EWFRFT communication method based on three-dimensional constellation scaling encryption

Abstract

The embodiment of the invention relates to an EWFRFT communication method based on three-dimensional constellation scaling encryption, and the method comprises the steps: sequentially carrying out the serial-parallel conversion processing and three-dimensional modulation processing of plaintext information through a transmitting end, and obtaining a plaintext signal; generating a chaos sequence through Henon and Logistic chaos mapping, controlling parameters of Brownian motion by using the chaos sequence, and generating a chaos Brownian motion sequence; generating a random scaling matrix by using the chaos Brownian motion sequence, and performing random scaling on the plaintext signal according to the random scaling matrix to generate a primary encrypted signal; using a chaos Brownian motion sequence to control transformation parameters of EWFRFT, and performing EWFRFT transformation processing on the primary encryption signal to obtain a secondary encryption signal; the receiving end carries out EWFRFT inverse transformation processing on the secondary encryption signal to obtain a preliminary decryption signal; performing random scaling on the preliminary decryption signal by using a random scaling matrix to generate a decryption signal; and performing three-dimensional demodulation and parallel-serial conversion processing on the decrypted signal to obtain decrypted information. According to the embodiment of the invention, the security of a communication system is remarkably improved.

Description

Technical Field

[0001] The present disclosure relates to the technical field of encrypted communications, and in particular to an EWFRFT communication method based on three-dimensional constellation scaling encryption. Background Art

[0002] With the rapid development of drone technology, its application in various fields is becoming more and more extensive, but the wireless characteristics of drone communication make it face security threats such as eavesdropping, tampering and hijacking. Physical layer security (PLS) can enhance the confidentiality capacity of the channel, reduce the advantage of eavesdropping channels, and ensure the security of communication data, so it is introduced into drone systems. Among them, modulation encryption, as an important technical means of physical layer security, can eliminate the statistical characteristics of the waveform and effectively disrupt the distribution law of the signal, thereby achieving low probability of interception communication.

[0003] In the related technologies, modulation encryption is mainly based on two-dimensional constellation modulation, but the two-dimensional constellation modulation encryption algorithm is single, the encryption system is relatively traditional, and there is a risk of being stolen. Therefore, encryption technology is gradually developing towards three-dimensional constellation modulation encryption. The current three-dimensional constellation modulation encryption mainly adopts the method of rotating the constellation points around the axis and quaternion rotation encryption, which have the defects of high computational complexity or insufficient encryption.

[0004] In terms of implementation technology, constellation scrambling encryption is mainly implemented using chaotic cryptography and weighted fractional Fourier transform (WFRFT) and other methods. When weighted fractional Fourier transform is combined with constellation encryption, it can enhance the security and concealment of the communication system to a certain extent. However, on the one hand, with the development of chaotic cryptanalysis technology, some digital chaos faces attack threats such as phase space reconstruction and deep learning, so higher requirements are placed on the randomness of chaotic sequences; on the other hand, the form of WFRFT signals is controlled by the order of transformation. If methods such as cyclic correlation method and high-order cumulants are used, the order of transformation of WFRFT can be accurately identified under unknown conditions, which poses a certain threat to the security of the communication system.

[0005] Therefore, it is necessary to provide a new technical solution to improve one or more problems existing in the above solutions.

[0006] It should be noted that the information disclosed in the above background technology 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 ordinary technicians in the field. Summary of the invention

[0007] The purpose of the disclosed embodiment is to provide an EWFRFT communication method based on three-dimensional constellation scaling encryption to perform multi-layer encryption on plaintext signals, so that originally overlapping constellation points become random and chaotic, thereby improving the security of the communication system.

[0008] According to an embodiment of the present disclosure, an EWFRFT communication method based on three-dimensional constellation scaling encryption is provided, including:

[0009] The sending end performs serial-to-parallel conversion and three-dimensional modulation on the plaintext information in sequence to obtain the plaintext signal for transmission;

[0010] A chaotic sequence is generated by Hénon and Logistic chaotic mapping, and the chaotic sequence is used to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence;

[0011] Generate a random scaling matrix using the chaotic Brownian motion sequence, and randomly scale the plaintext signal according to the random scaling matrix to generate a primary encrypted signal;

[0012] Using the chaotic Brownian motion sequence to control the transformation parameters of EWFRFT, the primary encrypted signal is subjected to EWFRFT transformation processing to obtain a secondary encrypted signal;

[0013] The receiving end performs an EWFRFT inverse transform process on the secondary encrypted signal to obtain a preliminary decrypted signal;

[0014] Randomly scaling the preliminary decryption signal using the random scaling matrix to generate a decryption signal;

[0015] The decrypted signal is subjected to three-dimensional demodulation processing and parallel-to-serial conversion processing in sequence to obtain decrypted information.

[0016] In an exemplary embodiment of the present disclosure, the method of generating a chaotic sequence by using Hénon and Logistic chaotic mapping, and using the chaotic sequence to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence includes:

[0017] In three-dimensional space, the expression of Brownian motion of a point is:

[0018]

[0019] Among them, τ∈[0,+∞) is the motion step, and α and β represent the direction of motion.

