A chaotic secure communication system and method based on multi-layer complex network

Abstract

The present invention discloses a chaotic secure communication system and method based on a multi-layer complex network, belonging to the field of chaotic secure communication technology. The chaotic secure communication system, firstly, sets the first and second chaotic driving networks for encryption at the transmitting end, and sets the first and second chaotic response networks for decryption at the receiving end, considering the parameter sensitivity of the chaotic sequence to achieve strong information encryption security. Secondly, each chaotic driving and response network includes multiple nodes. The design of the communication system in combination with the characteristics of a huge number of nodes and diverse edge relationships can improve the complexity of the overall system architecture. Thirdly, the first synchronization controller set at the receiving end controls the first chaotic driving network and the first chaotic response network to achieve generalized synchronization and improve noise robustness. Finally, even if the first chaotic driving and response networks are cracked, data recovery cannot be completed in the absence of a random sequence, further improving the system security.

Description

Technical Field

[0001] The invention belongs to the technical field of chaotic secure communication, and more specifically, relates to a chaotic secure communication system and method based on a multi-layer complex network. Background Art

[0002] With the rapid development of the industrial Internet, the types and quantities of data involved are also growing exponentially. This includes sensitive information such as production plans, process parameters, and equipment status. Once this information is leaked, it may lead to production interruptions, reduced business competitiveness, and even loss of intellectual property rights. Therefore, confidential communication has a wide range of application scenarios in the industrial Internet. First, it is reflected in the security of data transmission. By adopting advanced encryption algorithms and communication protocols, it can effectively prevent the risk of data being maliciously intercepted, tampered with, or stolen. Secondly, a secure and trusted communication channel is established between industrial equipment to ensure that information is not interfered with during transmission, thereby ensuring the accuracy of real-time control and monitoring. At the same time, in the context of the big data era, the proportion of multimedia information such as images, videos, and sounds in network transmission is growing rapidly. Due to the large amount of data information, the computer's computing speed and storage capacity are required to be high, and it is difficult to achieve fast and efficient encryption using traditional encryption methods. In order to solve this problem, researchers have been looking for new encryption methods to improve information security.

[0003] On the one hand, chaos has the characteristics of initial value sensitivity, spatial hybridity, and intermittent periodicity, which is conducive to increasing the complexity of the transmission signal, which is of great significance for improving the system performance of confidential communication such as anti-spectral analysis and anti-cracking capabilities. On the other hand, complex networks have characteristics such as small world and scale-free. The complexity of the network is reflected in the following aspects. First, the connection structure of the network is complex; second, the nodes of the network may have the same or different dynamics; in addition, the interaction between the interconnected nodes makes the dynamic characteristics of the nodes themselves more complex. How to combine the characteristics of chaos and complex networks to improve the complexity of confidential communication systems has become an urgent problem to be solved in the wireless communication environment. Summary of the invention

[0004] In response to the above defects or improvement needs of the prior art, the present invention provides a chaotic secure communication system and method based on a multi-layer complex network. Its purpose is to first consider utilizing the high parameter sensitivity of chaotic sequences to achieve strong information encryption security, and secondly utilize two groups of heterogeneous chaotic networks to increase the complexity of chaotic signals to further enhance communication security. Finally, it also involves using the generalized synchronization of chaotic networks to reduce the impact of noise on chaotic encryption; thereby solving the technical problem of how to combine the characteristics of chaos and complex networks to improve the complexity of secure communication systems.

[0005] To achieve the above object, according to one aspect of the present invention, a chaotic secure communication system based on a multi-layer complex network is provided, comprising:

[0006] The transmitting end includes a preprocessing module, a first chaos driving network and a second chaos driving network; the preprocessing module is used to scramble the binary original plaintext message of the same length using a random sequence seq to obtain a binary information sequence m; the first chaos driving network is used to encrypt the information sequence m to obtain a first chaotic sequence; the elements in the information sequence m are system parameters of the first chaos driving network; the second chaos driving network is used to encrypt the random sequence seq to obtain a second chaotic sequence;

[0007] The receiving end includes a first synchronization controller, a second synchronization controller, a first chaotic response network, a second chaotic response network and a post-processing module; the first synchronization controller is used to control the first chaotic driving network and the first chaotic response network to be synchronized when the l-th binary number m(l) in the information sequence m is 0, and to control the first chaotic driving network and the first chaotic response network to be asynchronous when the l-th binary number m(l) is 1; the second synchronization controller is used to control the second chaotic response network and the second chaotic driving network to achieve complete synchronization; the first chaotic response network is used to decrypt the first chaotic sequence according to the relationship between the value of the synchronization error of the first synchronization controller and the preset threshold value to obtain the first decrypted information The second chaotic response network is used to decrypt the second chaotic sequence to obtain the second decrypted information seq; the post-processing module is used to use the first decrypted information And the second decrypted information seq is reversely restored to obtain the decrypted information message*.

