WFRFT transmission method and system based on two-dimensional chaotic mapping constellation encryption

Abstract

The present disclosure is about a WFRFT transmission method and system based on two-dimensional chaotic mapping constellation encryption. The method comprises the following steps: the input signal is subjected to constellation mapping to obtain a modulation column vector; a first sequence and a second sequence are generated through two-dimensional chaotic mapping, and the modulation column vector is subjected to constellation encryption processing using the first sequence and the second sequence to generate an encrypted signal; the encrypted signal is subjected to WFRFT inverse transformation to complete mixed carrier modulation; the receiving end receives the mixed carrier signal and performs WFRFT transformation on the mixed carrier signal; a decryption matrix is ​​generated according to the parameters of the two-dimensional chaotic mapping, and the encrypted signal is decrypted using the decryption matrix to complete the demodulation process. The present disclosure further enhances the confidentiality performance of the WFRFT transmission method.

Description

Technical Field

[0001] The present disclosure relates to the field of secure communication technologies, and in particular, to a WFRFT transmission method and system based on two-dimensional chaotic mapping constellation encryption. Background Art

[0002] The Weighted Fractional Fourier Transform (WFRFT) is a special form of fractional Fourier transform, which has received attention in the fields of time-frequency analysis and has been gradually widely used in the field of wireless communication. The weighted fractional Fourier transform is a hybrid transform that combines time-domain and frequency-domain characteristics and can be expressed as a weighted sum of four-state functions of the traditional Fourier transform, thus presenting some new characteristics.

[0003] Although the WFRFT transform can improve the covert communication ability of a communication system, unauthorized receivers can still obtain demodulation parameters such as the WFRFT transform order through methods such as parameter scanning. Therefore, it is necessary to improve one or more problems existing in the above-mentioned related technical solutions to further enhance the security performance of the WFRFT transmission method.

[0004] It should be noted that the information disclosed in the above background art section is only used to enhance the understanding of the background of the present disclosure, and therefore may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0005] The purpose of the embodiments of the present disclosure is to provide a WFRFT transmission method and system based on two-dimensional chaotic mapping constellation encryption to enhance the security performance of the WFRFT transmission method.

[0006] According to the first aspect of the embodiments of the present disclosure, a WFRFT transmission method based on two-dimensional chaotic mapping constellation encryption is provided. The method includes the following steps:

[0007] The input signal is mapped by a constellation to obtain a modulated column vector;

[0008] A first sequence and a second sequence are generated through two-dimensional chaotic mapping, and the modulated column vector is encrypted by the constellation using the first sequence and the second sequence to generate an encrypted signal;

[0009] The encrypted signal is subjected to an inverse WFRFT transformation to complete hybrid carrier modulation;

[0010] The receiving end receives the hybrid carrier signal and performs a WFRFT transformation on the hybrid carrier signal;

[0011] Generate a decryption matrix according to the parameters of the two-dimensional chaotic mapping, and use the decryption matrix to decrypt the encrypted signal, thereby completing the demodulation process.

[0012] In an exemplary embodiment of the present disclosure, the step of performing constellation encryption processing on the modulation column vector by using the first sequence and the second sequence further includes the following steps:

[0013] Expand and encrypt the amplitude of the modulation symbol by using the first sequence, and rotate and encrypt the phase of the modulation symbol by using the second sequence to generate an encryption matrix for the amplitude and phase of the modulation symbol;

[0014] Perform encryption processing on the modulation column vector according to the encryption matrix.

[0015] In an exemplary embodiment of the present disclosure, in the step of expanding and encrypting the amplitude of the modulation symbol by using the first sequence, the first sequence first obtains an amplitude expansion factor r through formula (1) n , and then generates an amplitude encryption matrix R of the modulation symbol through formula (2);

[0016]

[0017] R = diag(r) (2);

[0018] where u is the first sequence, r = (r 0 , r 1 , …, r N-1 ) T .