[0020] In an exemplary embodiment of the present disclosure, the method of generating a chaotic sequence by using Hénon and Logistic chaotic mapping, and using the chaotic sequence to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence includes:

[0021] The Hénon mapping expression is:

[0022]

[0023] The mapping expression of the Logistic is:

[0024] x′ n+1 =cx′ n (1-x′ n )(3)

[0025] Where n represents the number of iterations of the chaotic sequence, x n ,y n represents the Hénon mapping sequence, x′ n represents the mapping sequence of Logistic, a, b, c represent the control parameters respectively; when 1.07≤a≤1.4, b=0.3, the Hénon mapping is in a chaotic state; when 3.57≤c≤4, the Logistic mapping is in a chaotic state;

[0026] Assume that the initial value of the Hénon map is (x0, y0), and after m1 iterations, a chaotic sequence (x n ,y n ), the initial value of the Logistic map is x′0, and the chaotic sequence x′ of the same length L is generated by iterating m2 times n , then the expression of the chaotic Brownian motion sequence is:

[0027]

[0028] Among them, mean(x n ) represents the Hénon mapping sequence x n The average value of .

[0029] In an exemplary embodiment of the present disclosure, the transmitting end sequentially performs serial-to-parallel conversion processing and three-dimensional modulation processing on the plaintext information to obtain a transmitted plaintext signal, including:

[0030] The plaintext information is mapped according to the three-dimensional constellation of the regular tetrahedron to obtain N constellation points, and the coordinates of the i-th constellation point are (x i ,y i ,z i ), then the plaintext signal is:

[0031]

[0032] Among them, x N ,y N 、z N Represents the coordinates of the Nth constellation point.

[0033] In an exemplary embodiment of the present disclosure, the method of generating a random scaling matrix by using the chaotic Brownian motion sequence, and randomly scaling the plaintext signal according to the random scaling matrix to generate a primary encrypted signal further includes the following steps:

[0034] Construct a random scaling matrix model in three-dimensional space;

[0035] Determining the direction vector and the scaling factor in the random scaling matrix model according to the parameters of the chaotic Brownian motion sequence;

[0036] Each of the constellation points is randomly scaled using the random scaling matrix to obtain the primary encrypted signal.

[0037] In an exemplary embodiment of the present disclosure, in the step of constructing a random scaling matrix model in a three-dimensional space, the random scaling matrix model is:

[0038]

[0039] Where n represents the direction vector, n x ,n y ,n z They represent the axis coordinates of the direction vector n, and k represents the scaling factor.

[0040] In an exemplary embodiment of the present disclosure, the step of determining the direction vector and the scaling factor in the random scaling matrix model according to the parameters of the chaotic Brownian motion sequence further includes the following steps:

[0041] constructing two groups of chaotic Brownian motion sequences;

[0042] The direction vector is determined by using one set of the chaotic Brownian motion sequences, and the scaling factor is determined by using another set of the chaotic Brownian motion sequences.

[0043] In an exemplary embodiment of the present disclosure, the step of randomly scaling the preliminary decrypted signal using the random scaling matrix to generate a decrypted signal further includes the following steps:

[0044] The constellation information to be scaled and decrypted of the constellation point is obtained according to the preliminary decrypted signal, and the constellation information to be scaled and decrypted of the constellation point is randomly scaled by using the random scaling matrix to generate a decrypted signal of the constellation point; wherein the decrypted signal of the i-th constellation point is:

[0045] R″ i =R′ i ×[S i (n i ,k i )] -1 (7)

[0046] Among them, R i represents the decrypted signal of the i-th constellation point, R′ i represents the constellation information to be scaled and decrypted of the i-th constellation point, S i (n i ,k i ) represents the i-th random scaling matrix, [·] -1 Represents the inverse of a matrix.

[0047] In an exemplary embodiment of the present disclosure, before the encrypted signal is subjected to EWFRFT transformation processing, the following steps are also included:

[0048] The primary encrypted signal is subjected to I / Q conversion processing and parallel-to-serial conversion processing.

[0049] In an exemplary embodiment of the present disclosure, in the step of using the chaotic Brownian motion sequence to control the transformation parameters of EWFRFT, performing EWFRFT transformation processing on the encrypted signal, and generating an encrypted conversion signal,

[0050] The expression of the encrypted conversion signal is:

[0051] M″′=EWFRFT{M″,(θ1,θ2,θ3,θ4)} (8)

[0052] Wherein, M″′ represents the encrypted conversion signal, M″ represents the encrypted signal, and θ1, θ2, θ3, θ4 represent multiple transformation parameters of EWFRFT.

[0053] The technical solution provided by the present disclosure may have the following beneficial effects:

[0054] In the embodiment of the present disclosure, the above method is combined with the randomness of Brownian motion, and the classical Hénon and Logistic chaotic mapping are used to generate a chaotic Brownian motion sequence, and the chaotic Brownian motion sequence is used to generate a random scaling matrix, and the plaintext signal is randomly scaled to complete the preliminary encryption operation to obtain the primary encrypted signal. The chaotic Brownian motion sequence is also used to control the transformation parameters of EWFRFT, and the encrypted signal after the preliminary encryption is subjected to EWFRFT transformation processing to complete the re-encryption operation to obtain the secondary encrypted signal, further disrupting the constellation distribution law. Through the above-mentioned scaling encryption operation and EWFRFT transformation encryption operation, multi-layer encryption of the plaintext signal is realized, so that the originally overlapping constellation points become random and messy, and the distribution law of the original baseband modulation signal is eliminated, which can effectively resist the statistical attack of the signal and the exhaustive attack of the key, improve the anti-detection and identification ability of the wireless transmission signal, and thus improve the security of the communication system.