[0008] In one embodiment, the first chaotic driving network adopts a unified chaotic system, and the first chaotic response network adopts a Lorenz chaotic system; the control law expression of the first synchronous controller is:

[0009] Where i is the node number, i = 1, 2, ..., N; N is the number of nodes in the first chaotic driving network; u i1 ,u i2 ,u i3 are all state variables of the first synchronous controller; x i1 ,x i2 ,x i3 are the chaotic data output by the first chaotic driving network respectively; i1 ,y i2 ,y i3are the chaotic data output by the first chaotic response network respectively; i =(e i1 ,e i2 ,e i3 ) T represents the generalized synchronization error between the first chaotic driving network and the first chaotic response network, and the first error parameter e i1 =y i1 -d1x i1 , the second error parameter e i2 =y i2 -d2x i2 , the third error parameter e i3 =y i3 -d3x i3 , d1, d2, d3 are three parameters of the first synchronous controller, h1, h2, h3 are preset constants and h1≥0, h2≥0, h3≥0.

[0010] In one embodiment, the three parameters d1, d2, d3 of the first synchronous controller are updated periodically and are denoted as d1(k), d2(k), d3(k);

[0011] The parameters d1(1), d2(1), and d3(1) corresponding to the first cycle are preset;

[0012] The parameters of the kth cycle are expressed as: d s (k) = mod (temp (s), R) + 1;

[0013] Where s is the parameter number, which can be 1, 2, or 3. The intermediate parameters temp(1), temp(2), and temp(3) are: bin2dec(·) means converting a binary number into a decimal number, mod(temp(s), R) means taking the remainder of temp(s) with respect to the constant R, dlen=floor(N / 3), and floor(·) means rounding down.

[0014] In one embodiment, the first chaotic response network is used to calculate the synchronization error e of the time interval [(k-1)T+Δt, kT] in the kth transmission cycle. i The integral of (t) Wherein the time interval Δt and the period T are preset constants;

[0015] like Then the decrypted information of the i-th node is like Then the decrypted information of the i-th node is Threshold e th is a preset constant;

[0016] Arrange the decryption information of each node in the order of node priority, and select the data between [1, length] in the sequence as the first decryption information length is the length of the information sequence m.

[0017] In one embodiment, the second chaotic driving network and the second chaotic response network both adopt a memristor chaotic system; the second chaotic driving network is used to integrate the random sequence seq into its own network parameters and perform parameter modulation to obtain the second chaotic sequence;

[0018] The rth parameter a of the i-th node in the second chaotic driving network ir The relevant mapping function is:

[0019]

[0020] Among them, r is the parameter number, r = 1, 2, 3, 4, max r ,min r is a preset constant, and the mapping function converts a ir The value range is limited to [min r ,max r ], p is the maximum value of the elements in the sequence seq; q is the minimum value of the elements in the sequence seq.

[0021] In one embodiment, the control law expression of the second synchronous controller is:

[0022]

[0023] The parameter adaptation law is:

[0024] Wherein, i represents the node number of the second chaotic response network, i=1, 2, ..., M; M is the number of nodes of the second chaotic driving network; u i1 ,u i2 ,u i3 ,u i4 are all state variables of the second synchronous controller; the four state errors are respectively expressed as: i1 =y i1 -x i1 , e i2 =y i2 -x i2 , e i3 =y i3 -x i3 , e i4 =y i4 -x i4 ;xi1 ,x i2 ,x i3 ,x i4 are the chaotic data output by the second chaotic driving network respectively; i1 ,y i2 ,y i3 ,y i4 are the chaotic data output by the second chaotic response network respectively; the intermediate variables and They are Constants h1, h2, h3, h4 ≥ 0, constants k1, k2, k3, k4 > 0.

[0025] In one embodiment, the second chaotic response network is used to utilize Decryption is performed to obtain the second decrypted information seq: i is the node sequence number of the second chaotic response network, and round(·) represents a rounding operation.

[0026] In one embodiment, the post-processing module is based on the first decryption information And the second decrypted information seq, using the formula Reverse recovery obtains the decrypted information message*, where l represents the sequence number, l=1, 2, ..., length, and length is the total length of the information sequence m.

[0027] In one embodiment, the number of nodes of the first chaotic driving network and the number of nodes of the first chaotic response network are equal, and the number of nodes N is greater than or equal to 4;

[0028] The number of nodes of the second chaotic driving network and the second chaotic response network is equal, and the relationship between the number of nodes M and the length of the information sequence m is: The function ceil(·) represents rounding up.