[0019] In an exemplary embodiment of the present disclosure, in the step of rotating and encrypting the phase of the modulation symbol by using the second sequence, the second sequence first obtains a phase rotation factor φ through formula (3) n , and then generates a phase encryption matrix Φ of the modulation symbol through formula (4);

[0020]

[0021]

[0022] where v is the second sequence.

[0023] In an exemplary embodiment of the present disclosure, in the step of performing encryption processing on the modulation column vector according to the encryption matrix, encryption is performed through formula (5);

[0024] X 0 = RΦx (5);

[0025] where x = (x0 , x 1 , …x N-1 ) T is the modulation column vector.

[0026] In an exemplary embodiment of the present disclosure, the decryption matrix and the encryption matrix are inverse matrices of each other.

[0027] In an exemplary embodiment of the present disclosure, in the step of generating a decryption matrix according to the parameters of the two-dimensional chaotic map and decrypting the encrypted signal by using the decryption matrix, the decryption formula is:

[0028] X d = R -1 Φ -1 y 0 (6);

[0029] where y 0 is the signal after the WFRFT transform;

[0030] R -1 is the amplitude decryption matrix of the modulation symbol, and

[0031] Φ -1 is the phase decryption matrix of the modulation symbol, and Φ -1 = Φ H .

[0032] In an exemplary embodiment of the present disclosure, the two-dimensional chaotic map is the Hénon chaotic map.

[0033] In an exemplary embodiment of the present disclosure, the modulation method of the input signal after constellation mapping is PSK modulation, ASK modulation or QAM modulation.

[0034] According to the second aspect of the embodiments of the present disclosure, a WFRFT transmission system based on two-dimensional chaotic map constellation encryption is provided, and the system includes:

[0035] A chaotic map constellation encryption unit, configured to generate a first sequence and a second sequence through a two-dimensional chaotic map, and perform constellation encryption processing on a modulation column vector generated through constellation mapping by using the first sequence and the second sequence to generate an encrypted signal;

[0036] A WFRFT inverse transform unit, configured to perform an inverse WFRFT transform on the encrypted signal to complete hybrid carrier modulation;

[0037] A WFRFT transform unit, configured to perform a WFRFT transform on the hybrid carrier signal after receiving the hybrid carrier signal at the receiving end;

[0038] The decryption unit is used to generate a decryption matrix according to the parameters of the two-dimensional chaotic map, and use the decryption matrix to decrypt the encrypted signal, thereby completing the demodulation process.

[0039] The technical solution provided by the present disclosure may include the following beneficial effects:

[0040] The transmitter uses a two-dimensional chaotic sequence to generate amplitude and phase encryption matrices respectively, so that the original constellation diagram is expanded in amplitude and controllably rotated in phase, and then the mixed carrier modulation is completed through the inverse WFRFT transform. After removing the cyclic prefix, the receiver performs a WFRFT transform on the mixed carrier signal, and then uses the same parameters as the transmitter to generate a decryption matrix to complete the reconstruction process of the original constellation. Due to the initial value sensitivity of the two-dimensional chaotic sequence, the cooperative receiver and the transmitter have the same modulation parameters and chaos initialization parameters, and the eavesdropper cannot correctly process the received signal even if there is a very small parameter deviation, thereby enhancing the confidentiality performance of the WFRFT transmission method.

[0041] It should be understood that the above general description and the following detailed description are merely exemplary and explanatory and cannot limit the present disclosure. Brief Description of the Figures

[0042] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present disclosure, and together with the specification, are used to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0043] Figure 1 A schematic diagram showing the steps of a WFRFT transmission method based on two-dimensional chaotic mapping constellation encryption in an exemplary embodiment of the present disclosure;

[0044] Figure 2 Shows a schematic diagram of amplitude and phase encryption in an exemplary embodiment of the present disclosure;

[0045] Figure 3 Showing an implementation block diagram of WFRFT in an exemplary embodiment of the present disclosure;

[0046] Figure 4 A system block diagram showing a transmission method in an exemplary embodiment of the present disclosure;

[0047] Figure 5 Shows the influence of Hénon initial value on chaotic sequence u in an exemplary embodiment of the present disclosure;

