Multi-level chaotic encryption-based mp-wfrft communication method and system

Abstract

The present disclosure relates to a multi-cascaded chaotic encryption-based MP-WFRFT communication method and system. The method comprises: building a multi-cascaded chaotic system model using Logistic mapping and Henon-Sine mapping, wherein the multi-cascaded chaotic system comprises a cryptographic kernel space having a bit scrambling matrix and a constellation rotation matrix; performing triple encryption processing on an input signal using the cryptographic kernel space of the multi-cascaded chaotic system and MP-WFRFT transformation, generating an encrypted signal, and completing hybrid carrier modulation; receiving the hybrid carrier signal at a receiving end and performing WFRFT inverse transformation on the hybrid carrier signal; generating a decryption matrix according to parameters of the multi-cascaded chaotic system, in combination with MP-WFRFT transformation parameters and a scale vector, and decrypting the encrypted signal using the decryption matrix to complete the demodulation process. The present disclosure improves the wireless communication physical layer security transmission performance through triple encryption processing, and can effectively prevent brute force attacks.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the field of encryption communication, in particular to a MP-WFRFT communication method and system based on multi-cascaded chaos encryption. BACKGROUND

[0002] Traditional secure communication methods are based on cryptography, which are usually implemented in the upper layer of the open system interconnection protocol stack and are widely used to prevent information leakage to unauthorized users. However, with the development of mobile Internet and the significant improvement of computing power, these currently considered secure encryption algorithms are facing great challenges.

[0003] As a supplement to higher level security, physical layer based security has attracted considerable attention. Weighted fractional Fourier transform (WFRFT) is a special fractional Fourier hybrid transform method, which has both time domain and frequency domain characteristics as a novel time-frequency analysis tool, can be expressed as a weighted summation of the four-state function of the traditional Fourier transform, and has received more and more attention in the field of wireless communication in recent years, and has been gradually applied to many wireless communication fields such as underwater acoustic communication and dual-polarized satellite communication.

[0004] Chaotic scrambling is considered as another encryption technology. Based on the high initial condition sensitivity of chaotic encryption communication, it has become a method for enhancing data confidentiality with wide application prospects.

[0005] However, the structure of the above existing chaotic encryption system is relatively simple, which is easy to be attacked and lead to encryption failure. Therefore, it is necessary to improve one or more problems existing in the above related technical solutions to improve the performance of wireless communication physical layer secure transmission.

[0006] It should be noted that the information disclosed in the above background section is only used to strengthen the understanding of the background of the present disclosure, and therefore can include information that does not constitute prior art known to those of ordinary skill in the art. SUMMARY

[0007] The purpose of the embodiments of the present disclosure is to provide a multi parameter-weighted fractional Fourier transform (MP-WFRFT) communication method and system based on multi-cascaded chaos encryption, so as to improve the performance of wireless communication physical layer secure transmission.

[0008] According to a first aspect of the embodiments of the present disclosure, a MP-WFRFT communication method based on multi-cascaded chaos encryption is provided, which comprises the following steps:

[0009] A multi-cascading chaotic system model is built by using a Logistic mapping and a Henon-Sine mapping, wherein the multi-cascading chaotic system includes a cryptographic core space having a bit scrambling matrix and a constellation rotation matrix;

[0010] The cryptographic core space of the multi-cascading chaotic system and an MP-WFRFT transform are used to perform triple encryption processing on an input signal, to generate an encrypted signal, and to complete hybrid carrier modulation;

[0011] A receiving end receives the hybrid carrier signal and performs MP-WFRFT inverse transform on the hybrid carrier signal;

[0012] According to parameters of the multi-cascading chaotic system, in combination with MP-WFRFT transform parameters and a scale vector, a decryption matrix is generated, the encrypted signal is decrypted by using the decryption matrix, and then a demodulation process is completed.

[0013] In an example embodiment of the present disclosure, building the multi-cascading chaotic system model includes the following steps:

[0014] A one-dimensional pseudo-random chaotic sequence L is generated by using a Logistic mapping, and the sequence L is divided into multiple groups of initial values (x i ,y i ) of Henon-Sine mapping, in combination with initial value keys (a i ,0.7), a two-dimensional pseudo-random chaotic sequence h i and m i is generated, and is converted into a bit scrambling matrix H i and a constellation rotation matrix M i , to constitute a cryptographic core space for data encryption.