[0029] According to another aspect of the present invention, a chaotic secure communication method based on a multi-layer complex network is provided, which is applied to the above-mentioned chaotic secure communication system, comprising:

[0030] The operation performed at the transmitting end includes: using a random sequence seq to scramble the binary original plaintext message of the same length to obtain a binary information sequence m, inputting the information sequence m into the first chaotic driving network for encryption to obtain a first chaotic sequence, and inputting the random sequence seq into the second chaotic driving network for encryption to obtain a second chaotic sequence; wherein the elements in the information sequence m are system parameters of the first chaotic driving network;

[0031] The operation performed at the receiving end includes: when the l-th binary number m(l)=0, the first synchronization controller controls the first chaotic driving network and the first chaotic response network to achieve synchronization; when m(l)=1, the first synchronization controller controls the first chaotic driving network and the first chaotic response network to be out of synchronization; and then the first chaotic driving network is used to decrypt the first chaotic sequence according to the relationship between the value of the synchronization error of the first synchronization controller and the preset threshold value to obtain the first decryption information The second chaotic response network and the second chaotic driving network are completely synchronized by using the second synchronous controller, and the second chaotic driving network is used to decrypt the second chaotic sequence to obtain the second decrypted information seq, and the first decrypted information is used to obtain the second chaotic response network and the second chaotic driving network. And the second decrypted information seq is reversely restored to obtain the decrypted information message*.

[0032] In general, the above technical solutions conceived by the present invention can achieve the following beneficial effects compared with the prior art:

[0033] (1) The present invention provides a chaotic secure communication system based on a multi-layer complex network. First, the first and second chaotic driving networks for encryption are arranged at the transmitting end, and the first and second chaotic response networks for decryption are arranged at the receiving end. Considering the high parameter sensitivity of the chaotic sequence, the information encryption security is strong. Secondly, each chaotic driving network and chaotic response network includes multiple nodes. The communication system is designed in combination with the characteristics of the huge number of nodes and diverse edge relationships of the two-layer network, which can improve the overall architecture complexity of the system. Thirdly, the first synchronization controller arranged at the receiving end controls the first chaotic driving network and the first chaotic response network to achieve generalized synchronization according to the binary information transmitted by the current link. Based on the generalized synchronization of the complex network, the transmission information is judged to be 0 or 1 by judging the error between the corresponding nodes, thereby improving the noise robustness. Finally, by using the random sequence transmitted by the second chaotic driving and response networks, even if the first chaotic driving and response networks are cracked, data recovery cannot be completed in the absence of the random sequence, further improving the security of the system.

[0034] (2) The control laws of the first synchronous controller in this scheme are:

[0035] It can be achieved that when the lth binary number m(l) in the information sequence m is 0, the first chaotic driving network and the first chaotic response network are controlled to be synchronized, and when the lth binary number m(l) is 1, the first chaotic driving network and the first chaotic response network are controlled to be asynchronous.

[0036] (3) In this solution, the three parameters d1, d2, and d3 of the first synchronous controller are updated periodically, and the parameters of the kth period are expressed as: d s (k) = mod(temp(s), R) + 1; the operation of adding 1 to the remainder of temp(s) with respect to the constant R is to avoid the occurrence of d s (k)=0, which results in failure to meet the generalized synchronization condition; communication security can be enhanced while controlling the first chaotic driving network and the first chaotic response network to achieve generalized synchronization.

[0037] (4) The first chaotic response network in this scheme uses Calculate the synchronization error e of the time interval [(k-1)T+Δt,kT] within the kth transmission cycle i The integral value of (t) means that the information decryption in each transmission cycle depends on the information in the previous transmission cycle, which increases the difficulty for attackers to crack the code.

[0038] (5) In this scheme, the second chaotic driving network is used to integrate the random sequence seq into its own network parameters and perform parameter modulation to obtain the second chaotic sequence; the encryption method is simple to operate but can achieve high computational complexity, thereby improving communication security.

[0039] (6) This scheme provides an optimal control law expression of the second synchronization controller, which can enable the second chaotic driving network and the second chaotic response network to achieve complete synchronization, and its control parameters can also be adaptively updated, thereby improving communication security.

[0040] (7) This scheme provides an optimal decryption method for the second chaotic response network, using The second decrypted information seq is obtained by decryption, and different value ranges can be set for different parameters, thereby reducing the risk of parameter leakage.

[0041] (8) In this scheme, based on the first decryption information And the second decrypted information seq, using the formula Reverse recovery to get the decrypted message * , increasing the coupling connection between the two systems and comprehensively improving the safety performance of the entire system.

[0042] (9) In this scheme, the node dynamics of the transmitter and receiver do not need to be consistent, which increases the flexibility of the design and the wide applicability of the system.

