A multi-carrier secure transmission method based on quantum random numbers

Abstract

The present invention relates to a multi-carrier secure transmission method based on quantum random numbers, which includes: at the transmitting end, using a quantum random number generator QRNG to generate original data, quantizing the original data to obtain quantization bits, and sending the quantization bits to the database at the transmitting end; processing the quantization bits through the database at the transmitting end to generate a quantum random number QRN; selecting the quantum random number QRN in the database at the transmitting end to perform UFMC modulation and encryption on the signal to be transmitted, obtaining an encrypted UFMC signal; transmitting the encrypted UFMC signal and the quantization bits to the receiving end through an optical network; at the receiving end, sending the received quantization bits into the database at the receiving end and processing them to generate the same quantum random number QRN as that of the database at the receiving end, and extracting the corresponding quantum random number QRN to demodulate the encrypted UFMC signal. The present invention can achieve multi-carrier secure transmission based on quantum random numbers.

Description

Technical Field

[0001] The present invention relates to the technical field of signal transmission, and in particular to a multi-carrier secure transmission method based on quantum random numbers. Background Art

[0002] A passive optical network (PON) uses passive devices such as optical fibers and splitters to replace active devices, distributes high-speed optical signals in the backbone network to end users, thereby improving the distribution efficiency and reducing energy consumption. PON has the advantages of flexible bandwidth, high spectral efficiency, low crosstalk, and low cost. The performance of the universal filter multi-carrier (UFMC) technology has been proven to be superior to the orthogonal frequency division multiplexed (OFDM) technology. The frequency band of UFMC is divided into several sub-bands, and each sub-band is filtered separately. Therefore, UFMC can provide lower out-of-band leakage, higher spectral efficiency, and greater time-offset robustness. UFMC-PON has the advantages of high bandwidth, low energy consumption, high anti-interference ability, and strong flexibility.

[0003] In addition, due to the broadcast nature of PON, there are usually inherent security vulnerabilities. The security of the network mainly depends on encryption protocols at the application layer, such as the data encryption standard protocol, the advanced encryption standard protocol, etc. However, it is difficult to prevent physical-layer attacks and theft. With the development of quantum computing and decoding technologies, information will be leaked. Therefore, physical-layer encryption is essential to fundamentally prevent eavesdropping and enhance system security. As an effective physical-layer encryption method, chaotic encryption has the advantages of confidentiality, randomness, and a large key space. Chaotic encryption schemes generally use digital chaotic algorithms to generate pseudo-random sequences, which are used to simulate the distribution statistics of random numbers and are used to encrypt constellations, sub-carriers, symbols, etc. of multi-carrier signals. The pseudo-random sequence is sensitive to the input parameters of the chaotic algorithm and has the periodicity of a long time series. With the help of powerful computing capabilities, the sequence can be predicted. Therefore, for digital security, a sequence with true randomness is required.

[0004] Quantum random numbers (QRN) based on quantum noise have true uncertainty and unpredictability. Due to the characteristics of quantum noise, a quantum random number generator (QRNG) can provide a random sequence with higher security and randomness than traditional random number generators. Various physics have been used to generate QRN. Currently, most research on QRN focuses on generation methods, and the random number generation rate of reported offline QRNGs has reached Tb / s. A few studies have begun to discuss how to transmit QRN, and the transmission rate is usually at the Gb / s level.

[0005] Therefore, the prior art has the following problems: the randomness and security problems of pseudo-random numbers, the problems in the secure transmission of signals, and the problem that the quantum random number transmission rate in the current simultaneous transmission of signal and encryption experiment is too low, far lower than the signal transmission rate. Summary of the Invention

[0006] For this reason, the technical problem to be solved by the present invention is to overcome the problem of potential security hazards in multi-carrier transmission in the prior art.

[0007] To solve the above technical problems, the present invention provides a multi-carrier secure transmission method based on quantum random numbers, including:

[0008] Step S1: At the sending end, use a quantum random number generator QRNG based on broadband light source ASE to generate original data, quantize the original data to obtain quantization bits, and send the quantization bits to the database at the transmitting end;

[0009] Step S2: Further process the quantization bits through the database at the transmitting end to generate a quantum random number QRN;

[0010] Step S3: Randomly select quantum random numbers QRN that have not been used for encryption in the database at the transmitting end, and encrypt the signal to be sent during the UFMC modulation process with the unused quantum random numbers QRN for encryption to obtain an encrypted UFMC signal;

[0011] Step S4: Transmit the encrypted UFMC signal and the quantization bits to the receiving end through an optical network;

[0012] Step S5: At the receiving end, send the received quantization bits into the database at the receiving end and further process them to generate the same quantum random number QRN as the database at the receiving end, and extract the corresponding quantum random number QRN to demodulate the received encrypted UFMC signal.

[0013] In an embodiment of the present invention, in step S2, further process the quantization bits through the database at the transmitting end to generate a quantum random number QRN. The method includes:

[0014] For the quantization bits, put the data stream of every n bits into the database at the transmitting end, calculate its SHA-512 value through the hash algorithm SHA-512 to obtain a hexadecimal string, and assign values to the hexadecimal string: assign 0 to values from 0 to 7, and assign 1 to other values to generate a quantum random number QRN.