[0048] Figure 6 Shows the attractor of the Hénon map in the exemplary embodiment of the present disclosure;

[0049] Figure 7 Show the bifurcation diagram of the Hénon map in an exemplary embodiment of the present disclosure;

[0050] Figure 8 Show the constellation diagram when α = 0.01 in an exemplary embodiment of the present disclosure;

[0051] Figure 9 Show the constellation diagram when α = 0.1 in an exemplary embodiment of the present disclosure;

[0052] Figure 10 Show the constellation diagram when α = 0.9 in an exemplary embodiment of the present disclosure;

[0053] Figure 11 Show the statistical quantity diagram after amplitude-phase encryption of the QPSK modulation signal in an exemplary embodiment of the present disclosure;

[0054] Figure 12 Show the statistical quantity diagram of the encrypted signal after WFRFT transformation when α = 0.1 in an exemplary embodiment of the present disclosure;

[0055] Figure 13 Show the statistical quantity diagram of the encrypted signal after WFRFT transformation when α = 0.3 in an exemplary embodiment of the present disclosure;

[0056] Figure 14 Show the statistical quantity diagram of the encrypted signal after WFRFT transformation when α = 0.5 in an exemplary embodiment of the present disclosure;

[0057] Figure 15 Show the statistical quantity diagram of the encrypted signal after WFRFT transformation when α = 0.9 in an exemplary embodiment of the present disclosure;

[0058] Figure 16 Show the statistical quantity diagram of the encrypted signal after WFRFT transformation when α = 1.5 in an exemplary embodiment of the present disclosure;

[0059] Figure 17 Show the constellation diagrams of the demodulated signals of the legitimate user and the eavesdropper when the signal-to-noise ratio is 15 dB in an exemplary embodiment of the present disclosure;

[0060] Figure 18 Show the anti-interception performance analysis in an exemplary embodiment of the present disclosure. Detailed implementation manners

[0061] Example embodiments will now be described more fully with reference to the accompanying drawings. However, the example embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of the example embodiments to those skilled in the art. The features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments.

[0062] In addition, the accompanying drawings are only schematic illustrations of the present disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and thus their repeated description will be omitted. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software form, or in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0063] In this example embodiment, a WFRFT transmission method based on two-dimensional chaotic mapping constellation encryption is first provided. As shown in Figure 1 , the method may include the following steps:

[0064] Step S101: The input signal is subjected to constellation mapping to obtain a modulated column vector;

[0065] Step S102: A first sequence and a second sequence are generated by two-dimensional chaotic mapping, and the modulated column vector is subjected to constellation encryption processing by using the first sequence and the second sequence to generate an encrypted signal;

[0066] Step S103: The encrypted signal is subjected to inverse WFRFT to complete hybrid carrier modulation;

[0067] Step S104: The receiving end receives the hybrid carrier signal and performs WFRFT transformation on the hybrid carrier signal;

[0068] Step S105: A decryption matrix is generated according to the parameters of the two-dimensional chaotic mapping, and the encrypted signal is decrypted by using the decryption matrix, thereby completing the demodulation process.

[0069] In the embodiments of the present disclosure, the transmitting end uses a two-dimensional chaotic sequence to generate an amplitude encryption matrix and a phase encryption matrix respectively, so that the original constellation diagram is expanded in amplitude and rotated controllably in phase. Then, through the inverse WFRFT transformation, the hybrid carrier modulation is completed. After removing the cyclic prefix, the receiving end performs the WFRFT transformation on the hybrid carrier signal, and then uses the same parameters as the transmitting end to generate a decryption matrix to complete the reconstruction process of the original constellation. Due to the initial value sensitivity of the two-dimensional chaotic sequence, the cooperative receiver and the transmitter have the same modulation parameters and chaotic initialization parameters. Even if there is a very small parameter deviation for the eavesdropper, it cannot correctly process the received signal, thereby enhancing the security performance of the WFRFT transmission method.

