An EWFRFT communication method based on three-dimensional constellation scaling encryption

Abstract

The disclosed embodiments relate to an EWFRFT communication method based on three-dimensional constellation scaling encryption, comprising: a transmitter sequentially performs serial-to-parallel conversion and three-dimensional modulation on plaintext information to obtain a plaintext signal; a chaotic sequence is generated using Hénon and Logistic chaotic mapping, and the chaotic sequence is used to control Brownian motion parameters to generate a chaotic Brownian motion sequence; a random scaling matrix is ​​generated using the chaotic Brownian motion sequence, and the plaintext signal is randomly scaled according to the random scaling matrix to generate a primary encrypted signal; the chaotic Brownian motion sequence is used to control EWFRFT transformation parameters, and the primary encrypted signal is subjected to EWFRFT transformation processing to obtain a secondary encrypted signal; a receiver performs an inverse EWFRFT transformation on the secondary encrypted signal to obtain a preliminary decrypted signal; the preliminary decrypted signal is randomly scaled using the random scaling matrix to generate a decrypted signal; and the decrypted signal is subjected to three-dimensional demodulation and parallel-to-serial conversion processing to obtain decrypted information. The disclosed embodiments significantly improve the security of communication systems.

Description

Technical Field

[0001] The present disclosure relates to the field of encrypted communication technology, 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 increasingly widespread. However, the wireless nature of drone communications exposes them to security threats such as eavesdropping, tampering, and hijacking. Physical Layer Security (PLS) is being introduced into drone systems because it can enhance channel confidentiality, reduce the advantages of eavesdropping channels, and ensure communication data security. Modulation encryption, a key technical approach to physical layer security, eliminates the statistical characteristics of waveforms and effectively disrupts the distribution of signals, thereby achieving low probability of intercept (PoI) communications.

[0003] In related technologies, modulation encryption primarily relies on two-dimensional constellation modulation. However, this encryption algorithm is simple, the encryption system is relatively traditional, and there is a risk of theft. Therefore, encryption technology is gradually evolving towards three-dimensional constellation modulation encryption. Currently, three-dimensional constellation modulation encryption primarily uses rotation encryption around the constellation points and quaternion rotation encryption. These methods suffer from high computational complexity and insufficient encryption.

[0004] In terms of implementation technology, constellation scrambling encryption primarily utilizes methods such as chaotic cryptography and the weighted fractional Fourier transform (WFRFT). Combining the WFRFT with constellation encryption can enhance the security and confidentiality of communication systems to a certain extent. However, with the advancement of chaotic cryptanalysis techniques, some digital chaos systems are threatened by attacks such as phase space reconstruction and deep learning, thus requiring a higher level of randomness in chaotic sequences. Furthermore, the form of the WFRFT signal is controlled by the transform order. Using methods such as cyclic correlation and high-order cumulants, the transform order can be accurately identified under unknown conditions, posing a certain threat to the security of communication systems.

[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 prior art known to ordinary technicians in the field. Summary of the Invention

[0007] The purpose of the embodiments of the present disclosure 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 to obtain the transmitted plaintext signal;

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

[0011] Generating a random scaling matrix using the chaotic Brownian motion sequence, and randomly scaling 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 on the secondary encrypted signal to obtain a preliminary decrypted signal;

[0014] Randomly scaling the preliminary decrypted signal using the random scaling matrix to generate a decrypted 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 controlling parameters of Brownian motion using the chaotic sequence 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 movement step, and α and β represent the direction of movement.

