阅读说明：本技术 一种五维超混沌耦合同步系统及卫星物理层加密传输方法 (Five-dimensional hyperchaotic coupling synchronization system and satellite physical layer encryption transmission method ) 是由 陈远祥 鲁帆 李嘉豪 邓怡珺 刘畅 马炳 张橹 程竟爽 余建国 于 2021-08-02 设计创作，主要内容包括：本发明公开了一种五维超混沌耦合同步系统及卫星物理层加密传输方法,由于双方初始密钥不同,产生的混沌序列值也不相同。随后驱动系统通过耦合项将响应系统对应的序列作为反馈对所产生的混沌序列进行调整从而逐渐到达同步。本发明通过使用非对称密钥的混沌耦合同步系统,在增大密钥空间提升安全性能的同时没有增加过多的计算量,相比于现有技术方案更加容易在卫星通信中实现。(The invention discloses a five-dimensional hyperchaotic coupling synchronization system and a satellite physical layer encryption transmission method. And then the driving system adjusts the generated chaotic sequence by taking the sequence corresponding to the response system as feedback through the coupling term so as to gradually reach synchronization. The chaotic coupling synchronization system of the asymmetric key is used, so that the key space is increased, the safety performance is improved, excessive calculation amount is not increased, and the chaotic coupling synchronization system is easier to realize in satellite communication compared with the prior art.)

1. A five-dimensional hyperchaotic coupling synchronization system is characterized by comprising:

the driving system is used as a transmitting end of a signal, and the expression of the driving system is shown as the formula (1):

the response system, as a receiving end of the signal, has an expression as shown in formula (2):

wherein, α ═ 21.25, β ═ 0.03, δ ═ 170, e ═ 0.9444, g ═ 14.62 are system parameters, δ is a system parameter_x、δ_y、δ_z、δ_w、δ_uIs the coupling coefficient; x is the number of₁，y₁，z₁，w₁，u₁Five sets of initial keys, x, for the drive system₂，y₂，z₂，w₂，u₂In response to the five sets of initial keys of the system,five sets of chaotic sequences are generated for driving the system,in order to respond to five groups of chaotic sequences generated by the system, the initial keys of the driving system and the responding system are different.

2. The satellite physical layer encryption transmission method of the five-dimensional hyperchaotic coupled synchronous system based on claim 1 is characterized by comprising the following steps:

s1, the transmitting end and the receiving end exchange keys at first, and the transmitting end generates a chaotic sequence according to the formula (1) by using two pairs of keys;

s2, the transmitting terminal takes the sequence corresponding to the receiving terminal as feedback through the coupling item to adjust the generated chaotic sequence according to the formula (2) so as to gradually reach synchronization;

s3, performing chaotic XOR operation on the originally sent data according to the formula (3), and mapping the data to a QAM constellation after serial-to-parallel S/P conversion to obtain XOR encryption S' of the bit stream;

where S is the original input data, K₁One of the chaotic sequences generated for the chaotic system;

s4, carrying out in-phase and quadrature shift encryption according to the formula (4) after carrying out 4-QAM mapping on S';

S″＝(S′_I±K₂)+j(S′_Q±K₃) (4)

wherein, S'_I、S′_QIs the original homodromous and quadrature components of 4-QAM constellation points, S' is the encrypted constellation points after chaotic parameter mapping, K₂And K₃Two independent chaotic sequences generated by a chaotic system are used for respectively encrypting in-phase components and orthogonal components;

s5, after chaotic encryption, converting the encrypted data into a time domain through inverse fast Fourier transform;

s6, adding a cyclic prefix CP before transmitting the signal.

Technical Field

The invention relates to the technical field of satellite communication, in particular to a five-dimensional hyperchaotic coupling synchronous system and a satellite physical layer encryption transmission method based on the five-dimensional hyperchaotic coupling synchronous system.

Background

Satellite communications are susceptible to eavesdropping by third party receivers during propagation due to the broadcast nature of their signals. When the signal is received and intercepted by others, the communication satellite can be tracked and the remote control signal can be interfered, and if some key signals are interfered during the control of the transmission and the operation of the satellite, the satellite is easy to lose control, so that the satellite communication system is paralyzed. Along with the rapid development of the computing power of the computer, the traditional confidential protocol mechanism based on the calculated amount has the security at risk. Therefore, how to eliminate illegal eavesdropping is a serious problem facing satellite communications.