[0043] (10) In this scheme, the first and second chaotic driving networks are used at the transmitting end to encrypt the information sequence and random sequence to be transmitted, and the first and second chaotic response networks are used at the receiving end to decrypt the information. Considering the high parameter sensitivity of the chaotic sequence, the information encryption security is strong. Secondly, at the receiving end, the first synchronization controller is used to control the first chaotic driving network and the first chaotic response network according to the binary information transmitted by the current link to achieve generalized synchronization. Based on the generalized synchronization of complex networks, the transmission information is judged to be 0 or 1 by judging the error between the corresponding nodes, thereby improving the noise robustness. Finally, by using the random sequence transmitted by the second chaotic driving and response networks, even if the first chaotic driving and response networks are cracked, data recovery cannot be completed in the absence of the random sequence, further improving the security of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a structural diagram of a chaotic secure communication system provided by Embodiment 1 of the present invention;

[0045] Figure 2 It is a secure communication framework diagram of the first chaotic driving network and the first chaotic response network provided in Example 1 of the present invention;

[0046] Figure 3 Schematic diagram of allocation rules and parameter update rules of sequence information m to be transmitted in embodiment 1 of the present invention;

[0047] Figure 4 It is a secure communication framework diagram of a second chaotic driving network and a second chaotic response network provided in Example 1 of the present invention;

[0048] Figure 5 Schematic diagram of bit error rate of the chaotic secure communication method provided by Embodiment 2 of the present invention under different signal-to-noise ratios;

[0049] Figure 6 This is a schematic diagram of information error after decryption error at the 7th node in the 5th cycle provided by Embodiment 2 of the present invention is not recovered by the subsystem sequence;

[0050] Figure 7 This is a schematic diagram of information error after decryption error at the 7th node in the 5th cycle provided by Embodiment 2 of the present invention is recovered through a subsystem sequence;

[0051] Figure 8 is a schematic diagram of a state variable error of a certain node when information is correctly transmitted provided by Embodiment 2 of the present invention;

[0052] Fig. 9 This is a schematic diagram of correct transmission information provided by Example 2 of the present invention. DETAILED DESCRIPTION

[0053] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0054] Example 1

[0055] like Figure 1 As shown, this embodiment provides a chaotic secure communication system, including: a transmitting end and a receiving end.

[0056] The transmitting end includes a preprocessing module, a first chaos driving network and a second chaos driving network. The preprocessing module is used to scramble the binary original plaintext message of the same length using a random sequence seq to obtain a binary information sequence m. The first chaos driving network is used to encrypt the information sequence m to obtain a first chaotic sequence. The elements in the information sequence m are system parameters of the first chaos driving network. The second chaos driving network is used to encrypt the random sequence seq to obtain a second chaotic sequence.

[0057] The receiving end includes a first synchronization controller, a second synchronization controller, a first chaotic response network, a second chaotic response network and a post-processing module. The first synchronization controller is used to control the first chaotic driving network and the first chaotic response network to be synchronized when the l-th binary number m(l) in the information sequence m is 0, and to control the first chaotic driving network and the first chaotic response network to be asynchronous when the l-th binary number m(l) is 0. The second synchronization controller is used to control the second chaotic response network and the second chaotic driving network to achieve complete synchronization. The first chaotic response network is used to decrypt the first chaotic sequence according to the relationship between the value of the synchronization error of the first synchronization controller and the preset threshold value to obtain the first decrypted information. The second chaotic response network is used to decrypt the second chaotic sequence to obtain the second decrypted information seq. The post-processing module is used to use the first decrypted information The decrypted information message* is obtained by reversely recovering the second decrypted information seq.

[0058] For the preprocessing module, it converts the original information into a binary sequence message, and first scrambles the order according to the rules. Taking message = [0,0,1,0,1,1] as an example, the random sequence is seq = [1,3,6,4,2,5], that is, m(1) = message(1) = 0, m(2) = message(3) = 1 and so on, and finally m = [0,1,1,0,0,1] is obtained, and then m is transmitted by the first chaotic driving network, and seq is transmitted by the second chaotic driving network.

[0059] For the first chaotic driving network and the first chaotic response network, as Figure 2 The encryption / decryption scheme structure shown in FIG. Assume that the first chaotic driving network has N nodes, and the first chaotic response network at the receiving end is symmetrically set with N nodes. The first chaotic driving network is composed of a chaotic system of N nodes, in which the state variables of each node are used as driving signals, and the parameters of the driving system are replaced by binary codes m(l), l = 1, 2, ..., length, and then encrypted information is generated; the first chaotic driving network and the first chaotic response network are controlled by a synchronous controller to achieve generalized synchronization, and then the generalized errors of the corresponding nodes of the two-layer network are calculated, and then compared with the error threshold, and then the original information is restored.

[0060] The first chaotic driving network's own dynamics adopts a unified parameter chaotic system, which is described by the following equation:

[0061]

[0062] i represents different nodes, i = 1, 2, ..., N; k represents the transmission cycle, m(N×(k-1)+i) is the information transmitted by the i-th node in the k-th transmission cycle, and its value is 0 or 1.

[0063] The first chaotic response network adopts the Lorenz system, and the dynamic equation can be described as:

[0064]

[0065] i represents different nodes, i=1,2,...,N; u i (t)=[u i1 ,u i2 ,u i3 ] T For synchronization controller.