[0070] Next, each step of the above method in this exemplary embodiment will be described in more detail.

[0071] In step S101, the modulation method of the input signal after constellation mapping is PSK modulation, ASK modulation or QAM modulation.

[0072] In this example, as Figure 2 shown, the QPSK constellation diagram using the phase mapping method is taken as an example for illustration. The marked point A is the original constellation mapping point, which corresponds to the current symbol x n , and the corresponding phase is θ n . In this example, the marked point B is the encrypted constellation mapping coordinate point obtained by using the two-dimensional chaotic mapping to simultaneously generate two groups of chaotic sequences and using them to encrypt the amplitude and phase of the QPSK modulation symbol at the same time. Its radius is r n , and at the same time, the phase is rotated by φ n angles, that is, the rotated phase is φ n +θ n .

[0073] Chaos reflects the inherent randomness of a deterministic system. It is extremely sensitive to the initial value. A very small perturbation can produce a huge deviation, that is, the phenomenon of "a miss is as good as a mile". In step S102, the two-dimensional chaotic mapping used in this example is the Hénon chaotic mapping. The Hénon chaotic mapping is a typical two-dimensional chaotic mapping that can simultaneously generate two groups of chaotic sequences, which is beneficial to controlling multiple system parameters at the same time. In this example, it is used to encrypt the amplitude and phase of the QPSK modulation symbol at the same time. Of course, the present disclosure does not limit this. In other examples, it can also be other chaotic mappings.

[0074] The step of encrypting the symbol column vector of the modulation signal using the first sequence and the second sequence in step S102 further includes the following steps:

[0075] Step S1021: Expand and encrypt the amplitude of the modulation symbols using the first sequence, and rotate and encrypt the phase of the modulation symbols using the second sequence to generate an encryption matrix for the amplitude and phase of the modulation symbols;

[0076] Step S1022: Encrypt the modulation column vector according to the encryption matrix.

[0077] Then in a specific example, the radius r n and the rotation angle φ n of the encrypted constellation mapping coordinate point B can be generated in the following manner:

[0078] Use the Hénon two-dimensional chaotic map to generate the first sequence u = [u 0 , u 1 , …, u N-1 T and the second sequence v = [v 0 , v 1 , …, v N-1 T , which are used to encrypt the amplitude and phase of the modulation column vector after serial-to-parallel conversion. Their generation formulas are as follows:

[0079]

[0080] v n+1 = bu n

[0081] In the above formula, when the parameter values a = 1.4 and b = 0.3, chaotic phenomena appear.

[0082] Then use the first sequence u = [u 0 , u 1 , …, u N-1 T and the second sequence v = [v 0 , v 1 , …, v N-1 T to expand and encrypt the amplitude and phase of the original constellation mapping point A respectively to obtain an encryption matrix for the amplitude and phase of the modulation symbols.

[0083] Specifically, the first sequence u first obtains the amplitude expansion factor through formula (1) to obtain the radius r n of the coordinate point B. In formula (1), max(|u|) means taking the absolute value of each element in the sequence u respectively and then taking the maximum value. Then generate a diagonal matrix from each element in formula (1) to obtain formula (2), which is used to expand and encrypt the amplitude information of the modulation symbols and obtain the amplitude encryption matrix R. In formula (2), r = (r 0 , r 1 , …, rN-1 ) T To generate a column vector composed of elements using formula (1), diag(·) is the diagonal matrix operation.

[0084]

[0085] R = diag(r) (2).

[0086] The second sequence v first obtains the phase rotation factor through formula (3), that is, the rotation angle φ of coordinate point B is obtained. n , and then the phase information of the modulation symbol is extended and encrypted using formula (4) to obtain the phase encryption matrix Φ.

[0087]

[0088]

[0089] Finally, according to the amplitude encryption matrix R and the phase encryption matrix Φ of the modulation symbol, the modulation column vector is encrypted using formula (5) to obtain the encrypted signal X 0 , where x = (x 0 , x 1 , … x N-1 ) T is the modulation column vector obtained after symbol mapping and serial-to-parallel conversion in the above QPSK modulation process.