[0020] In an exemplary embodiment of the present disclosure, 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 includes:

[0021] The mapping expression of Hénon is:

[0022]

[0023] The mapping expression of the Logistic is:

[0024] x′ n+1 =cx′ n (1-x′ n )(3)

[0025] Among them, n represents the number of iterations of the chaotic sequence, x n 、y n represents the Hénon mapping sequence, x′ n represents the Logistic mapping sequence, a, b, and 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 of length L is generated (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 and three-dimensional modulation on 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 a direction vector and a scaling factor in the random scaling matrix model according to 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] Among them, 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 determining of 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 sets 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 randomly scaling the preliminary decrypted signal using the random scaling matrix to generate a decrypted signal further includes the following steps:

[0044] Obtaining the to-be-scaled decrypted constellation information of the constellation point according to the preliminary decrypted signal, and randomly scaling the to-be-scaled decrypted constellation information of the constellation point 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 Denotes the decrypted signal of the i-th constellation point, R′ i Indicates 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 performing EWFRFT transformation on the encrypted signal, the following steps are further 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 controlling the transformation parameters of EWFRFT by using the chaotic Brownian motion sequence and performing EWFRFT transformation on the encrypted signal to generate the 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, and 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 disclosed embodiments, the aforementioned method, combined with the randomness of Brownian motion, utilizes classic Hénon and Logistic chaotic maps to generate a chaotic Brownian motion sequence. This chaotic Brownian motion sequence is then used to generate a random scaling matrix, which is then randomly scaled on the plaintext signal to complete a preliminary encryption operation and obtain a primary encrypted signal. Furthermore, the chaotic Brownian motion sequence is used to control the EWFRFT transformation parameters, and the encrypted signal after the preliminary encryption is subjected to an EWFRFT transformation to complete a secondary encryption operation and obtain a secondary encrypted signal, further disrupting the constellation distribution pattern. The aforementioned scaling encryption operation and EWFRFT transformation encryption operation enable multi-layer encryption of the plaintext signal, rendering previously overlapping constellation points random and chaotic, eliminating the distribution pattern of the original baseband modulated signal. This effectively counters statistical attacks on the signal and exhaustive key attacks, improving the anti-detection and identification capabilities of wireless transmission signals and thereby enhancing 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 disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] The accompanying drawings are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the specification, serve to explain the principles of the present disclosure. Obviously, the drawings described below are only some embodiments of the present disclosure, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

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

[0058] Figure 2 A schematic flow chart illustrating 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 illustrating 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 after 2000 iterations 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] Figure 9 An initially regularized constellation diagram in an exemplary embodiment of the present disclosure is shown;

[0066] Figure 10 FIG. 1 shows a constellation diagram after scaling and encryption in an exemplary embodiment of the present disclosure;

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

[0068] Figure 12 FIG. 1 shows a constellation diagram after EWFRFT encryption in an exemplary embodiment of the present disclosure;

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

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

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

[0072] Figure 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 embodied in many 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 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 merely schematic illustrations of the present disclosure and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different networks and / or processor devices and / or microcontroller devices.

[0075] This example embodiment first provides an EWFRFT communication method based on three-dimensional constellation scaling encryption. 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 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 EWFRFT transformation parameters, 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: Randomly scale the preliminary decrypted signal using a random scaling matrix to generate a decrypted signal;

[0082] Step S107: performing three-dimensional demodulation processing and parallel-to-serial conversion processing on the decrypted signal in sequence to obtain decrypted information.

[0083] In the disclosed embodiments, the aforementioned method, combined with the randomness of Brownian motion, utilizes classic Hénon and Logistic chaotic maps to generate a chaotic Brownian motion sequence. This chaotic Brownian motion sequence is then used to generate a random scaling matrix, which is then randomly scaled on the plaintext signal to complete a preliminary encryption operation and obtain a primary encrypted signal. Furthermore, the chaotic Brownian motion sequence is used to control the EWFRFT transformation parameters, and the encrypted signal after the preliminary encryption is subjected to an EWFRFT transformation to complete a secondary encryption operation and obtain a secondary encrypted signal, further disrupting the constellation distribution pattern. The aforementioned scaling encryption operation and EWFRFT transformation encryption operation enable multi-layer encryption of the plaintext signal, rendering previously overlapping constellation points random and chaotic, eliminating the distribution pattern of the original baseband modulated signal. This effectively counters statistical attacks on the signal and exhaustive key attacks, improving the anti-detection and identification capabilities of wireless transmission signals and thereby enhancing the security of the communication system.