[0055] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The accompanying drawings herein are incorporated into the specification and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification are used to explain the principles of the present disclosure. Obviously, the accompanying drawings described below are only some embodiments of the present disclosure, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0057] Figure 1 A schematic diagram showing the steps of an EWFRFT communication method based on three-dimensional constellation scaling encryption in an exemplary embodiment of the present disclosure;

[0058] Figure 2 A schematic flow chart of an EWFRFT communication method based on three-dimensional constellation scaling encryption in an exemplary embodiment of the present disclosure is shown;

[0059] Figure 3 A schematic diagram showing a three-dimensional constellation diagram in an exemplary embodiment of the present disclosure;

[0060] Figure 4 A schematic diagram showing a decision region of a constellation point in an exemplary embodiment of the present disclosure;

[0061] Figure 5 A schematic diagram showing a strange attractor of a Hénon map in an exemplary embodiment of the present disclosure;

[0062] Figure 6 A schematic diagram showing a strange attractor of a Logistic map in an exemplary embodiment of the present disclosure;

[0063] Figure 7 A schematic diagram showing the motion trajectory of chaotic Brownian motion iterated 2000 times in an exemplary embodiment of the present disclosure;

[0064] Figure 8 A schematic diagram showing vector scaling in a two-dimensional plane in an exemplary embodiment of the present disclosure is shown;

[0065] Fig. 9 An initially regularized constellation diagram in an exemplary embodiment of the present disclosure is shown;

[0066] Fig.10 The constellation diagram after scaling and encryption in an exemplary embodiment of the present disclosure is shown;

[0067] Fig.11 A constellation diagram showing the I / Q signals combined after scaling and encryption in an exemplary embodiment of the present disclosure;

[0068] Fig.12 The constellation diagram after EWFRFT encryption in the exemplary embodiment of the present disclosure is shown;

[0069] Fig.13 A schematic diagram showing the amplitude distribution of an encrypted signal in an exemplary embodiment of the present disclosure is shown;

[0070] Fig.14 A schematic diagram showing the phase distribution of an encrypted signal in an exemplary embodiment of the present disclosure is shown;

[0071] Fig.15 A key sensitivity analysis diagram in an exemplary embodiment of the present disclosure is shown;

[0072] Fig.16 A bit error rate analysis diagram in an exemplary embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0073] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the disclosure will be more comprehensive and complete and to fully convey the concepts of the example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0074] 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 figures represent the same or similar parts, and their repeated description will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software form, or implemented in one or more hardware modules or integrated circuits, or implemented in different networks and / or processor devices and / or microcontroller devices.

[0075] In this example implementation, an EWFRFT communication method based on three-dimensional constellation scaling encryption is first provided. Figure 1 and Figure 2 As shown in , the method may include the following steps:

[0076] Step S101: The transmitting end performs serial-to-parallel conversion and three-dimensional modulation on the plaintext information in sequence to obtain a plaintext signal for transmission;

[0077] Step S102: generating a chaotic sequence through Hénon and Logistic chaotic mapping, and using the chaotic sequence to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence;

[0078] Step S103: Generate a random scaling matrix using a chaotic Brownian motion sequence, and randomly scale the plaintext signal according to the random scaling matrix to generate a primary encrypted signal;

[0079] Step S104: using the chaotic Brownian motion sequence to control the transformation parameters of EWFRFT, performing EWFRFT transformation on the primary encrypted signal to obtain a secondary encrypted signal;

[0080] Step S105: The receiving end performs an EWFRFT inverse transform on the secondary encrypted signal to obtain a preliminary decrypted signal;

[0081] Step S106: using a random scaling matrix to randomly scale the preliminary decrypted signal to generate a decrypted signal;

[0082] Step S107: The decrypted signal is subjected to three-dimensional demodulation processing and parallel-to-serial conversion processing in sequence to obtain decrypted information.

[0083] In the embodiment of the present disclosure, the above method is combined with the randomness of Brownian motion, and the classical Hénon and Logistic chaotic mapping are used to generate a chaotic Brownian motion sequence, and the chaotic Brownian motion sequence is used to generate a random scaling matrix, and the plaintext signal is randomly scaled to complete the preliminary encryption operation to obtain the primary encrypted signal. The chaotic Brownian motion sequence is also used to control the transformation parameters of EWFRFT, and the encrypted signal after the preliminary encryption is subjected to EWFRFT transformation processing to complete the re-encryption operation to obtain the secondary encrypted signal, further disrupting the constellation distribution law. Through the above-mentioned scaling encryption operation and EWFRFT transformation encryption operation, multi-layer encryption of the plaintext signal is realized, so that the originally overlapping constellation points become random and messy, and the distribution law of the original baseband modulation signal is eliminated, which can effectively resist the statistical attack of the signal and the exhaustive attack of the key, improve the anti-detection and identification ability of the wireless transmission signal, and thus improve the security of the communication system.

[0084] Next, we will refer to Figures 1 to 16 Each step of the above method in this example implementation is described in more detail.

[0085] Before discussing this method, the following abbreviations are explained.

[0086] EWFRFT (Extended Weighted Fractional Fourier Transform), CP (Cyclic Prefix) refers to the prefix of a symbol.

[0087] In one embodiment, the three-dimensional modulation process in step S101 adopts a three-dimensional constellation modulation method, wherein the three-dimensional constellation modulation can be understood as designing a constellation point distribution in a three-dimensional space, mapping the transmission information to the constellation point, and using the amplitude, phase and transmitting antenna sequence number of the signal to perform joint modulation, thereby achieving efficient transmission of the signal. s =2 d The constellation points are evenly distributed on the sphere, where d is the number of bits of coded information. Figure 3 A schematic diagram of a three-dimensional constellation diagram is shown, which specifically shows that the constellation diagram is a three-dimensional space mapping of a regular tetrahedron, and the coordinates of the four constellation points S(0), S(1), S(2), and S(3) are S(0)=(0,0,1),

[0088]

[0089] At the sending end, every 2 bits of plaintext information are transmitted according to The corresponding relationship is mapped to a constellation point.