[0066] Preferably, the first chaotic driving network adopts a unified chaotic system, and the first chaotic response network adopts a Lorenz chaotic system. The control law expression of the first synchronous controller is:

[0067]

[0068] Where i is the node number, i = 1, 2, ..., N. N is the number of nodes in the first chaotic driving network, u i1 ,u i2 ,u i3 are the state variables of the first controller respectively. i1 ,x i2 ,x i3They are the chaotic data output by the first chaotic driving network. i1 ,y i2 ,y i3 are the chaotic data output by the first chaotic response network. Define the state error e i1 =y i1 -d1x i1 ,e i2 =y i2 -d2x i2 ,e i3 =y i3 -d3x i3 Therefore, the generalized synchronization error between the driving and chaotic response networks is expressed as Here the variables d1, d2, d3≠0 are generalized synchronous functions The corresponding parameters remain consistent in each node within each transmission cycle, but different cycles will be updated according to the rules. When the information to be transmitted m(l) = 0, the present invention designs the following synchronization controller to achieve generalized synchronization between the chaotic driving network and the chaotic response network. h1, h2, h3 are preset constants and h1≥0, h2≥0, h3≥0.

[0069] Preferably, the three parameters d1, d2, d3 of the first synchronous controller are updated periodically, and are denoted as d1(k), d2(k), d3(k). The parameters d1(1), d2(1), d3(1) corresponding to the first period are preset. The update rules of the three parameters d1(k), d2(k), d3(k) of the synchronous controller are as follows: Figure 3 As shown, the information transmitted in the previous cycle will be used to update the parameters of the next cycle, where the parameters of the first cycle can be defined as d1(1)=d2(1)=d3(1)=1. The parameters of the kth cycle are expressed as:

[0070] d s (k) = mod(temp(s), R) + 1. Where s is the parameter number, which can be 1, 2, or 3. The intermediate parameters temp(1), temp(2), and temp(3) are:

[0071]

[0072] bin2dec(·) means converting a binary number into a decimal number, mod(temp(s), R) means taking the remainder of temp(s) with respect to the constant R, dlen=floor(N / 3), and floor(·) means rounding down.

[0073] Preferably, the first chaotic response network is used to calculate the synchronization error e of the time interval [(k-1)T+Δt, kT] within the kth transmission cycle. i The integral value of (t) Wherein the time interval Δt and the period T are preset constants. Then the decrypted information of the i-th node like Then the decrypted information of the i-th node Threshold e th is a preset constant. Arrange the decryption information of each node in the order of node priority, and select the data between [1, length] in the sequence as the first decryption information length is the length of the information sequence m.

[0074] Specifically, the first chaotic response network extracts x from the transmission channel i , according to the first synchronous controller, the required chaotic sequence y is further generated in the first chaotic response network i , and then calculate the generalized synchronization error of the corresponding node states of the first chaotic response network and the first chaotic driving network Assuming that the transmission information m(l) of the sender is 0, the two-layer network is synchronized, that is, after Δt time || e i (t)||→0. For the kth transmission cycle, the synchronization error integral within [(k-1)T+Δt, kT] is calculated. Since m(l) = 0, then If the transmission information m(l) = 1, then Therefore, according to the above synchronization error integral value and threshold e th = 10, and then determine whether synchronization is achieved, thereby determining whether the sent information m(l) is 0 or 1. Finally, the information obtained after decryption of each node is reassembled according to the order of node priority, and the redundant transmission information at the end is removed according to the sequence length to obtain

[0075] For the second chaotic driving network and the second chaotic response network, the structural framework is as follows Figure 4 As shown. The second chaotic driving network is used to communicate seq confidentially. Its structure is similar to that of the first chaotic driving network and the first chaotic response network, and is also divided into three parts: the transmitter, the receiver, and the transmission channel. The second chaotic driving network at the transmitter has M nodes, and the second chaotic response network at the receiver has M nodes. Assuming that the driving signal is the node state variable of the network, the random sequence seq is integrated into the system parameters and modulated; by designing the corresponding synchronization controller and parameter update rules, the chaotic driving network at the transmitter and the chaotic response network at the receiver are synchronized, and then parameter identification is performed to restore the original information.

[0076] The dynamic equation of the second chaotic driving network adopts a memristor chaotic system, and the chaotic driving network is described by the following equation:

[0077]

[0078] Where i represents different nodes, i = 1, 2, ..., M, a i1 ,a i2 ,a i3 ,a i4 is the system parameter.

[0079] Preferably, the second chaotic driving network and the second chaotic response network both adopt a memristor chaotic system. The second chaotic driving network is used to integrate the random sequence seq into its own network parameters and perform parameter modulation to obtain a second chaotic sequence. The rth parameter a of the i-th node in the second chaotic driving network ir The relevant mapping function is:

[0080]

[0081] Among them, r is the parameter number, r = 1, 2, 3, 4, max r ,min r is a preset constant, and the mapping function converts a ir The value range is limited to [min r ,max r ], p is the maximum value of the elements in the sequence seq; q is the minimum value of the elements in the sequence seq.