[0084] Below, we will refer to Figures 1 to 16 Each step of the above method in this exemplary embodiment 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 points, and utilizing the amplitude, phase, and transmit antenna sequence characteristics of the signal for joint modulation, thereby achieving efficient signal transmission. s =2 d The constellation points are evenly distributed on the sphere, where d is the number of bits of coded information. Figure 3 The schematic diagram of the three-dimensional constellation diagram is shown, which specifically shows that the constellation diagram is a three-dimensional space mapping of a regular tetrahedron. 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 subject to interference such as noise 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 is required 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, plaintext information (i.e., a plaintext bit stream) is mapped to a three-dimensional constellation symbol through serial-to-parallel conversion. After the information is three-dimensionally mapped, each constellation point is expanded or contracted within its decision area using a shared key according to a specific mapping rule. The receiving end, which has the same key and mapping rule, can restore the shifted constellation point and complete signal demodulation.

[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 performs serial-to-parallel conversion and three-dimensional modulation on the plaintext information in sequence to obtain a plaintext signal for transmission, which also includes sub-step S1011:

[0094] In sub-step S1011, assuming that the three-dimensional constellation 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 parameters of Brownian motion are controlled by using the chaotic sequence 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 movement step, and α and β represent the direction of movement.

[0103] In step S102, a chaotic sequence is generated by using Hénon and Logistic chaotic mapping, and the parameters of Brownian motion are controlled by using the chaotic sequence to generate a chaotic Brownian motion sequence. The method also includes sub-step S1022:

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

[0105]

[0106] The mapping expression of Logistic is:

[0107] x′ n+1 =cx′n (1-x′ n )(3)

[0108] Among them, n represents the number of iterations of the chaotic sequence, x n 、y n represents the Hénon mapping sequence, x′ n represents the Logistic mapping sequence, a, b, and 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 of length L is generated (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 the Hénon and Logistic chaotic maps, after 2000 iterations of the chaotic three-dimensional Brownian motion, its motion trajectory is observed and compared with the strange attractors of the Hénon map and the Logistic map, see Figures 5 to 7 As shown in , it is not difficult to see that the chaotic three-dimensional Brownian motion sequence exhibits significant randomness and disorder. Spectral entropy (SE) can be used to quantitatively characterize the structural complexity of a 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 the spectral entropy value of the chaotic three-dimensional Brownian motion sequence is relatively higher than that of the original chaotic sequence, indicating that the chaotic three-dimensional Brownian motion sequence is more random and therefore has great application potential in cryptographic 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. 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, causing it to "stretch" or "squeeze." Factor k is the 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; and when k < 0, a reflection result is obtained. If the object is a point in a plane or space, when k > 1, it remains a point after expansion and moves upward or outward relative to the point. When 0 < k < 1, it remains a point after shortening and moves downward or inward relative to the point. When k = 1, the point does not move.

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

[0126]

[0127] Among them, 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 the other set of chaotic Brownian motion sequences to determine the scaling factor.

[0131] Specifically, in step S10321, two sets of chaotic Brownian motion sequences are constructed, and two sets 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). Assume that the first set of chaotic three-dimensional Brownian motion sequences is dx, dy, dz, and the second set of chaotic three-dimensional Brownian motion sequences is dx', dy', dz'.