[0090] It should be understood that since the signal is interfered by noise and other factors during spatial propagation, the received signal cannot be directly mapped to the original constellation point. During demodulation, a decision method such as the minimum distance needs to be adopted to map the received signal to the point with the closest Euclidean distance to the original constellation point. That is, each constellation point has its own decision area. As long as the signal falls into the decision area of ​​the constellation point, the original information will be restored according to the mapping relationship of the constellation point. Figure 4 The decision area of ​​the constellation point S(0) is shown. If the received signal falls into this area, the signal will be demodulated to 00.

[0091] Therefore, it can be understood that based on the above-mentioned three-dimensional constellation modulation method, at the transmitting end, the plaintext information (i.e., the plaintext bit stream) is mapped to the three-dimensional constellation symbol through serial-to-parallel conversion. After the information is three-dimensionally mapped, for each constellation point, a shared key is used to expand or shrink it within its decision area according to a specific mapping rule; the receiving end has the same key and mapping rule, and can restore the moved constellation point and complete the demodulation of the signal.

[0092] The encryption method adopted above provides a layer of encryption protection for the transmission signal without increasing the communication bit error rate, which helps to improve the signal's anti-interference and anti-interception capabilities.

[0093] In step S101, the transmitting end sequentially performs serial-to-parallel conversion and three-dimensional modulation on the plaintext information to obtain a plaintext signal for transmission, and further includes sub-step S1011:

[0094] In sub-step S1011, assuming that the three-dimensional constellation diagram is a regular tetrahedron, the plaintext information is mapped according to the three-dimensional constellation of the regular tetrahedron. Assuming that N constellation points are obtained after mapping, the coordinates of the i-th constellation point are (x i ,y i ,z i ), then the plaintext signal can be expressed as:

[0095]

[0096] Among them, x N ,y N 、z N Represents the coordinates of the Nth constellation point.

[0097] Step S102: generating a chaotic sequence through Hénon and Logistic chaotic mapping, and using the chaotic sequence to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence;

[0098] In step S102, Brownian motion is a common phenomenon in nature, and its motion trajectory has the natural advantages of irregularity and unpredictability. Using a chaotic sequence to control the parameters of the Brownian motion can not only further disrupt the distribution of the chaotic sequence, but also significantly improve the randomness of the sequence.

[0099] In step S102, a chaotic sequence is generated by using Hénon and Logistic chaotic mapping, and the chaotic sequence is used to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence, which also includes sub-step S1021:

[0100] In three-dimensional space, the expression of Brownian motion of a point is:

[0101]

[0102] Among them, τ∈[0,+∞) is the motion step, and α and β represent the direction of motion.

[0103] In step S102, a chaotic sequence is generated by using Hénon and Logistic chaotic mapping, and the chaotic sequence is used to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence, which also includes sub-step S1022:

[0104] In sub-step S1022, the chaotic sequence is generated using the classical Hénon and Logistic chaotic mappings. The mapping expression of Hénon is:

[0105]

[0106] The mapping expression of Logistic is:

[0107] x′ n+1 =cx′n (1-x′ n )(3)

[0108] Where n represents the number of iterations of the chaotic sequence, x n ,y n represents the Hénon mapping sequence, x′ n represents the mapping sequence of Logistic, a, b, c represent the control parameters respectively; when 1.07≤a≤1.4, b=0.3, the Hénon mapping is in a chaotic state; when 3.57≤c≤4, the Logistic mapping is in a chaotic state;

[0109] Assume that the initial value of the Hénon map is (x0, y0), and after m1 iterations, a chaotic sequence (x n ,y n ), the initial value of the Logistic map is x′0, and the chaotic sequence x′ of the same length L is generated by iterating m2 times n , then the expression of chaotic Brownian motion sequence is:

[0110]

[0111] Among them, mean(x n ) represents the Hénon mapping sequence x n The average value of .

[0112] According to the chaotic Brownian motion sequence obtained based on Hénon and Logistic chaotic mapping, after 2000 iterations of chaotic three-dimensional Brownian motion, its motion trajectory is observed and compared with the strange attractors of Hénon mapping and Logistic mapping, see Figures 5 to 7 As shown in , it is not difficult to see that the randomness and disorder of the chaotic three-dimensional Brownian motion sequence are significantly prominent. The spectral entropy (SE) can be selected to quantify the structural complexity of the chaotic system. By comparing the spectral entropy values ​​of the original chaotic sequence and its three-dimensional Brownian motion sequence, as shown in Table 1, it can be concluded that compared with the spectral entropy value of the original chaotic sequence, the spectral entropy value of the chaotic three-dimensional Brownian motion sequence is relatively high, indicating that the chaotic three-dimensional Brownian motion sequence is more random, so it has great application potential in encryption operations.

[0113] Table 1 Comparison of spectral entropy between the original chaotic sequence and the three-dimensional Brownian motion sequence

[0114]

[0115] In step S103, a random scaling matrix is ​​generated by using a chaotic Brownian motion sequence, and the plaintext signal is randomly scaled according to the random scaling matrix to generate a primary encrypted signal, and the following steps are also included:

[0116] Step S1031: constructing a random scaling matrix model in three-dimensional space;

[0117] Step S1032: determining the direction vector and scaling factor in the random scaling matrix model according to the parameters of the chaotic Brownian motion sequence;

[0118] Step S1033: Use a random scaling matrix to randomly scale each constellation point to obtain a primary encrypted signal.

[0119] For example, the scaling of the random scaling matrix in step S103 can be understood as: multiplying an object in a plane or space by a factor k to cause it to "stretch" or "squeeze". Factor k is a scaling factor that controls the effect of the object's change. If |k| < 1, the object will become "shorter" in a certain direction; when |k| > 1, the object will become "longer" in a certain direction; when k < 0, a reflection result is obtained. If the object is a point in a plane or space, when k > 1, it is still a point after expansion, and moves upward or outward relative to the point in position. When 0 < k < 1, it is still a point after shortening, and moves downward or inward relative to the point. When k = 1, the point will not move.