[0015] In an example embodiment of the present disclosure, the Logistics mapping is a nonlinear dynamic discrete chaotic mapping, and a mapping equation thereof includes:

[0016] c n+1 =qc n (1-c n ) (1)

[0017] wherein c n is an iterative value of a state quantity c at the nth moment; c n+1 is an iterative value of the state quantity c at the (n+1)th moment; n is a sequence iteration number; q is a chaotic system parameter, and when q ∈ [3.57, 4], the system is in a chaotic state;

[0018] The Henon-Sine mapping is a two-dimensional chaotic mapping, and a mapping equation thereof includes:

[0019]

[0020] wherein a, b are system control parameters; x n is the iterative value of state variable x at the n th moment; x n+1 is the iterative value of state variable x at the n+1 th moment; y n is the iterative value of state variable y at the n th moment; y n+1 is the iterative value of state variable y at the n+1 th moment; when a∈(-∞,-0.71)∪(0.71,+∞) and b=0.7, the Henon-Sine system is in a chaotic state.

[0021] In an example embodiment of the present disclosure, the Henon-Sine mapping comprises a Sine mapping and a Henon mapping, wherein the Sine mapping is a one-dimensional chaotic mapping, and the mapping equation thereof comprises:

[0022] x n+1 =λsin(πx n ) (3)

[0023] wherein x n is the iterative value of state variable x at the n th moment; x n+1 is the iterative value of state variable x at the n+1 th moment; λ is a system control parameter, and when λ∈[0.87,1], the Sine system is in a chaotic state.

[0024] The Henon mapping is a two-dimensional chaotic mapping, and the mapping equation thereof comprises:

[0025]

[0026] wherein x n is the iterative value of state variable x at the n th moment; x n+1 is the iterative value of state variable x at the n+1 th moment; y n is the iterative value of state variable y at the n th moment; y n+1 is the iterative value of state variable y at the n+1 th moment; when a∈[1.06,1.22]∪[1.27,1.29]∪[1.31,1.42] and b=0.3, the Henon system is in a chaotic state.

[0027] In an example embodiment of the present disclosure, the generation process of the password nucleus space comprises:

[0028] Let Q be the output sequence of the original baseband signal after channel coding, and the length is N; the hash value P of the sequence Q is obtained by using the SM3 algorithm, the length of P is 256 bits, which is divided into 32 groups, each group contains 8 bits, and P={p1,p2…p 32}; the calculation formula is

[0029] P = SM3(Q)

[0030]

[0031] The initial value key, the bifurcation parameter q and the pre-iteration number m of the multi-cascaded chaotic system are calculated, and a is agreed by the communication users i ; represents "XOR" operation; & represents "AND" operation.

[0032] In an exemplary embodiment of the present disclosure, the generation process of the cryptographic core space further includes:

[0033] The sequence Q is processed in blocks, and the block length is d 2 , d 2 should be divisible by N, N is a natural number, and the ith block is converted into a d×d matrix T i , where i takes values

[0034] The initial value key, the bifurcation parameter q and the pre-iteration number m are used as inputs of the Logistic mapping to generate a chaotic sequence with a length of U, every 2 values (x i , y i ) in the chaotic sequence are grouped as a group, and (a i , 0.7) is used as an input of a plurality of Henon-Sine mappings, the ith Henon-Sine mapping generates two one-dimensional sequences m 2 , h i with a length of g i ; the formula

[0035]

[0036] The data sorting process is performed on h i , and the original value is replaced by the number value, and then converted into a g×g bit scrambling matrix H i ;

[0037] The phase rotation factor r i is generated by using the sequence m ik , which is used for phase rotation of the symbol constellation, and the calculation formula of the phase rotation factor includes:

[0038]

[0039] wherein k = 1, 2, 3,..., g 2 ; m ik represents a chaotic sequence for generating r ik ; j represents an imaginary unit; and the phase rotation matrix M iThe calculation formulas include:

[0040]

[0041] In an exemplary embodiment of this disclosure, the triple encryption processing of the input signal using the cryptographic kernel space of the multi-cascaded chaotic system and the MP-WFRFT transform includes the following steps:

[0042] The input bit data is encrypted using a bit scrambling matrix to obtain the encrypted modulation symbol data.

[0043] The modulation symbol data is then encrypted using a second round of constellation rotation using a constellation rotation matrix.

[0044] Then, MP-WFRFT is used to perform a third round of encryption to obtain the final encrypted signal, and hybrid carrier modulation is completed.

[0045] In an exemplary embodiment of this disclosure, the first round of bit scrambling encryption includes: setting d=32, g=4, and utilizing H... i Matrix pair T i The matrix is ​​scrambled by first translating rows and then columns, with each scrambled object T. ij Size is g × g, H i The step size l is 1, and T is finally obtained. i The scrambling result is Y i .