[0090] X 0 = RΦx (5).

[0091] In step S103, the inverse WFRFT transform is performed on the encrypted signal X 0 to complete the hybrid carrier modulation.

[0092] WFRFT can encrypt and protect the transmission signal and the transmission process, effectively improving the security of the transmission system, and is gradually applied in the field of secure communication. Its essence is a hybrid carrier system that combines single-carrier and multi-carrier, and can be written as a combination form of 1-4 DFT transforms.

[0093] Performing 1 DFT transform on X 0 can be written as

[0094] X 1 = FX 0 (7);

[0095] In formula (7), F is the normalized DFT matrix, expressed as

[0096]

[0097] In formula (8), W N= e -2πj / N 。

[0098] And so on, X can be obtained respectively 0 Perform the DFT transform 2 - 3 times respectively to obtain X 2 、X 3 。Define the WFRFT of the discrete sequence based on the continuous function WFRFT, and its expression is:

[0099]

[0100] ω l (α) The expression is:

[0101]

[0102] In formula (10), l = 0, 1, 2, 3.

[0103] Formula (9) can be further written as:

[0104]

[0105] Among them,

[0106] The WFRFT of the discrete sequence can be realized through DFT, and its implementation process based on DFT is as Figure 3 shown. The signal after the inverse WFRFT of order α is briefly recorded as

[0107] X T = F W (-α)X 0 (13)

[0108] After adding the cyclic prefix (CP), it is transmitted through the channel to the receiving end.

[0109] After the receiving end removes the CP, it can be written as

[0110] y = X T + n (14)

[0111] Where n is the Gaussian white noise vector.

[0112] In step S104, after the receiving end completes synchronization, it removes the cyclic prefix (CP), and then performs the WFRFT transform on the received mixed carrier signal, which can be expressed as

[0113] y 0 = F W (α)y (15)

[0114] In step S105, since the receiver and the transmitter cooperate with each other, the initial value of the Hénon two-dimensional chaotic sequence and two-dimensional chaotic mapping parameters such as a and b can be accurately obtained. Therefore, the decryption matrix can be generated using the above parameters, where the decryption matrix and the encryption matrix are inverse matrices of each other.

[0115] The specific decryption formula is:

[0116] X d = R -1 Φ -1 y 0 (6)

[0117] where y 0 is the signal after the WFRFT transform.

[0118] Furthermore, since the amplitude encryption matrix R is a real diagonal matrix, the formula for its amplitude inverse matrix, i.e., the amplitude decryption matrix, is:

[0119]

[0120] The formula for the phase inverse matrix, i.e., the phase decryption matrix, is:

[0121] Φ -1 = Φ H (17)

[0122] Furthermore, the derived decryption formula can be written as:

[0123]

[0124] Finally, the data after amplitude and phase decryption is judged. The system block diagram of the above entire process can be referred to Figure 4 .

[0125] A computer simulation experiment is carried out on the above encrypted information to prove its encryption effect:

[0126] Experiment 1. Influence of the initial value on the amplitude encrypted sequence

[0127] Figure 5 is the variation of the amplitude values of the first sequence u generated by the Hénon two-dimensional chaotic mapping under different initial values. Obviously, in the process of sequence generation, the amplitude values of the first few chaotic sequences are relatively close, but as the number of iterations increases, the amplitude values of the generated chaotic sequences change greatly and the correlation is small.

[0128] Figure 6 and Figure 7 are the attractor and bifurcation diagram of the Hénon mapping respectively. Fix the parameter b value at 0.3, u 0 and v 0The initial value is taken as (0, 0), the value range of a is 0 - 1.4. When a = 0.32, the sequence u enters a period of 2. When a = 0.9, it enters a period of 4. When a = 1.4, the sequence u shows a full mapping.

[0129] Experiment 2. Influence of the amplitude-phase encryption module and WFRFT on the signal constellation diagram

[0130] The influence of WFRFT on the signal constellation diagram can be described by the following formula:

[0131]

[0132] The angle θ R is the rotation trend of the weighted signal on the complex plane.