[0082] Regarding the dynamic equation of the second chaotic response network, assuming that the dynamics of the chaotic response network nodes themselves are different from those of the chaotic driving network, the chaotic response network can be described as:

[0083]

[0084] Where i represents different nodes, i = 1, 2, ..., M, u i (t)=[u i1 ,u i2 ,u i3 ,u i4 ] T For synchronization controller.

[0085] Preferably, the control law expressions of the second synchronous controller are respectively:

[0086]

[0087] The parameter adaptation laws are: Among them, u i1 ,u i2 ,u i3 ,u i4 are all state variables of the second controller. The four state errors are expressed as: ei1 =y i1 -x i1 , e i2 =y i2 -x i2 , e i3 =y i3 -x i3 , e i4 =y i4 -x i4 .x i1 ,x i2 ,x i3 ,x i4 They are the chaotic data output by the second chaotic driving network. i1 ,y i2 ,y i3 ,y i4 are the chaotic data output by the second chaotic response network. and They are i represents the node number of the second chaotic response network. Constants h1, h2, h3, h4 ≥ 0, constants k1, k2, k3, k4 > 0.

[0088] Preferably, the second chaotic response network is used to utilize Decryption is performed to obtain the second decrypted information seq: i is the node number of the second chaotic response network, and round(·) represents the rounding operation. That is, the second chaotic response network is obtained at the receiving end by receiving the chaotic signal and using the synchronization controller and parameter identification rules for synchronization. Then use the recovery function to get the sequence seq:

[0089] Preferably, the post-processing module is based on the first decryption information And the second decrypted information seq, using the formula Reverse recovery obtains the decrypted information message*, where l represents the sequence number, l=1, 2, ..., length, and length is the total length of the information sequence m.

[0090] Preferably, the number of nodes in the first chaotic driving network and the first chaotic response network is equal, and the number of nodes N is ≥ 4. The number of nodes in the second chaotic driving network and the second chaotic response network is equal, and the relationship between the number of nodes M and the length of the information sequence m is: The function ceil(·) represents rounding up. The information m(l) is allocated in the order that satisfies the node arrangement first, and is transmitted in multiple cycles. For example, the information transmitted by the i-th node in the k-th transmission cycle is m(N×(k-1)+i). When the last bit of m(l) is allocated, the remaining nodes in the cycle will randomly transmit 0 or 1. The total number of transmission cycles is The function ceil(·) represents rounding up. The relationship between the number of nodes in the second chaotic driving network and the length of the binary information sequence is: The function ceil(·) represents rounding up.

[0091] Example 2

[0092] This embodiment provides a chaotic secure communication method, which is applied to the above-mentioned chaotic secure communication system, including:

[0093] The operation performed at the transmitting end includes: using a random sequence seq to scramble the binary original plaintext message of the same length to obtain a binary information sequence m, inputting the information sequence m into the first chaotic driving network for encryption to obtain a first chaotic sequence, and inputting the random sequence seq into the second chaotic driving network for encryption to obtain a second chaotic sequence. The elements in the information sequence m are system parameters of the first chaotic driving network.

[0094] The operation performed at the receiving end includes: when the l-th binary number m(l)=0, the first synchronization controller controls the first chaotic driving network and the first chaotic response network to achieve synchronization; when m(l)=1, the first synchronization controller controls the first chaotic driving network and the first chaotic response network to be out of synchronization; and then the first chaotic driving network is used to decrypt the first chaotic sequence according to the relationship between the value of the synchronization error of the first synchronization controller and the preset threshold value to obtain the first decryption information The second chaotic response network and the second chaotic driving network are completely synchronized by using the second synchronous controller, and the second chaotic driving network is used to decrypt the second chaotic sequence to obtain the second decrypted information seq, and the first decrypted information seq is used to obtain the second chaotic response network and the second chaotic driving network. The decrypted information message* is obtained by reversely recovering the second decrypted information seq.

[0095] Assuming that 100 bits of information are transmitted, the number of nodes of the main system including the first chaotic driving network and the first chaotic response network is 10, and the transmission period of the main system is 10. The present invention adds a noise component to the transmission channel, and the actual information obtained by the receiving end is {x i1 +n i1 ,x i2 +n i2 ,x i3 +n i3}, where the superimposed component ni1 ,n i2 ,n i3 For noise.

[0096] This embodiment uses Gaussian white noise for simulation, and studies whether the scheme is effective when the security system has noise in the channel based on experiments. Gaussian white noise follows a normal distribution, and after Fourier transform, the power spectrum is equal at different frequencies, and there is no correlation between different moments. In the field of communications, the signal-to-noise ratio refers to the effective power ratio of the signal to the noise, and the calculation formula is as follows: Where P s ,P n The effective power of the signal and noise are respectively expressed in W, and the SNR unit is dB. The present invention changes the power of the noise and tests the bit error rate of the system transmission information under different signal-to-noise ratios. Some of the results are shown in Figure 5 It can be seen that when the noise is higher, that is, the signal-to-noise ratio is lower, the system bit error rate is higher, but when the signal-to-noise ratio is above 29dB, it can be effectively decrypted.