[0132] Specifically, in step S10322, the first set 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; and N new sequences are selected from the second set 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]. This is conducive to ensuring that the scaled and encrypted constellation points fall within 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 according to 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 N constellation points. The primary encrypted signal M′ can be expressed as:

[0139]

[0140] Where 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, the Weighted Fractional Fourier Transform (WFRFT) is a new signal processing method that disrupts the signal distribution pattern by adjusting the transformation order. The WFRFT transform has three basic properties: continuity, boundary properties, and order additivity. The transformation order determines the transformation form, so 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 properties, 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 perform the inverse operation on the parameters to restore the original signal, that is, Inverse transform for:

[0157]

[0158] By setting different transformation parameters, the modulated signal is transformed and processed using EWFRFT to present different constellations, expanding the signal form. Compared with WFRFT, the EWFRFT used in this embodiment has four independent parameters that control signal changes, making the system more resilient 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: The product of the sequence dz' generated in step S10321 and π is used as the transformation parameter θ of the EWFRFT;

[0161] Step S1042: Group the primary encrypted transmission signal M″, and perform EWFRFT transformation processing on the grouped primary encrypted transmission signal M″ using the EWFRFT determined in step S1041 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] Wherein, 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 the receiving end receives 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 transform process in step S105.

[0167] The following describes step S105, step S106, and step S107 in this exemplary embodiment in more detail.

[0168] In this embodiment, the legitimate receiving end (i.e., the legitimate receiver) and the sending end share a key 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 scaling factor, and then constructs a random scaling matrix and selects the transformation parameters of EWFRFT.

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

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

[0171] Step S1052: Perform EWFRFT inverse transformation 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] Wherein, 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 and imaginary parts 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 points, 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. 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. 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 Denotes the decrypted signal of the i-th constellation point, R′ i Indicates 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 to the original constellation diagram. Then, the three-dimensional demodulation process and parallel-to-serial conversion process 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 this application, this application conducted the following simulation experiments.

[0182] The security and effectiveness analysis of the proposed EWFRFT communication method based on 3D constellation scaling encryption plays a crucial role in encryption design. This paper simulates and analyzes the proposed EWFRFT communication method based on 3D constellation scaling encryption, analyzing its constellation encryption characteristics, resistance to statistical attacks, resistance to exhaustive attacks, and bit error rate (BER), to evaluate its performance. The simulation experiments were conducted on the following platform: an Intel Core i3-5005U 4G CPU, an NVDIA GeForce 920A 4G GPU, Windows 10 Home Edition, and 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 for the three-dimensional constellation. Figures 9 to 12 The constellation diagrams before and after encryption are shown in FIG. Figure 9 shows the initial regular constellation diagram, Figure 10 shows the constellation diagram after scaling and encryption, Figure 11 The constellation diagram of the I / Q signal after scaling and encryption is shown. Figure 12 The following figure shows the constellation diagram after EWFRFT encryption. As can be seen, the initially regular constellation points are spread out after scaling and encryption, creating a noise-like interference effect. This can confuse unauthorized eavesdroppers. Even if useful signals are isolated using methods to combat artificial noise, they are only partially encrypted. Without the key, no useful information can be obtained, providing good protection for secure information transmission.

[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 EWFRFT transform encryption to perform secondary encryption on the signal to reduce the risk of the above-mentioned information being leaked. Figure 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 Figure 13 and Figure 14 As shown in the figure, the histogram shows the statistical distribution of the amplitude and phase of the encrypted signal under the simulation parameters. The two red dashed lines in the figure represent the Rayleigh distribution and the uniform distribution with a probability density of 1 / 2π, respectively. The mean and variance of the Rayleigh distribution are equal to the mean and variance of the complex envelope amplitude of the encrypted modulated signal, respectively.

[0191] from Figure 13 and Figure 14 As can be seen in the figure, after encrypting the three-dimensional constellation using the method proposed in this application, the signal amplitude exhibits characteristics close to the Rayleigh distribution, while the signal phase is basically consistent with a uniform distribution with a probability density of 1 / 2π. This characteristic makes statistical attacks that rely on characteristic parameters difficult 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 the initial value and control parameters of chaos, specifically including the initial value (x0, y0) of the Hénon map, control parameters a, b and the initial value x′0 of the Logistic map, 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, 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 curve of the information bit error rate after decryption. Figure 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, if the wrong key is used, 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 around 0.5, indicating that the method proposed in this application can ensure the security of information even in the face of a small risk of key leakage. Therefore, without considering the number of chaotic pre-iterations and the key value step size, 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 Assuming a computing speed of 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 exhaustive attacks.