[0046] In an exemplary embodiment of this disclosure, the process of the second round of constellation rotation encryption includes:

[0047] The symbol matrix B to be encrypted ij Flattened by rows, it becomes a one-dimensional vector u;

[0048] Vector u multiplied by diagonal rotation matrix M i Perform constellation rotation, and then transform the resulting one-dimensional vector u' into a B of size g×g. ij ′, B ij ′ refers to B ij The encrypted symbol matrix covers matrix B. i B in ij Its calculation formula includes:

[0049]

[0050] Following the principle of row-first, column-later, the shift constellation is encrypted using a step size l=1.

[0051] A second aspect of this disclosure provides an MP-WFRFT communication system based on multi-cascaded chaotic encryption. This communication system utilizes a Logistic mapping to generate a one-dimensional pseudo-random chaotic sequence L, and divides the sequence L into multiple sets of initial values ​​(x) of Henon-Sine mappings. i ,y i ), combined with the initial value key (a i (0.7), generate a two-dimensional pseudo-chaotic sequence h i and m i And convert it into a bit scrambling matrix H i And constellation rotation matrix M i This constitutes a cryptographic kernel space for data encryption; wherein, the MP-WFRFT transform unit is used to perform MP-WFRFT transform on the encrypted signal to complete hybrid carrier modulation.

[0052] The technical solution provided in this disclosure may include the following beneficial effects:

[0053] In the embodiments of this disclosure, a multi-cascaded chaotic system is constructed by combining Logistic mapping and Henon-Sine mapping. This increases the structural complexity and key space of the chaotic system, making it more difficult to decipher the chaotic mapping sequence. It ensures that the original data information can only be recovered when both the key and the system structure are known. In this implementation, the multi-cascaded chaotic system based on Logistic and Henon-Sine mapping achieves a first round of bit scrambling encryption of bit data, a second round of constellation rotation of symbol data, and a third round of encryption using MP-WFRFT. This triple encryption scheme greatly improves the security performance of the communication system, effectively preventing brute-force attacks and enabling secure information transmission without affecting transmission performance.

[0054] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0055] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0056] Figure 1 A schematic diagram illustrating the steps of the MP-WFRFT communication method based on multi-cascaded chaotic encryption in an exemplary embodiment of this disclosure is shown.

[0057] Figure 2 The diagram illustrates the phase diagram, bifurcation diagram, and Lyapunov index of three chaotic systems in an exemplary embodiment of this disclosure.

[0058] Figure 3 This diagram illustrates the structure of an L-2D-HSM multi-cascaded chaotic system in an exemplary embodiment of this disclosure.

[0059] Figure 4 A system block diagram is shown for the MP-WFRFT communication method based on multi-cascaded chaotic encryption in an exemplary embodiment of this disclosure;

[0060] Figure 5 This diagram illustrates a bit scrambling operation in an exemplary embodiment of this disclosure.

[0061] Figure 6 This diagram illustrates the original distribution of data and the distribution after bit scrambling in an exemplary embodiment of this disclosure.

[0062] Figure 7 This diagram illustrates the rotation operation of the moving constellation in an exemplary embodiment of this disclosure.

[0063] Figure 8 This diagram illustrates the original constellation diagram, the scrambled and encrypted constellation diagram, and the constellation diagram with encrypted constellations in an exemplary embodiment of this disclosure.

[0064] Figure 9 A schematic diagram showing the time-domain waveforms of the signals before and after encryption in an exemplary embodiment of this disclosure;

[0065] Figure 10 This diagram illustrates the effect of the initial values ​​of the Logistic and Henon-Sine mappings on chaotic sequences in an exemplary embodiment of this disclosure.

[0066] Figure 11 This diagram illustrates the bit error rate curves corresponding to different initial values ​​of the chaotic key in an exemplary embodiment of this disclosure.

[0067] Figure 12 The diagram illustrates the bit error rate curves corresponding to different transformation parameters in the exemplary embodiments of this disclosure. Detailed Implementation

[0068] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary 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.