[0097] Here, the transmission period is set to dimensionless time T = 1. Assuming that the decryption information of node 7 is wrong in the fifth transmission period, the decryption result of the main system is as follows: Figure 6 As shown in the figure, the information transmitted by node 7 in the fifth transmission cycle does not match the correct information, and the decryption of variables d1(6), d2(6), and d3(6) after this cycle is wrong, resulting in the failure of synchronization between the first chaotic driving network and the receiving end in the sixth cycle. Therefore, the decrypted data is 1, which causes a chain reaction and causes all the decrypted information in subsequent cycles to be 1. After further subsystem information recovery, the final decrypted data is as follows: Figure 7 As shown, the subsystem includes a second chaotic driving network and a second chaotic response network. It can be concluded that as long as there are a few nodes that make cracking errors for the attacker, the subsequent transmission cycles will decrypt the information to 1, resulting in errors, and after the random sequence of the subsystem is restored, the error will be spread to the entire transmission sequence.

[0098] The two-level system transmits information correctly, and a master system node is randomly selected to calculate the synchronization error. The results are as follows Figure 8 As shown. It can be seen that if the previous cycle is not synchronized and the next cycle is synchronized, the error will be large at the initial moment of the synchronization cycle, but it can still be reduced later. In the 1st, 5th, and 7th transmission cycles, the node transmission error is approximately reduced to 0, while the node error in the remaining transmission cycles is much larger than 0. Therefore, it is judged that the node transmission information is [0,1,1,1,0,1,0,1,1,1], and the experimental verification result is correct. The entire decrypted information sequence is as follows Fig. 9 In summary, the two-level chaotic security system designed by the present invention can effectively improve the anti-cracking capability and make information transmission more secure and effective.

[0099] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A chaotic secure communication system based on a multi-layer complex network, characterized in that: include: A transmitting end, comprising a preprocessing module, a first chaos driving network and a second chaos driving network; The preprocessing module is used to scramble the binary original plaintext message of the same length using the random sequence seq to obtain a binary information sequence m; The first chaotic driving network is used to encrypt the information sequence m to obtain a first chaotic sequence; the elements in the information sequence m are system parameters of the first chaotic driving network; The second chaotic driving network is used to encrypt the random sequence seq to obtain a second chaotic sequence; The receiving end includes a first synchronization controller, a second synchronization controller, a first chaotic response network, a second chaotic response network and a post-processing module; the first synchronization controller is used to control the first chaotic driving network and the first chaotic response network to be synchronized when the l-th binary number m(l) in the information sequence m is 0, and to control the first chaotic driving network and the first chaotic response network to be asynchronous when the l-th binary number m(l) is 1; the second synchronization controller is used to control the second chaotic response network and the second chaotic driving network to achieve complete synchronization; the first chaotic response network is used to decrypt the first chaotic sequence according to the relationship between the value of the synchronization error of the first synchronization controller and the size of the preset threshold to obtain the first decrypted information The second chaotic response network is used to decrypt the second chaotic sequence to obtain second decrypted information The post-processing module is used to utilize the first decryption information and the second decrypted information Reverse recovery to obtain the decrypted information message*; The first chaotic driving network adopts a unified chaotic system, which is expressed as: The first chaotic response network adopts the Lorenz chaotic system as: The control law of the first synchronous controller is: i is the node number, i=1,2,...,N; N is the number of nodes in the first chaotic driving network; k represents the transmission period, u i (t)=[u i1 ,u i2 ,u i3 ] T is the synchronization controller, m(N×(k-1)+i) is the information transmitted by the i-th node in the k-th transmission cycle; u i1 ,u i2 ,u i3 are all state variables of the first synchronous controller; x i1 ,x i2 ,x i3 are the chaotic data output by the first chaotic driving network respectively; i1 ,y i2 ,y i3 are the chaotic data output by the first chaotic response network respectively; i =(e i1 ,e i2 ,e i3 ) T represents the generalized synchronization error between the first chaotic driving network and the first chaotic response network, and the first error parameter e i1 =y i1 -d1x i1 , the second error parameter e i2 =y i2 -d2x i2 , the third error parameter e i3 =y i3 -d3x i3 , d1, d2, d3 are three parameters of the first synchronous controller, h1, h2, h3 are preset constants and h1≥0, h2≥0, h3≥0; The second chaotic driving network and the second chaotic response network both adopt a memristor chaotic system; Representation of the second chaotic driving network: The second chaotic response network is: The control law of the second synchronous controller is: The parameter adaptation law expression is: i represents the node number of the second chaotic response network, i=1, 2, ..., M; M is the number of nodes of the second chaotic driving network; a i1 ,a i2 ,a i3 ,a i4 is the system parameter; u i1 ,u i2 ,u i3 ,u i4 are all state variables of the second synchronous controller; the four state errors are expressed as: e i1 =y i1 -x i1 , e i2 =y i2 -x i2 , e i3 =y i3 -x i3 , e i4 =y i4 -x i4 ;x i1 ,x i2 ,x i3 ,x i4 are the chaotic data output by the second chaotic driving network respectively; i1 ,y i2 ,y i3 ,y i4 are respectively chaotic data output by the second chaotic response network; Intermediate variables and They are Constants h1, h2, h3, h4 ≥ 0, constants k1, k2, k3, k4 >