[0015] In an embodiment of the present invention, in step S3, a quantum random number QRN not used for encryption is randomly selected from the database at the transmitting end, and the signal to be transmitted is encrypted by the quantum random number QRN not used for encryption during the UFMC modulation process. The method includes:

[0016] Implement encryption of the signal to be transmitted during the UFMC modulation process in the constellation, subcarrier, subband, and symbol dimensions through the quantum random number QRN not used for encryption. Specifically:

[0017] Extract the quantum random number QRN not used for encryption from the database at the transmitting end and convert it into a decimal sequence y of every A bits. The range of the sequence y is from 0 to 2 A -1; then divide the sequence y into several subsequences of equal length, and the several subsequences of equal length form a matrix with respect to the sequence y;

[0018] Based on the matrix of the sequence y, set y C 、y Sc 、y Sb 、y Sym to be the matrices for encrypting the signal to be transmitted in the constellation, subcarrier, subband, and symbol dimensions respectively;

[0019] Implement encryption of the signal to be transmitted through y C 、y Sc 、y Sb 、y Sym .

[0020] In an embodiment of the present invention, the matrix y C =[y C(1) ; y C(2) ;…; y C(k) ;…; y C(K) is a QRN-based matrix for encrypting UFMC signals in the constellation dimension. Among them, y C(k) is the constellation masking sequence of the kth UFMC symbol with a length of B×m, B is the number of frequency bands, and M is the number of subcarriers in each frequency band; then the masking factor of the ith constellation point constellation phase θ i (k) of the kth UFMC symbol is expressed as:

[0021]

[0022] where i ∈ [0, B×M];

[0023] Then the masked constellation point C’ (k) , with a phase rotation θ (k) , is expressed as:

[0024] C' (k) =C(k) ·exp(jθ (k) )。

[0025] In an embodiment of the present invention, the matrix y Sc = [y1 Sc ; y2 Sc ; …, y k Sc ; …; y K Sc is a QRN-based matrix for encrypting UFMC signals in the subcarrier dimension, where y k Sc is the subcarrier masking sequence of the k-th UFMC symbol with a length of B×m, B is the number of frequency bands, and M is the number of subcarriers in each frequency band;

[0026] Then, the subcarrier masking matrix P Sc(k) of the k-th UFMC symbol is:

[0027] P Sc(k) = Mat{sort[y Sc(k) T × reciproc[y Sc(k)}

[0028] where k ranges from 1 to K, sort[] represents the operation of sorting the row sequence; [] T is the transpose operation; reciproc[] is the operation of calculating the reciprocal of each element of the matrix; Mat{} is the operation of setting the non-1 elements in the matrix to zero.

[0029] In an embodiment of the present invention, the matrix y Sb = [y Sb(1) ; y Sb(2) ; …, y Sb(k) ; …; y Sb(K) is a QRN-based matrix for encrypting UFMC signals in the subband dimension, where y Sb(k) is the subband masking sequence with a length of B;

[0030] Then, the subband masking matrix P Sb(k) of the k-th UFMC symbol is:

[0031] P Sb(k) = Mat{sort[y Sb(k) T × reciproc[y Sb(k)}

[0032] where k ranges from 1 to K, sort[] represents the operation of sorting the row sequence; [] T ​​is the transpose operation; reciproc[] is the operation of calculating the reciprocal of each element of the matrix; Mat{} is the operation of setting the elements in the matrix that are not 1 to zero.

[0033] In an embodiment of the present invention, the matrix y Sym = [y1 Sym , y2 Sym , …, y k Sym , …, y K Sym is a QRN-based matrix for encrypting UFMC signals in the symbol dimension;

[0034] Then the symbol masking matrix P Sym is expressed as:

[0035] P Sym = Mat{sort[y Sym T ×reciproc[y Sym}

[0036] where sort[] represents the operation of sorting the row sequence; [] T is the transpose operation; reciproc[] is the operation of calculating the reciprocal of each element of the matrix; Mat{} is the operation of setting the elements in the matrix that are not 1 to zero.

[0037] In an embodiment of the present invention, the signal x' encrypted in the constellation, subcarrier, subband, and symbol dimensions is represented in the time domain as:

[0038]

[0039] where f b represents the impulse response of the filter, is convolution, and IFFT represents the inverse Fourier transform.