[0069] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0070] The first aspect of this exemplary implementation provides an MP-WFRFT communication method based on multi-cascaded chaotic encryption, referencing... Figure 1 As shown, the method may include the following steps:

[0071] Step S101: Construct a multi-cascade chaotic system model using the Logistic mapping and Henon-Sine mapping, wherein the multi-cascade chaotic system includes a cryptographic kernel space with a bit scrambling matrix and a constellation rotation matrix;

[0072] Step S102: Using the cryptographic kernel space of the multi-cascaded chaotic system and the MP-WFRFT transform, the input signal is triple-encrypted to generate an encrypted signal and complete hybrid carrier modulation;

[0073] Step S103: The receiving end receives the mixed carrier signal and performs an MP-WFRFT inverse transform on the mixed carrier signal;

[0074] Step S104: Based on the parameters of the multi-cascaded chaotic system, combined with the MP-WFRFT transform parameters and the scaling vector, a decryption matrix is ​​generated. The encrypted signal is then decrypted using the decryption matrix, thereby completing the demodulation process.

[0075] The steps of the method described above in this example implementation will now be explained in more detail.

[0076] In step S101, since chaotic signals have the characteristics of long-period ergodicity and long-term unpredictability, they have advantages such as strong confidentiality, good randomness, large key quantity, and convenient key replacement, making them very suitable for physical layer encryption. This disclosure uses Logistic mapping and Henon-Sine mapping to build an L-2D-HSM multi-cascade chaotic system, thereby improving the structural complexity of the chaotic encryption system and increasing the key space.

[0077] Logistic mappings are currently the most widely used type of nonlinear dynamic discrete chaotic mapping system. (Refer to...) Figure 2 As shown, its mapping equations include:

[0078] cn+1 =qc n (1-c n (1)

[0079] Among them, c n Let c be the iterative value of the state variable at time n; n+1 Let c be the iteration value of the state variable at time n+1; n is the number of iterations in the sequence; q is the chaotic system parameter, and the system is in a chaotic state when q∈[3.57,4].

[0080] The Henon-Sine mapping is a two-dimensional chaotic mapping, and its mapping equations include:

[0081]

[0082] Where a and b are system control parameters; x n Let x be the iterative value of the state variable at time n; n+1 Let y be the iteration value of state variable x at time n+1; n Let y be the iterative value of the state variable y at time n; n+1 Let y be the iteration value of the state variable at time n+1; when a∈(-∞,-0.71)∪(0.71,+∞) and b=0.7, the Henon-Sine system is in a chaotic state.

[0083] The Henon-Sine mapping includes the Sine mapping and the Henon mapping, where,

[0084] The Sine mapping is a one-dimensional chaotic mapping, and its mapping equation is:

[0085] x n+1 =λsin(πx) n (3)

[0086] Where, x n Let x be the iterative value of the state variable at time n; n+1 Let x be the iterative value of the state variable at time n+1; λ is the system control parameter. When λ∈[0.87,1], the Sine system is in a chaotic state.

[0087] The Henon mapping is a two-dimensional chaotic mapping, and its mapping equations include:

[0088]

[0089] Where, x n Let x be the iterative value of the state variable at time n; n+1 Let y be the iteration value of state variable x at time n+1; n Let y be the iterative value of the state variable y at time n; n+1Let y be the iteration value of the state variable at time n+1; when a∈[1.06,1.22]∪[1.27,1.29]∪[1.31,1.42] and b=0.3, the Henon system is in a chaotic state.

[0090] Because the parameter range of Henon and Sine mappings is relatively limited and the dynamic trajectories are relatively simple, this disclosure proposes a Henon-Sine mapping, also known as the 2D-HSM mapping. Compared with many existing chaotic systems, it has better ergodicity and pseudo-randomness, a wider chaotic range for its parameters, and is more difficult to predict. To better describe the 2D-HSM mapping system, Figure 2 The diagram shows the phase diagram, bifurcation diagram, and Lyapunov index spectrum of these three types of chaotic systems. It can be seen that the 2D-HSM system is distributed across the entire phase plane, has a larger distribution area, and has a larger LE value. Therefore, it has a more complex trajectory and its output is more unpredictable.

[0091] like Figure 3 As shown, the L-2D-HSM multi-cascade chaotic system constructed in this disclosure utilizes the Logistic map as a random sequence generator to generate a one-dimensional pseudo-random chaotic sequence L, and divides this sequence L into multiple sets of initial values ​​(x) of Henon-Sine maps. i ,y i ), combined with the initial value key (a i (0.7), generate a two-dimensional pseudo-chaotic sequence h i and m i And convert it into a bit scrambling matrix H i And constellation rotation matrix M i This constitutes the cryptographic kernel space used for data encryption.