In order to prevent the signal from being intercepted, a physical layer encryption scheme is required to be adopted to encrypt Orthogonal Frequency Division Multiplexing (OFDM), and the chaotic signal is sensitive to initial conditions, similar to noise, and has the characteristics of low cross correlation among signals generated under different initial conditions and the like, so that the chaotic encryption is researched by the communication field.

At present, most of chaotic encryption is that a transmitting party and a receiving party use the same initial value as a secret key. Usama M et al propose a new Chaos-based symmetric key encryption technique (Usama M, Khan MK, Alghathbar K,3,2.Chaos-based secure software encryption system [ J ]. Computers & Mathesics With Applications,2010,60(2): 326-. Bentoutouu Y et al propose an encryption method based on chaotic mapping and advanced encryption standard, which improves security by chaotic grouping and key stream selection (Bentoutoutouu Y, Bensikaddour E, Taleb N, Bouneua N.an improved image encryption for satellite applications [ J ]. Advances In Space Research,12020,66(1): 176-.

The existing chaotic encryption is an encryption technology based on a symmetric key, and most of the schemes improve a key space through a plurality of chaotic systems or combination of the chaotic systems and a traditional encryption means. However, this method increases the security level and increases the computational complexity greatly, so it requires high computational power and long processing time, which is not easy to implement in satellite communication with limited computational power.

Disclosure of Invention

Aiming at the technical problems, the invention provides a five-dimensional hyper-chaotic coupling synchronization system and a satellite physical layer encryption transmission method based on the five-dimensional hyper-chaotic coupling synchronization system.

In order to achieve the above purpose, the invention provides the following technical scheme:

the invention provides a five-dimensional hyperchaotic coupling synchronization system, which comprises:

the driving system is used as a transmitting end of a signal, and the expression of the driving system is shown as the formula (1):

the response system, as a receiving end of the signal, has an expression as shown in formula (2):

wherein, α ═ 21.25, β ═ 0.03, δ ═ 170, e ═ 0.9444, g ═ 14.62 are the systemParameter, δ_x、δ_y、δ_z、δ_w、δ_uIs the coupling coefficient; x is the number of₁，y₁，z₁，w₁，u₁Five sets of initial keys, x, for the drive system₂，y₂，z₂，w₂，u₂In response to the five sets of initial keys of the system,five sets of chaotic sequences are generated for driving the system,in order to respond to five groups of chaotic sequences generated by the system, the initial keys of the driving system and the responding system are different.

The invention also provides a satellite physical layer encryption transmission method based on the five-dimensional hyperchaotic coupling synchronization system, which comprises the following steps:

s1, the transmitting end and the receiving end exchange keys at first, and the transmitting end generates a chaotic sequence according to the formula (1) by using two pairs of keys;

s2, the transmitting terminal takes the sequence corresponding to the receiving terminal as feedback through the coupling item to adjust the generated chaotic sequence according to the formula (2) so as to gradually reach synchronization;

s3, performing chaotic XOR operation on the originally sent data according to the formula (3), and mapping the data to a QAM constellation after serial-to-parallel S/P conversion to obtain XOR encryption S' of the bit stream;

where S is the original input data, K₁One of the chaotic sequences generated for the chaotic system;

s4, carrying out in-phase and quadrature shift encryption according to the formula (4) after carrying out 4-QAM mapping on S';

S″＝(S′_I±K₂)+j(S′_Q±K₃) (4)

wherein, S'_I、S′_QIs the original in-phase and quadrature components of the 4-QAM constellation point, S' is the encrypted constellation point after chaotic parameter mapping, K₂And K₃Two independent chaotic sequences generated by a chaotic system are used for respectively encrypting in-phase components and orthogonal components;

s5, after chaotic encryption, converting the encrypted data into a time domain through inverse fast Fourier transform;

s6, adding a cyclic prefix CP before transmitting the signal.