[0120] Example, reference Figure 8 As shown in , in the two-dimensional plane, the vector v is scaled by the scaling factor k2 along the direction parallel to the direction vector n2 to obtain the vector v * , can be represented by the scaling matrix S2(n2,k2), where the scaling matrix S2(n2,k2) can be represented as:

[0121]

[0122] v * =v×S(n2,k2)(10)

[0123] where k2 is the scaling factor applied to the line through the origin that is perpendicular to n2, and n x represents the horizontal coordinate of the direction vector n2, n y Represents the ordinate of direction vector n2.

[0124] Therefore, it can be understood that in three-dimensional space, a three-dimensional matrix can be generated, which will be stretched or squeezed according to the scaling factor in any direction specified by the direction vector to construct a random scaling matrix model in three-dimensional space.

[0125] In one embodiment, in the step of constructing a random scaling matrix model in a three-dimensional space in step S1031, the random scaling matrix model may be constructed as:

[0126]

[0127] Where n represents the direction vector, n x ,n y ,n z They represent the axis coordinates of the direction vector n, and k represents the scaling factor.

[0128] In one embodiment, the step S1032 of determining the direction vector and the scaling factor in the random scaling matrix model according to the parameters of the chaotic Brownian motion sequence further includes the following steps:

[0129] Step S10321: construct two sets of chaotic Brownian motion sequences;

[0130] Step S10322: using one set of chaotic Brownian motion sequences to determine the direction vector, and using another set of chaotic Brownian motion sequences to determine the scaling factor.

[0131] Specifically, in step S10321, two groups of chaotic Brownian motion sequences are constructed, and two groups of different initial values ​​and control parameters are used to generate chaotic three-dimensional Brownian motion sequences of length N according to formulas (2) to (4). The first group of chaotic three-dimensional Brownian motion sequences is assumed to be dx, dy, dz, and the second group of chaotic three-dimensional Brownian motion sequences is assumed to be dx', dy', dz'.

[0132] Specifically, in step S10322, the first group of chaotic three-dimensional Brownian motion sequences dx, dy, dz are used as the x-axis coordinates, y-axis coordinates, and z-axis coordinates of the direction vector n, respectively; N new sequences are selected from the second group of chaotic three-dimensional Brownian motion sequences dx', dy', dz' as the scaling factor k. Further, after determining the direction vector n and scaling factor k of the random scaling matrix model based on step S10322, N random scaling matrices can be obtained according to formula (6), where the i-th random scaling matrix can be expressed as S i (n i ,k i ).

[0133] Preferably, N new sequences can be selected from the second group of chaotic three-dimensional Brownian motion sequences dx', dy', dz' as the scaling factor k, and the value of the scaling factor k is ensured to be in the range of [0.8, 1.6], which is conducive to ensuring that the scaled and encrypted constellation points fall in their respective decision areas.

[0134] It should be noted that in the above step of obtaining the random scaling matrix, the direction vector n needs to be normalized. Specifically, each element of the direction vector is divided by the modulus of the direction vector so that the modulus of the direction vector is equal to 1, that is, the direction vector n is normalized.

[0135] Specifically, in step S1033, each constellation point is randomly scaled using the random scaling matrix obtained in step S10322 by formula (11):

[0136] M′ i =M i ×S i (n i ,k i ) (11)

[0137] Among them, M′ i is the primary encryption information of the i-th constellation point after scaling and encryption;

[0138] The primary encrypted signal M′ is obtained by scaling and encrypting the N constellation points. The primary encrypted signal M′ can be expressed as:

[0139]

[0140] Among them, x′ N , y′ N , z′ N Represents the coordinates of the Nth constellation point.

[0141] In one embodiment, between step S103 and step S104, the following steps are further included:

[0142] The primary encrypted signal M′ is subjected to I / Q conversion and parallel-to-serial conversion to obtain a primary encrypted transmission signal M″. In step S104, the primary encrypted transmission signal M″ obtained after the I / Q conversion and parallel-to-serial conversion is subjected to EWFRFT conversion. The signal M″ can be expressed as:

[0143]

[0144] in,(·) T Represents the transpose of a matrix.

[0145] For example, Weighted Fractional Fourier Transform (WFRFT) is a new type of signal processing method. It disrupts the signal distribution law by adjusting the transformation order. The WFRFT transformation has three basic properties: continuity, boundary and order additivity. The transformation order determines the transformation form. Therefore, it is widely used in constellation scrambling encryption.

[0146] Among them, WFRFT can be defined as:

[0147]

[0148] Where α represents the transformation order, α∈[0,4), F(x) is the Fourier transform of f(x), ω l (α) represents the weighting coefficient, j represents the imaginary unit, Represents WFRFT transform, q represents the number of terms, q = 0, 1, 2, 3.

[0149] Among them, EWFRFT can be defined as:

[0150]

[0151] Where θ represents the transformation parameter, θ=[θ0,θ1,θ2,θ3]; θ p ∈[0,2π),p=0,1,2,3;w n (θ) represents the weighting coefficient, n = 0, 1, 2, 3; Represents the EWFRFT transform.

[0152] It should be noted that EWFRFT has three basic properties: continuity, boundary and parameter additivity, and the transformation parameter θ determines the transformation form.

[0153] In one embodiment, taking a discrete signal as an example, the discrete signal X=[x1, x2, ..., x m The EWFRFT of ] can be defined as:

[0154]

[0155] Among them, X j is the jth discrete Fourier transform of X, j = 1, 2, 3; w n (θ) represents the weighting coefficient, n = 0, 1, 2, 3, w n The expression of (θ) is the same as the above formula (17); Represents the EWFRFT transform.