[0133] From Figures 8 - 10 it can be seen that after the QPSK constellation diagram undergoes the WFRFT transformation, phase rotation and confusion occur, and as the value of the modulation order α increases continuously, the degree of rotation and confusion of the constellation diagram increases.

[0134] Using the chaotic sequences generated by the Hénon two-dimensional chaotic mapping respectively to encrypt the amplitude and phase of the original constellation diagram, it can be seen that compared with the original QPSK constellation mapping, the constellation diagram after amplitude-phase encryption has significantly different random characteristics. Even when the WFRFT order is small, it is still almost diffusely distributed throughout the space. Of course, as the WFRFT transformation order increases continuously, the random distribution of the constellation diagram becomes more obvious.

[0135] Experiment 3. Probability density distribution

[0136] From Figure 11 it can be seen that after using the two-dimensional Hénon sequence for amplitude and phase encryption, the in-phase and quadrature components of the signal are randomly distributed between [-2, +2]. The random distribution characteristics are closely related to the initial value and parameters a, b of the two-dimensional Hénon sequence. The amplitude values of the encrypted signal are randomly distributed in the interval [1, 2], which is also closely related to the initial value of the two-dimensional Hénon sequence and the parameters a, b.

[0137] Figures 12 - 16When the value of α increases from 0.1 to 1.5, the statistics of the encrypted signal after WFRFT transformation. It can be seen that when α = 0.1 and α = 0.3, the proportion of the single - carrier component is relatively large. Therefore, for both the in - phase and quadrature components, even after WFRFT transformation, the statistics are still quite different from the Gaussian distribution. However, as the value of α gradually increases, when α = 0.5, the in - phase and quadrature components are already relatively close to the Gaussian distribution. As α gradually increases to α = 0.9 and α = 1.5, the in - phase and quadrature components are very close to the Gaussian distribution. The main reason is that when the value of α is close to α = 1, the proportion of the multi - carrier component in the whole signal becomes larger, and FFT has a whitening effect on the in - phase and quadrature components of the base - band signal. In terms of amplitude, as the value of α continuously increases, the statistics of the amplitude gradually approach the Rayleigh distribution. Whether encrypted or not, the phase after WFRFT transformation follows a uniform distribution in the interval [-π, π].

[0138] Experiment 4. Analysis of Key Sensitivity and Anti - Interception Performance

[0139] To simulate the key sensitivity and anti - interception performance of the proposed system, multiple groups of simulation experiments are carried out respectively, and the parameters are shown in Table 1.

[0140] Table 1 Simulation Parameters

[0141] Modulation method QPSK Block length 1024 WFRFT transform order α＝0.5 CP length 128 Hénon chaotic sequence parameter <![CDATA[a = 1.4, b = 0.3, initial value (u 0 = 0, v 0 = 0)]]>

[0142] Since legitimate users cooperate with each other, the receiving end can accurately obtain all modulation parameters of the transmitting end, including the WFRFT transformation order, block length, modulation method, and generation parameters of the Hénon chaotic sequence. To verify the superiority of the algorithm proposed in this application, we set the simulation conditions extremely harsh, that is, assuming that the eavesdropper can accurately obtain information such as the WFRFT transformation order, CP length, symbol mapping, etc. through appropriate algorithms, and knows that the transmitting end uses a two - dimensional Hénon chaotic sequence for encryption, but cannot accurately obtain the specific parameters of the chaotic sequence. To verify the key sensitivity of the system, in this experiment, the initial value of the two - dimensional Hénon chaotic sequence is set with a very small deviation, and computer simulation experiments are carried out on the encrypted signal constellation diagram and the anti - interception performance of the system respectively.

[0143] Figure 17 For the QPSK signal constellation diagrams demodulated by legitimate users and eavesdroppers when the signal - to - noise ratio is 15 dB. Since legitimate users can accurately know the chaotic encryption parameters of the sender, they can successfully carry out demodulation processing. For eavesdroppers, since they cannot accurately obtain the chaotic encryption parameters, even a very small key deviation (1e -10 ) magnitude cannot achieve accurate signal demodulation.

