the processor is used for operating according to the instructions to execute the encrypted communication method in the embodiment 1.

[0113] Those skilled in the art will appreciate that embodiments of the application can be devised for a method, a system, or a computer program product. Accordingly, the present application can be embodied in the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present application can take the form of a computer program product on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) embodying computer readable program code.

[0114] The present application is described in reference to the flowchart and / or block diagrams of the methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart and / or block diagrams, and combinations of blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processing system or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0115] These computer program instructions can also be stored in a computer- readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the function specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0116] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in the flowchart and / or block diagram block or blocks.

[0117] The above description is only preferred embodiment of the present application, it should be pointed out that, for those skilled in the art, without departing from the technical principles of the present application, can make a number of improvements and variations, these improvements and variations should be considered as the protection scope of the present application.

Claims

1. A method of encrypting a communication based on selective traversal of a binary tree encryption, characterized by, The method comprises the following steps: Receive the original bit stream and the initial key, and generate chaotic sequences according to the initial key by using a four-dimensional fractional-order Xu hyperchaotic model , chaotic sequences , chaotic sequences , and chaotic sequences ​ Utilizing chaotic sequences and chaotic sequences The original bit stream is subjected to selective traversal binary tree encryption to obtain a first-level encrypted signal; the first-level encrypted signal is subjected to SCMA encoding and constellation mapping processing to obtain a 16QAM constellation diagram; Utilizing chaotic sequences and chaotic sequences The 16QAM constellation is selected to perform a binary tree encryption to obtain a second level encrypted signal; The time domain transmission signal is sent to the receiver through the transmitter; The time domain transmission signal is decoded according to the initial key to obtain the original bit stream in response to the receiver receiving the time domain transmission signal.

2. The encrypted communication method of claim 1, wherein, Chaotic sequences are generated from initial keys respectively by using a four-dimensional fractional-order Xu's hyperchaotic model chaotic sequence chaotic sequence chaotic sequence and the process comprises: Input the initial key into the four-dimensional fractional-order Xu's hyperchaotic model to obtain state variables , state variables , state variables and state variables , the process comprises: ； In the formula, the initial value of the first group of keys is a state variable , a state variable , a state variable , and the initial value of a state variable , , b, c, d, e, and f are parameters of the four-dimensional fractional-order Xu hyperchaotic model; , , and represent the first derivative of the state variable , the state variable , the state variable , and the state variable , is expressed as a Caputo fractional derivative, and are the upper and lower limits of integration, is the order of the fractional order; State variables , state variables , state variables and state variables ; chaotic sequences , chaotic sequences , chaotic sequences and chaotic sequences are generated from state variables , state variables , state variables and state variables .

3. The encrypted communication method of claim 1, wherein, Utilizing chaotic sequences and chaotic sequences The original bit stream is selected to traverse the binary tree encryption to obtain the first level of encryption signal, the process includes: According to the chaotic sequence and the chaotic sequence The encryption factor A and the encryption factor B are calculated, and the expression formula is: ； In the formula, is a floor function to negative infinity; is a remainder operation function; According to the encryption factor A, the selected traversal mode in the traversal rule table is deleted ; the traversal mode is selected according to the encryption factor B from the traversal rule table ; the selected traversal mode in the traversal rule table is deleted according to the encryption factor B ; According to the traversal mode Adding the bits in the original bit stream to the nodes on the pre-constructed binary tree; and according to the traversal mode Reading the nodes on the binary tree to obtain the first-level encrypted signal.

4. The encrypted communication method of claim 1, wherein, The first-level encrypted signal is subjected to SCMA encoding and constellation mapping to obtain a 16QAM constellation, and the process comprises the following steps: The bit sequence in the first-level encrypted signal is mapped to a high-dimensional code word through a sparse codebook, and the high-dimensional code word is subjected to constellation mapping to obtain a 16QAM constellation.