0.

2. The chaotic secure communication system based on a multi-layer complex network as claimed in claim 1, characterized in that: The three parameters d1, d2, d3 of the first synchronous controller are updated periodically and are denoted as d1(k), d2(k), d3(k); The parameters d1(1), d2(1), and d3(1) corresponding to the first cycle are preset; The parameters of the kth cycle are expressed as: d s (k) = mod (temp (s), R) + 1; Where s is the parameter number, which can be 1, 2, or 3. The intermediate parameters temp(1), temp(2), and temp(3) are: bin2dec(·) means converting a binary number into a decimal number, mod(temp(s), R) means taking the remainder of temp(s) with respect to the constant R, dlen=floor(N / 3), and floor(·) means rounding down.

3. The chaotic secure communication system based on a multi-layer complex network as claimed in claim 1, characterized in that: The first chaotic response network is used to calculate the synchronization error e of the time interval [(k-1)T+Δt, kT] within the kth transmission cycle. i The integral of (t) Among them, the time interval Δt and the period T are preset constants; like Then the decrypted information of the i-th node like Then the decrypted information of the i-th node Threshold e th is a preset constant. Arrange the decryption information of each node in the order of node priority, and select the data between [1, length] in the sequence as the first decryption information length is the length of the information sequence m.

4. The chaotic secure communication system based on a multi-layer complex network as claimed in claim 1, characterized in that: The second chaotic driving network is used to integrate the random sequence seq into its own network parameters and perform parameter modulation to obtain the second chaotic sequence; The rth parameter a of the i-th node in the second chaotic driving network ir The relevant mapping function is: Among them, r is the parameter number, r = 1, 2, 3, 4, max r ,min r is a preset constant, and the mapping function converts a ir The value range is limited to [min r ,max r ], p is the maximum value of the elements in the sequence seq; q is the minimum value of the elements in the sequence seq.

5. The chaotic secure communication system based on a multi-layer complex network as claimed in claim 4, characterized in that: The second chaotic response network is used to utilize Decrypt to obtain the second decrypted information i is the node number of the second chaotic response network, and round(·) indicates rounding operation.

6. The chaotic secure communication system based on a multi-layer complex network as claimed in claim 1, characterized in that: The post-processing module is used to and the second decrypted information Using the formula Reverse recovery obtains the decrypted information message*, where l represents the sequence number, l=1, 2, ..., length, and length is the total length of the information sequence m.

7. The chaotic secure communication system based on a multi-layer complex network according to any one of claims 1 to 6, characterized in that: The number of nodes of the first chaotic driving network and the number of nodes of the first chaotic response network are equal, and the number of nodes N is ≥ 4; The number of nodes of the second chaotic driving network and the second chaotic response network is equal, and the relationship between the number of nodes M and the length of the information sequence m is: The function ceil(·) represents rounding up.

8. A chaotic secure communication method based on a multi-layer complex network, characterized in that: The chaotic secure communication system based on a multi-layer complex network applied to any one of claims 1 to 7 comprises: The operation performed at the transmitting end includes: using a random sequence seq to scramble the binary original plaintext message of the same length to obtain a binary information sequence m, inputting the information sequence m into the first chaotic driving network for encryption to obtain a first chaotic sequence, and inputting the random sequence seq into the second chaotic driving network for encryption to obtain a second chaotic sequence; wherein the elements in the information sequence m are system parameters of the first chaotic driving network; The operation performed at the receiving end includes: when the l-th binary number m(l)=0, the first synchronization controller controls the first chaotic driving network and the first chaotic response network to achieve synchronization; when m(l)=1, the first synchronization controller controls the first chaotic driving network and the first chaotic response network to be out of synchronization; and then the first chaotic driving network is used to decrypt the first chaotic sequence according to the relationship between the value of the synchronization error of the first synchronization controller and the preset threshold value to obtain the first decryption information The second chaotic response network and the second chaotic driving network are completely synchronized by using the second synchronous controller, and the second chaotic driving network is used to decrypt the second chaotic sequence to obtain second decrypted information. Using the first decrypted information and the second decrypted information Reverse recovery obtains the decrypted information message*.

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