[0144] From Figure 18It can be seen that since the legitimate user can accurately obtain various parameters of the system, its system performance has a very significant advantage compared to the eavesdropping user. Even if we assume that the receiver can obtain all information except the initial value of the Hénon two-dimensional chaotic map, and the difference between the initial value of the chaotic sequence obtained by the eavesdropping party and the correct value is only of the order of 1e -10 magnitude, the interception performance of the eavesdropping party is still very poor, and the bit error rate (BER) is always close to the performance of about 0.5, indicating that the proposed algorithm has high key sensitivity and can meet the requirements of secure communication.

[0145] Experiment 5. Key Cracking Analysis

[0146] If the quantization precision is defined as 10 -15 , then the parameters encrypted by the two-dimensional Hénon chaotic map include (a, b, u 0 , v 0 , α). Even if the WFRFT transform parameter α is ignored, the key in this application can still reach the order of 10 60 magnitude, which is much higher than the order of 2 100 magnitude required to resist brute force cracking.

[0147] In summary, the WFRFT transmission method based on two-dimensional chaotic map constellation encryption provided by the present disclosure uses the two-dimensional chaotic map to generate two groups of chaotic sequences simultaneously, and uses them to encrypt the amplitude and phase of the QPSK modulation symbols simultaneously, achieving the purpose of amplitude expansion and constellation rotation of the original constellation mapping, and further improving the physical layer transmission performance of the WFRFT system.

[0148] It should be noted that although the steps of the method in the present disclosure are described in a specific order in the drawings, this does not require or imply that these steps must be executed in that specific order, or that all the steps shown must be executed to achieve the desired result. Additionally or alternatively, some steps may be omitted, multiple steps may be combined into one step for execution, and / or one step may be decomposed into multiple steps for execution, etc. Also, it is easily understood that these steps may be executed synchronously or asynchronously, for example, in multiple modules / processes / threads.

[0149] Furthermore, in the present exemplary embodiment, a WFRFT transmission system based on two-dimensional chaotic mapping constellation encryption is further provided. The system may include a chaotic mapping constellation encryption unit, an inverse WFRFT unit, a WFRFT transformation unit, and a decryption unit. Among them, the chaotic mapping constellation encryption unit is used to generate a first sequence and a second sequence through two-dimensional chaotic mapping, and perform constellation encryption processing on the modulation column vector generated by constellation mapping by using the first sequence and the second sequence to generate an encrypted signal. The inverse WFRFT unit is used to perform an inverse WFRFT transformation on the encrypted signal to complete hybrid carrier modulation. The WFRFT transformation unit is used to perform a WFRFT transformation on the hybrid carrier signal after receiving the hybrid carrier signal at the receiving end. The decryption unit is used to generate a decryption matrix according to the parameters of the two-dimensional chaotic mapping, and decrypt the encrypted signal by using the decryption matrix, thereby completing the demodulation process.

[0150] Regarding the system in the above embodiments, the specific manners in which each unit performs operations have been described in detail in the embodiments related to the method, and will not be elaborated herein.

[0151] It should be noted that although several units of the system for action execution are mentioned in the above detailed description, this division is not mandatory. In fact, according to the embodiments of the present disclosure, the features and functions of two or more of the above-described units may be embodied in one unit. Conversely, the features and functions of one unit described above may be further divided and embodied by multiple units. One may choose some or all of the units according to actual needs to achieve the purpose of the solution of the present disclosure. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0152] After considering the specification and practicing the invention disclosed herein, those skilled in the art will readily conceive of other embodiments of the present disclosure. This application is intended to cover any variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common general knowledge or conventional technical means in the technical field not disclosed in the present disclosure. The specification and examples are only to be regarded as exemplary, and the true scope and spirit of the present disclosure are pointed out by the appended claims.