[0092] In the generation of this cryptographic kernel space, let Q be the output sequence of the original baseband signal after channel coding, with a length of N; using the SM3 algorithm, the hash value P of the sequence Q is obtained, with a length of 256 bits, which is divided into 32 groups, each containing 8 bits, denoted as P = {p1, p2, ..., p...} 32}; through calculation formula

[0093] P = SM3(Q)

[0094]

[0095] The initial value key, bifurcation parameter q, and pre-iteration number m of the multi-cascaded chaotic system are calculated, and then a is agreed upon by the two communicating users. i ; The symbol '&' represents the "exclusive OR" operation; '&' represents the "AND" operation.

[0096] Furthermore, the sequence Q is divided into blocks of length d. 2 d 2 It should be divisible by N, where N is a natural number. Transform the i-th block into a matrix T of size d×d. i The value of i is...

[0097] Using the initial value key `key`, the bifurcation parameter `q`, and the pre-iteration number `m` as input to the Logistic mapping, a chaotic sequence of length `U` is generated. Then, each pair of values ​​(x...) is... i ,y i Group them into groups and combine them with (a) i ,0.7) as input to multiple Henon-Sine mappings, the i-th Henon-Sine mapping generates two mappings of length g. 2 One-dimensional sequence m i h i Using formulas

[0098]

[0099] For h i The data is sorted, and its index value is used to replace the original value, which is then converted into a bit scrambling matrix H of size g×g. i ;

[0100] Using sequence m i Generate phase rotation factor r ik This is used to generate phase rotation in a symbolic constellation diagram, and the formula for calculating the phase rotation factor includes:

[0101]

[0102] Where k = 1, 2, 3…g 2 ;m ik Represented as generating r ik The chaotic sequence; j represents the imaginary unit; then the phase rotation matrix M i The calculation formulas include:

[0103]

[0104] Through the above operations, the block matrix T used for encryption was obtained using the L-2D-HSM system. i Bit scrambling matrix H i and phase rotation matrix M i .

[0105] In step S102, the input signal is triple-encrypted using the cryptographic kernel space of the multi-cascaded chaotic system and the MP-WFRFT transform to generate an encrypted signal and complete hybrid carrier modulation; specifically, the following steps are included:

[0106] Step S1021: Use the bit scrambling matrix to perform the first round of bit scrambling encryption on the input bit data to obtain the encrypted modulation symbol data;

[0107] Step S1022: Perform a second round of constellation rotation encryption on the modulation symbol data using a constellation rotation matrix;

[0108] Step S1023: Then use MP-WFRFT to perform a third round of encryption to obtain the final encrypted signal and complete the hybrid carrier modulation.

[0109] Specifically, refer to Figure 5 and Figure 6 As shown, the first round of bit scrambling encryption includes: setting d=32 and g=4 in the experiment, and using H... i Matrix pair T i The matrix is ​​scrambled by first translating rows and then columns, with each scrambled object T. ij Size is g × g, H i The step size l is 1, and T is finally obtained. i The scrambling result is Y i .

[0110] Specifically, refer to Figure 7 and Figure 8 As shown, B i For Y i The complex signal obtained after QPSK mapping, B i The size is The second round of constellation rotation encryption process includes:

[0111] The symbol matrix B to be encrypted ij Flattened by rows, it becomes a one-dimensional vector u;

[0112] Vector u multiplied by diagonal rotation matrix M i Perform constellation rotation, and then transform the resulting one-dimensional vector u' into a B of size g×g. ij ′, B ij ′ refers to B ij The encrypted symbol matrix covers matrix B. i B in ij Its calculation formula includes:

[0113]

[0114] Following the principle of row-first, column-later, the shift constellation is encrypted using a step size l=1.

[0115] Reference Figure 4 As shown, Figure 4 The system block diagram of the MP-WFRFT communication method based on multi-level chaotic encryption is shown. Based on the MP-WFRFT system, this disclosure adds a bit scrambling module and a constellation rotation module to its data transmitter. Through MP-WFRFT and L-2D-HSM multi-level chaotic encryption, the original bit stream is scrambled, and the constellation diagram of the signal is confused and disturbed, thereby achieving encryption of the transmitted information. Furthermore, to achieve the "one-time pad" effect, this disclosure uses the SM3 algorithm to solve the hash value of the original bit stream and uses formula (5) to calculate and determine the various parameters required by the chaotic system. Combined with the MP-WFRFT transformation parameter α and the scale vector [MV, NV], the security of the communication data is ensured. The working principle of the MP-WFRFT communication method based on multi-level chaotic encryption in this disclosure is as follows:

[0116] The input signal undergoes bit scrambling, QPSK mapping, constellation encryption, MP-WFRFT, CP addition, and digital-to-analog conversion before up-conversion and transmission via satellite wireless channel. The receiving process involves down-conversion, CP removal, analog-to-digital conversion, inverse MP-WFRFT, constellation decryption, QPSK demodulation, and bit inverse scrambling.