[0156] Based on the parameter additivity of EWFRFT, EWFRFT can be applied to communication systems. For example, at the transmitting end, the signal is processed by EWFRFT, and the receiving end only needs to invert the parameters to restore the original signal, that is, Inverse transformation for:

[0157]

[0158] By setting different transformation parameters, the modulated signal is transformed and processed by EWFRFT to present different constellation diagrams and expand the signal form. Compared with WFRFT, the EWFRFT used in this embodiment has four independent parameters to control the change of the signal, so that the system can show stronger resistance to parameter scanning and modulation recognition attacks.

[0159] Specifically, in step S104, the chaotic Brownian motion sequence is used to control the transformation parameters of EWFRFT, and the primary encrypted signal is subjected to EWFRFT transformation processing to obtain the secondary encrypted signal, which also includes the following steps:

[0160] Step S1041: taking the product of the sequence dz' generated in step S10321 and π as the transformation parameter θ of EWFRFT;

[0161] Step S1042: Group the primary encrypted transmission signal M″, and use the EWFRFT determined in step S1041 to perform EWFRFT transformation processing on the grouped primary encrypted transmission signal M″ to obtain a secondary encrypted signal M″′.

[0162] The expression of the secondary encrypted signal M″′ in the above step S104 is:

[0163] M″′=EWFRFT{M″,(θ1,θ2,θ3,θ4)} (8)

[0164] Among them, M″′ represents the secondary encrypted signal, M″ represents the primary encrypted transmission signal, and θ1, θ2, θ3, and θ4 represent multiple transformation parameters of EWFRFT.

[0165] After obtaining the secondary encrypted signal M'', the secondary encrypted signal M''' is subjected to CP processing and then transmitted to the receiving end.

[0166] In this embodiment, after receiving the secondary encrypted signal after the CP addition process, the receiving end first performs CP removal process on the secondary encrypted signal, and then performs the EWFRFT inverse transformation process in step S105.

[0167] Step S105 , step S106 , and step S107 in this example implementation are described in more detail below.

[0168] In this embodiment, the legitimate receiving end (i.e., the legitimate receiving party) shares a key with the sending end in advance through a secure channel. The legitimate receiving end generates two sets of chaotic three-dimensional Brownian motion sequences in the same way as the sending end, determines the direction vector and the scaling factor, and then constructs a random scaling matrix and selects the transformation parameters of the EWFRFT.

[0169] Specifically, in step S105, the receiving end performs an EWFRFT inverse transform process on the secondary encrypted signal to obtain a preliminary decrypted signal, and further includes the following steps:

[0170] Step S1051: grouping the secondary encrypted signal after the CP removal process;

[0171] Step S1052: Perform an EWFRFT inverse transform process on the secondary encrypted signal after grouping in step S1051 to obtain a preliminary decrypted signal R′.

[0172] The expression of the preliminary decrypted signal R′ in the above step S105 is:

[0173] R′=EWFRFT{R,(-θ1,-θ2,-θ3,-θ4)} (20)

[0174] Among them, R represents the secondary encrypted signal received by the receiving end, and -θ1, -θ2, -θ3, and -θ4 represent the inversion of multiple transformation parameters θ1, θ2, θ3, and θ4 of EWFRFT.

[0175] After obtaining the preliminary decrypted signal R′, the real part and the imaginary part of the preliminary decrypted signal R′ are separated, and inverse I / Q transformation and serial-to-parallel conversion are performed to obtain the constellation information to be scaled and decrypted of the three-dimensional constellation point, and then the scaling and decryption operation in step S106 is performed.

[0176] Specifically, in step S106, the random scaling matrix is ​​used to randomly scale the preliminary decrypted signal to generate a decrypted signal, and the following steps are also included:

[0177] The constellation information to be scaled and decrypted of the constellation point is obtained according to the preliminary decrypted signal, and the constellation information to be scaled and decrypted of the constellation point is randomly scaled using a random scaling matrix to generate a decrypted signal of the constellation point; wherein the decrypted signal of the i-th constellation point is:

[0178] R″ i =R′ i ×[S i (n i ,k i )] -1 (7)

[0179] Among them, R i represents the decrypted signal of the i-th constellation point, R′ i represents the constellation information to be scaled and decrypted of the i-th constellation point, S i (n i ,k i ) represents the i-th random scaling matrix, [·] -1 Represents the inverse of a matrix.

[0180] In one embodiment, after obtaining the decrypted signal R″ of the i-th constellation point iFinally, the Euclidean distance between the decrypted signal of each constellation point and the four constellation points in the original constellation diagram is calculated, and the constellation point corresponding to the decrypted signal of each constellation point is determined to be the constellation point with the minimum Euclidean distance from the original constellation diagram, and then the three-dimensional demodulation processing and parallel-to-serial conversion processing in step S107 are performed to demodulate and obtain the final decrypted information.

[0181] In order to verify the EWFRFT communication method based on three-dimensional constellation scaling encryption of the present application, the present application conducted the following simulation experiments.

[0182] The security and effectiveness analysis of the EWFRFT communication method based on three-dimensional constellation scaling encryption in this application plays an important role in the encryption design process. This application simulates and analyzes the proposed EWFRFT communication method based on three-dimensional constellation scaling encryption by analyzing the constellation encryption characteristics, anti-statistical attack, anti-exhaustive attack, bit error rate, etc., and evaluates its performance. The simulation experiment was completed on the following platform: CPU Intel Core i3-5005U4G, GPU NVDIA GeForce 920A4G, Windows 10 Home Edition, Matlab R2016. The simulation parameters are shown in Table 2.