[0194] (4) Bit Error Rate Analysis

[0195] During spatial propagation, signals are inevitably interfered with 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. Figure 16 As shown in , compared with the theoretical bit error rate of QPSK, the proposed method has a lower bit error rate. Furthermore, simulation results further verify that the proposed method of scaling and encrypting constellation points within the decision region can ensure accurate and reliable information transmission. It also shows that the range of values ​​selected for the scaling factor [0.8, 1.6] is relatively reasonable, ensuring the flexibility and adequacy of encryption to a certain extent.

[0196] In summary, the method proposed in this application is suitable for addressing security issues such as the vulnerability of wireless communication signals to interception, analysis, interference, and disruption. The method proposed in this application eliminates the distribution pattern of the original baseband modulated signal after encryption, effectively countering statistical attacks on the signal and exhaustive attacks on the key, greatly improving 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 variations, uses, or adaptations of the present disclosure that follow the general principles of the present disclosure and include common knowledge or customary techniques in the art not disclosed herein. The description and examples are to be considered as exemplary only, with the true scope and spirit of the present disclosure being 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 to obtain the transmitted plaintext signal; A chaotic sequence is generated by Hénon and Logistic chaotic mapping, and the parameters of Brownian motion are controlled by using the chaotic sequence to generate a chaotic Brownian motion sequence; Generating a random scaling matrix using the chaotic Brownian motion sequence, and randomly scaling 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 on the secondary encrypted signal to obtain a preliminary decrypted signal; Randomly scaling the preliminary decrypted signal using the random scaling matrix to generate a decrypted 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, 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 includes: In three-dimensional space, the expression of Brownian motion of a point is: （1） in, is the movement step length, 、 Indicates the direction of movement.

3. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 2, 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 mapping expression of Hénon is: （2） The mapping expression of the Logistic is: （3） in, represents the number of iterations of the chaotic sequence, 、 represents a sequence of Hénon mappings, Represents the mapping sequence of Logistic, a, b, c represent the control parameters respectively; when When , the Hénon map is in a chaotic state; when When , the Logistic map is in a chaotic state; Assume that the initial value of the Hénon map is , iteration The length of the generated Chaotic sequence , the initial value of the Logistic map is , iteration Generate the same length Chaotic sequence , then the expression of the chaotic Brownian motion sequence is: （4） in, Represents a Hénon mapping sequence 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 plaintext signal for transmission, including: The plaintext information is mapped according to the three-dimensional constellation of the regular tetrahedron to obtain constellation point, The coordinates of the constellation points are , then the plaintext signal is: （5） in,( , , ) indicates the The coordinates of the constellation points.

5. The EWFRFT communication method based on three-dimensional constellation scaling encryption according to claim 4, 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 a direction vector and a scaling factor in the random scaling matrix model according to 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: （6） in, represents the direction vector, Represents the direction vector The axis coordinates of 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 sets 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 randomly scaling the preliminary decrypted signal using the random scaling matrix to generate a decrypted signal further comprises the following steps: Obtain the to-be-scaled decrypted constellation information of the constellation point according to the preliminary decrypted signal, and use the random scaling matrix to randomly scale the to-be-scaled decrypted constellation information of the constellation point to generate a decrypted signal of the constellation point; wherein the first The decrypted signal of each constellation point is: （7） in, Indicates the The decrypted signal of each constellation point, Indicates the The constellation information to be scaled and decrypted for each constellation point, Indicates the A random scaling matrix, 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 performing EWFRFT transformation on the primary encrypted signal, the method further includes the following steps: 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 and performing EWFRFT transformation on the primary encrypted signal to generate a secondary encrypted signal, The expression of the secondary encryption signal is: （8） in, Indicates the secondary encryption signal, Represents the primary encryption signal, Represents multiple transformation parameters of EWFRFT.

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