[0117] In step S103, the receiving end receives the mixed carrier signal and performs an inverse WFRFT transform on the mixed carrier signal;

[0118] In step S104, a decryption matrix is ​​generated based on the parameters of the multi-cascaded chaotic system, combined with the MP-WFRFT transform parameters and the scaling vector. The decryption matrix is ​​then used to decrypt the encrypted signal, thereby completing the demodulation process.

[0119] Specifically, refer to Figure 4 and Figure 8 As shown, in steps S103 and S104, Figure 8 The original and encrypted constellation diagrams are shown. When the data volume is large enough, the encrypted constellation diagram forms a circular distribution, causing phase ambiguity of the symbols, thereby achieving secure data transmission. This method is applicable to both PSK digital modulation and QAM digital modulation.

[0120] Assuming the channel model is an additive white Gaussian noise channel, and H[·] and M[·] represent the scrambling and rotation operations performed on the signal, the signal received by the receiver can be expressed as:

[0121]

[0122] Where n(t) represents additive white Gaussian noise; m k n k The scale vector of MP-WFRFT is represented by the correct initial key, bifurcation parameters, and number of iterations. The legitimate receiver uses the correct initial key, bifurcation parameters, and number of iterations to obtain the H[·] and M[·] encryption matrices generated by the L-2D-HSM chaotic system, and can correctly perform the inverse operation to recover the modulated signal. However, the eavesdropper does not know the parameters of the L-2D-HSM chaotic system and MP-WFRFT, and cannot correctly recover the modulated signal. Therefore, this method can achieve secure transmission of the signal.

[0123] It should also be noted that in the MP-WFRFT disclosed in this publication, let x0(n) be any complex sequence, and perform 1 to 3 DFTs on it respectively, the result is {x1(n),x2(n),x3(n)}, where the DFT adopts a normalized form, as shown in the formula.

[0124]

[0125] As shown, the 4-WFRFT of the sequence x0(n) is defined as a linear weighted sum of four state functions {x0(n), x1(n), x2(n), x3(n)}, as shown in the following formula:

[0126]

[0127] Where the weighting coefficient ω p (α,m k ,n k ) is defined as:

[0128]

[0129] Parameter {m k n k The values ​​of k (k = 0, 1, 2, 3) constitute the scaling vector [MV, NV] of the MP-WFRFT transform, with values ​​being arbitrary floating-point numbers. The period of parameter α is 4, and its value range is typically chosen to be [-2, 2]. The weighting coefficients ω are affected by adjusting the transform order α and the value of the scaling vector [MV, NV]. p (α,m k ,n k Because the rotation angles corresponding to each weighting coefficient are different, a relative rotation occurs between the constellation points, causing the overall signal constellation diagram to rotate and split. As ω... p (α,m k ,n kAs the number of constellation points increases, the boundaries between them become increasingly blurred, eventually leading to indistinguishable overlapping constellations that exhibit a Gaussian-like distribution on the complex plane. The modulation and demodulation principle of WFRFT is proven by its additivity, which is expressed as:

[0130] F α [F β [x0(n)]]=F α+β [x0(n)] (14)

[0131] When α = -β, the result obtained after performing two WFRFTs is x0(n), therefore the expression for the demodulated signal x0(n) is defined as:

[0132]

[0133] Where {S0(n),S1(n),S2(n),S3(n)} are the 0th to 3rd DFT transformations of S0(n).

[0134] The present disclosure presents the above communication method through the following simulation experiments to demonstrate the encryption effect of the scheme:

[0135] The simulation parameters are set as shown in Table 1:

[0136] Table 1 Simulation Parameters

[0137]

[0138]

[0139] Experiment 1: Time-domain waveform analysis of signals before and after encryption using the disclosed scheme

[0140] like Figure 9 As shown, the experiment demonstrates the time-domain signal waveforms output under two conditions: using the communication method disclosed herein and not using it. The results show that the real and imaginary envelopes of the signal waveform exhibit random differences, indicating that the scheme produces a random encryption effect on the transmitted data.

[0141] Experiment 2: Key Sensitivity and Spatial Analysis

[0142] A good encryption scheme should be sensitive to the key and have a sufficiently large key space that cannot be attacked by brute force. Chaotic sequences are highly sensitive to small changes in their initial values. Figure 10 The Logistic mapping and Henon-Sine mapping are shown for initial values ​​of 10. -15 The distribution of the sequence under small changes clearly shows that both mappings have good sensitivity to initial values.