Compared with the prior art, the invention has the beneficial effects that:

the five-dimensional hyperchaotic coupling synchronous system provided by the invention has different chaos sequence values due to different initial keys of the two parties. And then the driving system adjusts the generated chaotic sequence by taking the sequence corresponding to the response system as feedback through the coupling term so as to gradually reach synchronization. Because the initial value keys at the transmitting end and the receiving end can be two groups of keys which are completely different, only the key at the transmitting end or the key at the receiving end is known, and a correct chaotic sequence cannot be obtained, an eavesdropper needs to know two pairs of keys which are extremely sensitive to the initial value at the same time to crack.

Compared with the chaotic encryption technology of a symmetric key, the satellite system safety transmission method based on the five-dimensional hyperchaotic coupling synchronous system provided by the invention has lower encryption complexity and larger key space without increasing the calculation complexity.

The invention increases the space of the secret key, improves the safety performance, does not increase excessive calculation amount and is easier to realize in satellite communication by using the chaotic coupling synchronous system of the asymmetric secret key. The sensitivity of the chaos coupling synchronous system to the initial key is very high (10)^-19) And the system encrypts the original communication system with negligible impact on the communication quality itself.

Drawings

In order to more clearly illustrate the embodiments of the present application or technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments described in the present invention, and other drawings can be obtained by those skilled in the art according to the drawings.

Fig. 1 is a schematic diagram of a five-dimensional hyper-chaotic coupling synchronization system according to an embodiment of the present invention.

Fig. 2 is a phase diagram of a five-dimensional hyper-chaotic coupling synchronization system according to an embodiment of the present invention, where fig. 2(a) is an x-y-z phase diagram, fig. 2(b) is a z-u-w phase diagram, and fig. 2(c) is a z-w phase diagram.

Fig. 3 is a conventional QAM4 constellation point diagram and a five-dimensional hyper-chaotic encrypted constellation point diagram according to an embodiment of the present invention, where fig. 3(a) is a conventional QAM4 constellation point, and fig. 3(b) is a five-dimensional hyper-chaotic encrypted constellation point.

Fig. 4 is a schematic diagram of a chaotic encryption system for OFDM according to an embodiment of the present invention.

Fig. 5 is a bit error rate curve and a corresponding constellation diagram of an original OFDM, a chaotic OFDM, and an illegal receiver according to an embodiment of the present invention.

Fig. 6 is a graph of the error rate according to the variation of the key error value according to the embodiment of the present invention.

Detailed Description

For a better understanding of the present solution, the method of the present invention is described in detail below with reference to the accompanying drawings.

The invention provides a five-dimensional hyperchaotic coupling synchronous system, as shown in figure 1, in the coupling synchronous system, due to the difference of initial keys of the two parties, the generated chaotic sequence values are different. And then the driving system adjusts the generated chaotic sequence by taking the sequence corresponding to the response system as feedback through the coupling term so as to gradually reach synchronization. Because the initial value keys at the transmitting end and the receiving end can be two groups of keys which are completely different, only the key at the transmitting end or the key at the receiving end is known, and a correct chaotic sequence cannot be obtained, an eavesdropper needs to know two pairs of keys which are extremely sensitive to the initial value at the same time to crack.

The five-dimensional hyperchaotic coupling synchronous system provided by the invention can be expressed as follows:

wherein, the expression (1) is a transmitting end system, the expression (2) is a receiving end system, α ═ 21.25, β ═ 0.03, δ ═ 170, e ═ 0.9444, g ═ 14.62 are system parameters, δ is a system parameter, δ is a transmitting end system, δ is a receiving end system, and β ═ 21.25, β ═ 0.03, δ ═ 170, e ═ 0.9444, g ═ 14.62 are system parameters_x、δ_y、δ_z、δ_w、δ_uIs the coupling coefficient. x is the number of₁，y₁，z₁，w₁，u₁Five sets of initial keys, x, for the drive system₂，y₂，z₂，w₂，u₂In response to the five sets of initial keys of the system,five sets of chaotic sequences are generated for driving the system,in order to respond to five groups of chaotic sequences generated by the system, the initial keys of the driving system and the responding system are different.

The phase diagram is shown in fig. 2. Wherein FIG. 2(a) is an x-y-z phase diagram, FIG. 2(b) is a z-u-w phase diagram, and FIG. 2(c) is a z-w phase diagram.