5. The encrypted communication method of claim 1, wherein, Utilizing chaotic sequences and chaotic sequences The 16QAM constellation is selected to perform a binary tree encryption to obtain a second level encrypted signal, the process including: According to the chaotic sequence and the chaotic sequence The encryption factor C and the encryption factor D are calculated, and the expression formula is: ； In the formula, is a floor function to negative infinity; is a remainder operation function; According to the encryption factor C, the selected traversal mode is deleted from the traversal rule table, and the selected traversal mode is selected from the traversal rule table according to the encryption factor D ; the traversal mode is deleted from the traversal rule table According to the encryption factor C, the selected traversal mode is deleted from the traversal rule table, and the selected traversal mode is selected from the traversal rule table according to the encryption factor D ; According to the traversal mode Adding the bits in the original bit stream to the nodes on the pre-constructed binary tree; and traversing the binary tree Reading the nodes on the binary tree to obtain the second-level encrypted signal.

6. The encrypted communication method according to claim 3 or 5, characterized by, The traversal rule table comprises a hierarchical traversal mode, a pre-order traversal mode, an in-order traversal mode and a post-order traversal mode.

7. The encrypted communication method of claim 1, wherein, The time domain transmission signal is obtained by performing time extraction-fast Hartley transform on the second-level encrypted signal after inserting a pilot into the second-level encrypted signal, and the process comprises the following steps: The pilot is inserted into the second-level encrypted signal to obtain a frequency domain transmission signal; the frequency domain transmission signal is decomposed into sub-sequences according to the parity of bit serial numbers and sub-sequences , and the expression formula is: ； In the formula, and is a frequency domain transmission signal, is a bit serial number; is the number of bits in the frequency domain transmission signal; subsequences and subsequences The time-domain transmission signal is obtained by performing a fast Hartley transform, and is expressed by the following equation. ； ； In the formula, is a time domain transmission signal, is a frequency domain transmission signal, n is a bit sequence number, ; k is a bit sequence number, ; is a circular constant; is a fast Hartley transform function; is an input variable; is a set trigonometric function; is a cosine function; is a sine function.

8. The encrypted communication method of claim 1, wherein, The time domain transmission signal is sent to the receiver through the transmitter, and the process comprises the following steps: The serial transmission signal is obtained by performing serial-parallel conversion on the time domain transmission signal after the transmitter adds a cyclic prefix to the time domain transmission signal; the transmission signal is obtained by performing up-conversion processing on the serial transmission signal, and the transmission signal is sent to the receiver through a transmission channel; The parallel reception signal is obtained by performing down-conversion processing and serial-parallel conversion on the transmission signal through the receiver, and the time domain transmission signal is obtained by removing the cyclic prefix from the parallel reception signal.

9. An encryption communication system based on selective traversal of a binary tree encryption, characterized by The method comprises the following steps: The receiving unit receives an original bit stream and an initial key, and generates chaotic sequences according to the initial key by using a four-dimensional fractional-order Xu hyperchaotic model , chaotic sequences , chaotic sequences , and chaotic sequences ; Encryption unit, utilizing chaotic sequence and chaotic sequence The original bit stream is selectively traversed by a binary tree to obtain a first-level encrypted signal; the first-level encrypted signal is processed by SCMA encoding and constellation mapping to obtain a 16QAM constellation diagram; the 16QAM constellation diagram is selectively traversed by a binary tree to obtain a second-level encrypted signal; and the second-level encrypted signal is processed by SCMA encoding and constellation mapping to obtain a 64QAM constellation diagram. and chaotic sequence The 64QAM constellation diagram is selectively traversed by a binary tree to obtain a third-level encrypted signal. The time domain transmission signal is obtained by performing time extraction-fast Hartley transform on the second-level encrypted signal after a signal conversion unit inserts a pilot into the second-level encrypted signal; the time domain transmission signal is sent to the receiver through the transmitter; The time domain transmission signal is decoded according to the initial key to obtain the original bit stream in response to the receiver receiving the time domain transmission signal.

10. An electronic device comprising a storage medium and a processor; the storage medium is configured to store instructions; characterized in that, The processor is configured to operate according to the instructions to perform the encryption communication method of any one of claims 1 to 8.

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