[0143] Key space is a crucial factor in system security. For a good cryptosystem, the key space should be as large as possible. In a Logistic chaotic system, the initial value key, bifurcation parameter q, pre-iteration number m, and the MP-WFRFT transformation parameters α and scaling vector [MV, NV] can all be used as the key. On a 64-bit computer, the floating-point precision can reach 10^60. -16 Therefore, the key space of the encryption algorithm proposed in this disclosure can be calculated to be approximately 10. 16 ×10 16 ×10 16 ×(10 16 ) 8 ×(10 16N ) = 10 1N6+17 , where N is the number of plaintext blocks, which already meets the security level of the key space.

[0144] Experiment 3: Bit Error Rate Curve Analysis

[0145] Figure 11 This section presents the bit error rate (BER) performance curves for demodulating the received signal by a legitimate receiver and an illegitimate receiver in an AWNG channel. The curves indicate that, due to the sensitivity of the Logistic mapping to the initial value, when the initial value key has an error Δ of 10... -1 10 -5 10 -10 10 -15 At that time, the system bit error rate was always close to 50%, and the communication security was guaranteed. Moreover, when the key was correct, the bit error rate curve of the encrypted QPSK signal was basically consistent with the bit error rate curve of the theoretical QPSK signal. This shows that the encryption algorithm disclosed in this paper does not affect the performance of QPSK communication.

[0146] Figure 12 The bit error rate performance curves for the receiver demodulating the received signal under different values ​​of MP-WFRFT transform parameters are shown. Figure 12 Figure a shows the bit error rate curves for the transform parameter α under four different error values ​​Δ: 0.01, 0.1, 0.3, and 0.5. Figure 12 b and Figure 12 c shows the bit error rate curves for four different cases where the error Δ of the scaling vector [MV,NV] is 1, 3, 5, and 7.

[0147] Figure 12 The bit error rate curve results show that, provided the shift constellation encryption key is correct, MP-WFRFT has good sensitivity to the scale vector key, but the transform parameter α is vulnerable to scanning attacks. Therefore, combining shift constellation encryption with MP-WFRFT can significantly improve the security performance of the communication system.

[0148] Regarding the system in the above embodiments, the specific manner in which each unit performs operations has been described in detail in the embodiments related to the method, and will not be elaborated here.

[0149] It should be noted that although several units of the system for executing actions have been mentioned in the detailed description above, this division is not mandatory. In fact, according to embodiments of this disclosure, the features and functions of two or more units described above can be embodied in one unit. Conversely, the features and functions of one unit described above can be further divided and embodied by multiple units. Some or all of the units can be selected to achieve the purpose of this disclosure according to actual needs. Those skilled in the art can understand and implement this without any inventive effort.

[0150] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. An MP-WFRFT communication method based on multi-cascaded chaotic encryption, characterized in that, Includes the following steps: A multi-cascaded chaotic system model is constructed using the Logistic mapping and Henon-Sine mapping. This multi-cascaded chaotic system includes a cryptographic kernel space with a bit scrambling matrix and a constellation rotation matrix. The input signal is triple-encrypted using the cryptographic kernel space of the multi-cascaded chaotic system and the MP-WFRFT transform to generate an encrypted signal and complete hybrid carrier modulation. The receiving end receives the hybrid carrier signal and performs an MP-WFRFT inverse transform on the hybrid carrier signal; Based on the parameters of the multi-cascaded chaotic system, combined with the MP-WFRFT transform parameters and the scaling vector, a decryption matrix is ​​generated. The encrypted signal is then decrypted using the decryption matrix, thereby completing the demodulation process.

2. The communication method according to claim 1, characterized in that, The steps for constructing the multi-cascade chaotic system model are as follows: Generating one-dimensional pseudo-random chaotic sequences using Logistic mapping and the sequence Initial values ​​for dividing into multiple Henon-Sine mappings Combined with the initial value key Generate a two-dimensional pseudo-chaotic sequence and And convert it into a bit scrambling matrix. And constellation rotation matrix This constitutes the cryptographic kernel space used for data encryption.