[0183] Table 2 Simulation parameters

[0184]

[0185] (1) Analysis of Constellation Encryption Characteristics

[0186] The method proposed in this application implements double encryption on the three-dimensional constellation. Figures 9 to 12 The constellation diagrams before and after encryption are shown in FIG. Fig. 9 shows the initial regular constellation diagram, Fig.10 shows the constellation diagram after scaling and encryption, Fig.11 The constellation diagram of the I / Q signal after scaling and encryption is shown. Fig.12 The figure shows the constellation diagram after EWFRFT encryption. It can be seen from the figure that the initial regular constellation points are scattered around after being scaled and encrypted, forming an interference effect similar to noise. This can cause some confusion to illegal eavesdroppers. Even if the useful signal is separated from it according to the method of counteracting artificial noise, it is only partially encrypted information. No useful information can be obtained when the key is unknown, which provides better protection for the secure transmission of information.

[0187] However, the scaled and encrypted constellation diagram, whether it is a three-dimensional constellation or after being combined into an I / Q signal, still retains the clustering distribution pattern of the original constellation points, so there is still a risk of modulation style information leakage.

[0188] The method proposed in this application further uses the EWFRFT transform encryption method to perform secondary encryption on the signal to reduce the risk of the above-mentioned information being leaked. Fig.12 As shown in , the constellation points in the figure become random and disordered, completely eliminating the clustered distribution pattern of the original constellation points. It can be seen that the method proposed in this application can effectively resist the detection and identification of modulated signals and significantly improve the security of the communication system.

[0189] (2) Analysis of Anti-Statistical Attacks

[0190] refer to Fig.13 and Fig.14 As shown in the figure, the bar graph is the statistical distribution of the amplitude and phase of the encrypted signal under the simulation parameters. The two red dotted lines in the figure are the Rayleigh distribution and the uniform distribution with a probability density of 1 / 2π. Among them, the mean and variance of the Rayleigh distribution are equal to the mean and variance of the complex envelope amplitude of the encrypted modulation signal.

[0191] from Fig.13 and Fig.14 It can be seen that after the three-dimensional constellation is encrypted by the method proposed in this application, the amplitude of the signal shows a characteristic close to Rayleigh distribution, while the phase of the signal is basically consistent with the uniform distribution with a probability density of 1 / 2π. This characteristic makes it difficult for statistical attacks that rely on characteristic parameters to work, thereby greatly weakening the accuracy of modulation recognition.

[0192] (3) Analysis of Anti-Exhaustive Attack

[0193] As the core component of the encryption method, the key is directly related to the security of the entire communication system and the effectiveness of the encryption method. With the improvement of computing power, an excellent encryption method must not only have a large enough key space to resist brute force cracking, but also be highly sensitive to small changes in the key. For the method proposed in this application, the key system is composed of chaotic initial values ​​and control parameters, including the initial value (x0, y0) of the Hénon map, control parameters a, b and the initial value x′0 of the Logistic map, and the control parameter c. The value range of the key is -1<x0<1, -1<y0<1, 1.07≤a≤1.4, 0<x′0<1, and 3.57≤c≤4. In order to further verify the sensitivity of the encryption method to key changes, an experimental analysis was carried out using the control variable method. In the simulation experiment, each key parameter was adjusted one by one, and the correct parameters were used for the remaining keys to obtain a reference for the information bit error rate curve after decryption. Fig.15 As shown in the figure, when the correct key is used to decrypt the encrypted information, the bit error rate decreases as the signal-to-noise ratio E bThe increase of / N0 decreases rapidly, proving the effectiveness of the method proposed in this application. However, using the wrong key, even if only one parameter among x0, y0, a, b, c changes by 10 -15 Change, the key x′0 has 10 -16 The bit error rate of the decrypted information remains at about 0.5, indicating that the method proposed in this application can ensure the security of information even if there is a small risk of key leakage. Therefore, without considering the number of chaotic pre-iterations and the key value step, the key space of the method proposed in this application is 10 15 ×10 15 ×10 15 ×10 15 ×10 16 ×10 15 =10 91 Assume that the computing speed is 3.38×10 per second. 17 A supercomputer with double-precision floating-point operations tries to traverse the key value decryption. It takes at least 9.38×10 65 This shows that the key space of the method proposed in this application can resist brute force attacks.

[0194] (4) Bit Error Rate Analysis

[0195] In the process of spatial propagation, the signal will inevitably be interfered by noise. Compared with the two-dimensional constellation diagram, the three-dimensional modulation constellation diagram has a larger minimum Euclidean distance, which means that under the condition of transmitting the same energy, the bit error rate at the receiving end can be effectively reduced. Fig.16 As shown in , compared with the theoretical bit error rate of QPSK, the method proposed in this application has a lower bit error rate. In addition, the simulation results further verify that the scaling encryption of constellation points in the decision area proposed in this application can ensure accurate and reliable transmission of information; it also shows that the range of values ​​[0.8, 1.6] selected for the scaling factor in this application is relatively considerable, which can ensure the flexibility and adequacy of encryption to a certain extent.

[0196] In summary, the method proposed in this application is suitable for solving the security problems of wireless communication signals being easily intercepted, analyzed, interfered and destroyed. The method proposed in this application eliminates the distribution law of the original baseband modulation signal after encryption, can effectively resist statistical attacks on signals and exhaustive attacks on keys, and greatly improves the anti-detection and identification capabilities of wireless transmission signals.

[0197] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the specification and practicing the invention disclosed herein. This application is intended to cover any modification, use or adaptation of the present disclosure, which follows the general principles of the present disclosure and includes common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the appended claims.