The exclusive-or encryption of the bit stream in the encryption scheme used can be represented as the following equation:

where S is the original input data, K₁One of the chaotic sequences generated for the chaotic system. And 4-QAM mapping is carried out on S', and then chaotic amplitude phase encryption is carried out, wherein the encryption can be represented by the following formula:

S″＝(S′_I±K₂)+j(S′_Q±K₃) (4)

wherein, S'_I、S′_QIs the original homodromous and quadrature components of the 4-QAM constellation points, and S' is the encrypted constellation points after chaotic parameter mapping. K₂And K₃Two independent chaotic sequences generated by the chaotic system are used for encrypting the in-phase component and the quadrature component respectively.

Fig. 3(a) shows conventional 4-QAM constellation points, and the mapped constellation points are shown in fig. 3 (b). For the condition of more input data, the coverage range of the constellation diagram can be completely filled by adopting chaotic QAM symbol mapping. Such noise-like constellation points thus greatly increase the security level.

The invention also provides a satellite physical layer encryption transmission method based on the five-dimensional hyper-chaotic coupling synchronization system, and as shown in fig. 4, the chaotic encryption for the OFDM comprises the following steps:

the transmitting end and the receiving end exchange keys at first, the transmitting end uses two pairs of keys to generate a chaotic sequence according to the formula (1), the key of the transmitting end is taken as the main key, and the key of the receiving end is used for feedback to complete the synchronization of the two chaotic systems. The originally transmitted data first performs a chaotic exclusive or (XOR) operation according to equation (3). After serial-to-parallel (S/P) conversion, the data is mapped to a 4-QAM constellation and then encrypted with in-phase and quadrature shifts according to equation (4). After chaotic encryption, the encrypted data is converted to the time domain by Inverse Fast Fourier Transform (IFFT), and finally a Cyclic Prefix (CP) is added before transmitting the signal.

In a similar way, the receiving end uses two pairs of keys to generate a chaotic sequence according to the equation (2), takes the key of the receiving end as the main key, and feeds back the chaotic sequence through the key of the receiving end to complete the synchronization of the two chaotic systems. Removing Cyclic Prefix (CP) from received data, performing serial-to-parallel (S/P) conversion, performing Fast Fourier Transform (FFT) to convert encrypted data into a frequency domain, performing certain repair on the received data by using an equalization technology, and performing in-phase and quadrature component decryption, QAM demapping and chaotic XOR operation to finish decryption of the data.

In a specific embodiment, we set the sender initial value to { x }₁ y₁ z₁ w₁ u₁(0.0005438432, 0.0025437654, 0.0005254376, 0.0034562123, 0.2234562345), and the initial value at the receiving end is { x }₂ y₂ z₂w₂ u₂}＝(1.0145467111，1.0012454633，1.5767895435，1.3457345347，1.2346474435)。

1000 simulation simulations were performed by the monte carlo method. The Bit Error Rate (BER) and corresponding constellation are shown in fig. 5. As can be seen from the BER curve, the proposed chaotic orthogonal frequency division multiplexing scheme and the original OFDM scheme show almost the same performance when the correct security key is used. Simulations show that a legitimate receiver can correctly recover the encrypted data signal. The error rate is about 0.3 when the signal is decrypted by an illegal receiver.

When the key has a very small error, the key cannot be correctly decrypted. As shown in fig. 6, when the key appears 10^-19In error of (e.g. { x) }₁ y₁ z₁ w₁ u₁When the OFDM signal is (0.0005438432+10-19, 0.0025437654, 0.0005254376, 0.0034562123, 0.2234562345), the OFDM signal cannot be solved normally, and the error rate is about 0.3.

In conclusion, the chaotic coupling synchronization system using the asymmetric key is adopted, so that the key space is increased, the safety performance is improved, excessive calculation amount is not increased, and the chaotic coupling synchronization system is easier to realize in satellite communication. The sensitivity of the chaos coupling synchronous system to the initial key is very high (<<10^-19) And the system encrypts the original communication system with negligible impact on the communication quality itself.

The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: it is to be understood that modifications may be made to the technical solutions described in the foregoing embodiments, or equivalents may be substituted for some of the technical features thereof, but such modifications or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.