Claims

1. A WFRFT transmission method based on two-dimensional chaotic mapping constellation encryption, characterized in that: The following steps are involved: The input signal is mapped to a constellation to obtain a modulated column vector; Generate a first sequence and a second sequence through a two-dimensional chaotic mapping, and perform constellation encryption processing on the modulated column vector using the first sequence and the second sequence to generate an encrypted signal; The encrypted signal is subjected to inverse WFRFT transformation to complete hybrid carrier modulation; The receiving end receives the mixed carrier signal and performs WFRFT transformation on the mixed carrier signal; Generate a decryption matrix according to the parameters of the two-dimensional chaotic map, and use the decryption matrix to decrypt the encrypted signal, thereby completing the demodulation process; The step of performing constellation encryption processing on the modulation column vector using the first sequence and the second sequence further includes the following steps: Using the first sequence to extend and encrypt the amplitude of the modulation symbol, and using the second sequence to rotate and encrypt the phase of the modulation symbol, to generate an encryption matrix of the amplitude and phase of the modulation symbol; The modulation column vector is encrypted according to the encryption matrix.

2. The transmission method according to claim 1, characterized in that: In the step of using the first sequence to expand and encrypt the amplitude of the modulation symbol, the first sequence first obtains the amplitude expansion factor r by formula (1): n , and then generate the amplitude encryption matrix R of the modulation symbol through formula (2); R = diag(r) (2); Among them, u is the first sequence, r=(r0,r1,…,r N-1 ) T .

3. The transmission method according to claim 2, characterized in that: In the step of rotating and encrypting the phase of the modulation symbol using the second sequence, the second sequence first obtains a phase rotation factor φ by formula (3): n , and then generate the phase encryption matrix Φ of the modulation symbol through formula (4); Among them, v is the second sequence.

4. The transmission method according to claim 3, characterized in that: In the step of encrypting the modulated column vector according to the encryption matrix, encryption is performed using formula (5); X0=RΦx (5); Where x=(x0,x1,…x N-1 ) T is the modulation column vector.

5. The transmission method according to claim 4, characterized in that: The decryption matrix and the encryption matrix are inverse matrices of each other.

6. The transmission method according to claim 5, characterized in that: In the step of generating a decryption matrix according to the parameters of the two-dimensional chaotic map and decrypting the encrypted signal using the decryption matrix, the decryption formula is: X d =R -1 F -1 y0 (6); Wherein, y0 is the signal after the WFRFT transformation; R -1 is the amplitude decryption matrix of the modulation symbol, and Φ -1 is the phase decryption matrix of the modulation symbol, and Φ -1 =Φ H .

7. The transmission method according to claim 1, characterized in that: The two-dimensional chaotic map is a Hénon chaotic map.

8. The transmission method according to claim 1, characterized in that: The modulation mode of the input signal after constellation mapping is PSK modulation, ASK modulation or QAM modulation.

9. A WFRFT transmission system based on two-dimensional chaotic mapping constellation encryption, characterized in that: include: A chaotic mapping constellation encryption unit, used to generate a first sequence and a second sequence through two-dimensional chaotic mapping, and perform constellation encryption processing on the modulation column vector generated by constellation mapping using the first sequence and the second sequence to generate an encrypted signal; A WFRFT inverse transformation unit, used for performing WFRFT inverse transformation on the encrypted signal to complete hybrid carrier modulation; A WFRFT transformation unit, after receiving the mixed carrier signal at the receiving end, is used to perform WFRFT transformation on the mixed carrier signal; A decryption unit, used to generate a decryption matrix according to the parameters of the two-dimensional chaotic map, and use the decryption matrix to decrypt the encrypted signal, thereby completing the demodulation process; The process of performing constellation encryption processing on the modulation column vector by using the first sequence and the second sequence includes: Using the first sequence to extend and encrypt the amplitude of the modulation symbol, and using the second sequence to rotate and encrypt the phase of the modulation symbol, to generate an encryption matrix of the amplitude and phase of the modulation symbol; The modulation column vector is encrypted according to the encryption matrix.

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