3. The communication method according to claim 2, characterized in that, The Logistic mapping is a nonlinear dynamic discrete chaotic mapping, and its mapping equations include: （1） in, State variables c No. n The iteration value at time step; State variables c No. n The iteration value at time +1; n This represents the number of sequence iterations. For parameters of a chaotic system, when At that time, the system was in a chaotic state; The Henon-Sine mapping is a two-dimensional chaotic mapping, and its mapping equations include: （2） in, , These are system control parameters; State variables x No. n The iteration value at time step; State variables x No. n The iteration value at time +1; State variables y No. n The iteration value at time step; State variables y No. n The iteration value at time +1; when and At that time, the Henon-Sine system was in a chaotic state.

4. The communication method according to claim 3, characterized in that, The Henon-Sine mapping comprises a Sine mapping and a Henon mapping, wherein the Sine mapping is a one-dimensional chaotic mapping, and its mapping equation includes: （3） in, State variables x No. n The iteration value at time step; State variables x No. n The iteration value at time +1; For system control parameters, when At that time, the Sine system was in a chaotic state; The Henon mapping is a two-dimensional chaotic mapping, and its mapping equations include: （4） in, State variables x No. n The iteration value at time step; State variables x No. n The iteration value at time +1; State variables y No. n The iteration value at time step; State variables y No. n The iteration value at time +1; when ,and At that time, the Henon system was in a chaotic state.

5. The communication method according to claim 4, characterized in that, The generation process of the cryptographic kernel space includes: make The output sequence of the original baseband signal after channel coding has a length of [length missing]. N The sequence is obtained using the SM3 algorithm. hash value P , P The length is 256 bits, divided into 32 groups, each containing 8 bits. ; through calculation formula （5） Calculate the initial value key for a multi-cascaded chaotic system key bifurcation parameters q and the number of pre-iterations m Then it is agreed upon by both communication users. ; This represents the "XOR" operation; It represents the "AND" operation.

6. The communication method according to claim 5, characterized in that, The generation process of the cryptographic kernel space also includes: For sequence Perform block processing, with a block length of... , Should be Divisible For natural numbers, the first... Each block is converted into size matrix ,in The value is ; Using the initial value key key bifurcation parameters q and the number of pre-iterations m As input to the Logistic mapping, the generated sequence length is A chaotic sequence, where every two values Grouping into groups and combining them. As input to multiple Henon-Sine mappings, the first Each Henon-Sine mapping generates two lengths of... One-dimensional sequence , Using formulas （6） right Perform data sorting, replace the original value with its index value, and then convert it to a value of size . Bit scrambling matrix ; Using sequences Generate phase rotation factor This is used to generate phase rotation in a symbolic constellation diagram, and the formula for calculating the phase rotation factor includes: （7） in, ; Represented as generation A chaotic sequence; j The imaginary unit is represented; therefore, the phase rotation matrix... The calculation formulas include: （8）。 7. The communication method according to claim 6, characterized in that, The triple encryption process of the input signal using the cryptographic kernel space of the multi-cascaded chaotic system and the MP-WFRFT transform includes the following steps: The input bit data is encrypted using a bit scrambling matrix to obtain the encrypted modulation symbol data. The modulation symbol data is then encrypted using a second round of constellation rotation using a constellation rotation matrix. Then, MP-WFRFT is used to perform a third round of encryption to obtain the final encrypted signal, and hybrid carrier modulation is completed.

8. The communication method according to claim 7, characterized in that, The first round of bit scrambling encryption includes: setting d=32, g=4, and using... Matrix pairs The matrix is ​​scrambled by first translating rows and then columns. The objects scrambled each time... Size is , Movement step size The value is 1, and the final result is... The result of the scrambling is .

9. The communication method according to claim 8, characterized in that, The second round of constellation rotation encryption process includes: The matrix of symbols to be encrypted Flattened into a one-dimensional vector by rows ; vector Multiply by diagonal rotation matrix Perform constellation rotation, and then obtain a one-dimensional vector. Transform into Size , It means Encrypted symbol matrix, overlay matrix In Its calculation formula includes: （9） Following the principle of "row first, column second", based on the step size. =1 is used for shift constellation encryption.

10. MP based on multi-cascaded chaotic encryption The WFRFT communication system is characterized by, This includes generating one-dimensional pseudo-random chaotic sequences using Logistic mapping. and the sequence Initial values ​​for dividing into multiple Henon-Sine mappings Combined with the initial value key Generate a two-dimensional pseudo-chaotic sequence and And convert it into a bit scrambling matrix. And constellation rotation matrix This constitutes the cryptographic kernel space used for data encryption; The MP-WFRFT transform unit is used to perform triple encryption processing on the input signal using the cryptographic kernel space of the multi-cascaded chaotic system and the MP-WFRFT transform, to generate an encrypted signal and complete hybrid carrier modulation.

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