Claims

1. An EWFRFT communication method based on three-dimensional constellation scaling encryption, characterized in that: include: The sending end performs serial-to-parallel conversion and three-dimensional modulation on the plaintext information in sequence to obtain the plaintext signal for transmission; A chaotic sequence is generated by Hénon and Logistic chaotic mapping, and the chaotic sequence is used to control the parameters of Brownian motion to generate a chaotic Brownian motion sequence; Generate a random scaling matrix using the chaotic Brownian motion sequence, and randomly scale the plaintext signal according to the random scaling matrix to generate a primary encrypted signal; Using the chaotic Brownian motion sequence to control the transformation parameters of EWFRFT, the primary encrypted signal is subjected to EWFRFT transformation processing to obtain a secondary encrypted signal; The receiving end performs an EWFRFT inverse transform process on the secondary encrypted signal to obtain a preliminary decrypted signal; Randomly scaling the preliminary decryption signal using the random scaling matrix to generate a decryption signal; The decrypted signal is subjected to three-dimensional demodulation processing and parallel-to-serial conversion processing in sequence to obtain decrypted information.

2. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 1 is characterized in that: The method of generating a chaotic sequence by using Hénon and Logistic chaotic mapping and controlling the parameters of Brownian motion by using the chaotic sequence to generate a chaotic Brownian motion sequence comprises: In three-dimensional space, the expression of Brownian motion of a point is: Among them, τ∈[0,+∞) is the motion step, and α and β represent the direction of motion.

3. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 2 is characterized in that: The method of generating a chaotic sequence by using Hénon and Logistic chaotic mapping and controlling the parameters of Brownian motion by using the chaotic sequence to generate a chaotic Brownian motion sequence comprises: The Hénon mapping expression is: The mapping expression of the Logistic is: x′ n+1 =cx′ n (1-x′ n )(3) Where n represents the number of iterations of the chaotic sequence, x n ,y n represents the Hénon mapping sequence, x′ n represents the mapping sequence of Logistic, a, b, c represent the control parameters respectively; when 1.07≤a≤1.4, b=0.3, the Hénon mapping is in a chaotic state; when 3.57≤c≤4, the Logistic mapping is in a chaotic state; Assume that the initial value of the Hénon map is (x0, y0), and after m1 iterations, a chaotic sequence (x n ,y n ), the initial value of the Logistic map is x′0, and the chaotic sequence x′ of the same length L is generated by iterating m2 times n , then the expression of the chaotic Brownian motion sequence is: Among them, mean(x n ) represents the Hénon mapping sequence x n The average value of .

4. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 1, characterized in that: The transmitting end sequentially performs serial-to-parallel conversion and three-dimensional modulation on the plaintext information to obtain a transmitted plaintext signal, including: The plaintext information is mapped according to the three-dimensional constellation of the regular tetrahedron to obtain N constellation points, and the coordinates of the i-th constellation point are (x i ,y i ,z i ), then the plaintext signal is: Among them, x N ,y N 、z N Represents the coordinates of the Nth constellation point.

5. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 4 is characterized in that: The method of generating a random scaling matrix by using the chaotic Brownian motion sequence, and randomly scaling the plaintext signal according to the random scaling matrix to generate a primary encrypted signal, further includes the following steps: Construct a random scaling matrix model in three-dimensional space; Determining the direction vector and the scaling factor in the random scaling matrix model according to the parameters of the chaotic Brownian motion sequence; Each of the constellation points is randomly scaled using the random scaling matrix to obtain the primary encrypted signal.

6. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 5, characterized in that: In the step of constructing a random scaling matrix model in a three-dimensional space, the random scaling matrix model is: Where n represents the direction vector, n x ,n y ,n z They represent the axis coordinates of the direction vector n, and k represents the scaling factor.

7. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 5, characterized in that: The step of determining the direction vector and the scaling factor in the random scaling matrix model according to the parameters of the chaotic Brownian motion sequence further includes the following steps: constructing two groups of chaotic Brownian motion sequences; The direction vector is determined by using one set of the chaotic Brownian motion sequences, and the scaling factor is determined by using another set of the chaotic Brownian motion sequences.

8. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to any one of claims 4 to 7, characterized in that: The step of randomly scaling the preliminary decrypted signal by using the random scaling matrix to generate a decrypted signal further includes the following steps: The constellation information to be scaled and decrypted of the constellation point is obtained according to the preliminary decrypted signal, and the constellation information to be scaled and decrypted of the constellation point is randomly scaled by using the random scaling matrix to generate a decrypted signal of the constellation point; wherein the decrypted signal of the i-th constellation point is: R″ i =R′ i ×[S i (n i ,k i )] -1 (7) Among them, R i represents the decrypted signal of the i-th constellation point, R′ i represents the constellation information to be scaled and decrypted of the i-th constellation point, S i (n i ,k i ) represents the i-th random scaling matrix, [·] -1 Represents the inverse of a matrix.

9. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 1, characterized in that: Before the encrypted signal is subjected to EWFRFT transformation processing, the following steps are also included: The primary encrypted signal is subjected to I / Q conversion processing and parallel-to-serial conversion processing.

10. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 8, characterized in that: In the step of controlling the transformation parameters of EWFRFT by using the chaotic Brownian motion sequence, performing EWFRFT transformation processing on the encrypted signal to generate an encrypted conversion signal, The expression of the encrypted conversion signal is: M″′=EWFRFT{M″,(θ1,θ2,θ3,θ4)} (8) Wherein, M″′ represents the encrypted conversion signal, M″ represents the encrypted signal, and θ1, θ2, θ3, θ4 represent multiple transformation parameters of EWFRFT.

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