[0040] In an embodiment of the present invention, in step S3, a quantum random number QRN that has not been used for encryption is randomly selected from the database at the transmitting end, and the signal to be transmitted is encrypted by the quantum random number QRN that has not been used for encryption during the UFMC modulation process. The method further includes:

[0041] Extracting the quantum random number QRN that has not been used for encryption from the database at the transmitting end to implement encryption of the signal to be transmitted in the phase dimension during the UFMC modulation process, specifically:

[0042] Using the SLM algorithm to suppress the PAPR of the encrypted UFMC signal, setting the number of phase factors to b, and normalizing the phase factors to 1; thus the phase is written as ​where j is the unit imaginary number; convert every b bits of the binary QRN into a decimal number, generating a decimal number sequence ψ, whose values range from 0 to 2 b -1 and are not equal, where ψ = [ψ 1 ; ψ 2 ; ψ s ; …; ψ S , ψ s is a subsequence of ψ, and the range of s is 1 to S; the phase masking sequence Q is:

[0043]

[0044] Multiply the frequency-domain UFMC signal X encrypted in the constellation, subcarrier, subband, and symbol dimensions by the phase masking sequence Q to obtain a set of signals:

[0045]

[0046] Inverse Fourier transform all the signals X 1 , X 2 ,... X S in the group to the time domain and calculate their peak-to-average power ratio PAPR:

[0047]

[0048] Take the index s* of the signal x s* with the minimum peak-to-average power ratio PAPR corresponding to the sequence ψ s* ; Therefore, the signal x s* to be transmitted after phase encryption is:

[0049]

[0050] In an embodiment of the present invention, when implementing encryption of the signal to be sent in the constellation, subcarrier, subband, symbol, and phase through the quantum random number QRN not used for encryption, it further includes setting an index for positioning the quantum random number QRN:

[0051] Calculate the SHA-256 values of the used encryption sequence y and the sequence ψ s* respectively, and use the corresponding SHA-256 values as the indexes of the corresponding quantum random number QRN. Store the index SHA-256 values at the heads of the sequence y and the sequence ψ s* . After obtaining the encrypted UFMC signal, extract the corresponding index SHA-256 values of the sequence y and the sequence ψ s* , and transmit the corresponding index SHA-256 values together with the encrypted UFMC signal to the receiving end. At the receiving end, accurately locate the encrypted UFMC signal through the index SHA-256 values.

[0052] The above technical solution of the present invention has the following advantages compared with the prior art:

[0053] The present invention processes the quantum random number QRN into a truly meaningful quantum random number, which is used for signal encryption and decryption, completing the processing and transmission of quantum random numbers. Compared with pseudo-random numbers, the autocorrelation of the processed quantum random number is reduced by 98.2%, having higher randomness and confidentiality;

[0054] The encryption algorithm based on quantum random numbers of the present invention effectively shields the five-dimensional features of the UFMC signal: constellation, symbol, subcarrier, subband, and phase. This encryption scheme has been proven to resist brute force cracking;

[0055] The phase dimension of the signal of the present invention is encrypted using the SLM algorithm based on quantum random numbers, while reducing the signal PAPR and improving the signal performance, enhancing the confidentiality of the signal; since the phase sequence is provided by the database, there is no need to transmit the phase sequence, thus reducing the redundancy in the transmission process. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the drawings.

[0057] Figure 1 is the flowchart of the method of the present invention;

[0058] Figure 2 is the schematic diagram of the principle of the multi-carrier secure transmission method based on quantum random numbers in the embodiment of the present invention;

[0059] Figure 3 is the schematic diagram of the autocorrelation function of the pseudo-random number generated by the Lorenz model in the embodiment of the present invention;

[0060] Figure 4 is the schematic diagram of the autocorrelation function of the quantum random number in the embodiment of the present invention;

[0061] Figure 5 is the process diagram of processing the quantum random number QRN based on SHA-512 in the embodiment of the present invention;

[0062] Figure 6 is the schematic diagram of the NIST test result in the embodiment of the present invention;

[0063] Figure 7 is the schematic diagram of the UFMC modulation principle in the embodiment of the present invention;

[0064] Figure 8 is the block diagram of the five-dimensional UFMC encryption principle based on the quantum random number QRN in the embodiment of the present invention;

[0065] Figure 9 It is a schematic diagram of the data structure of sequence y and sequence ψ in the database in the embodiment of the present invention;

[0066] Figure 10 It is a schematic diagram of the principle of the SLM algorithm based on the quantum random number QRN in the embodiment of the present invention;

[0067] Figure 11 It is a schematic diagram of the experimental device of the multi - carrier secure transmission method based on the quantum random number QRN in the embodiment of the present invention;

[0068] Figure 12 It is a curve graph of the bit error rate (BER) of key reception in the embodiment of the present invention;

[0069] Figure 13 It is a CCDF curve graph under different numbers of phase sequences in the embodiment of the present invention;

[0070] Figure 14 It is a curve graph of the fitting bit error rate of the UFMC signal with or without using SLM in the BTB, 7 - core optical fiber and illegal channel in the embodiment of the present invention;

[0071] Figure 15 It is a distribution graph of the bit error rate under different time synchronizations in the embodiment of the present invention. Detailed implementation manners

[0072] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited are not intended to limit the present invention.

[0073] Embodiment 1

[0074] Referring to Figure 1 as shown, the present invention relates to a multi - carrier secure transmission method based on quantum random numbers, including:

[0075] Step S1: At the sending end, use a quantum random number generator QRNG based on a broadband light source ASE to generate original data, quantize the original data to obtain quantization bits, and send the quantization bits to the database at the transmitting end;

[0076] Step S2: Further process the quantization bits through the database at the transmitting end to generate a quantum random number QRN;

[0077] Step S3: Randomly select quantum random numbers QRN that have not been used for encryption in the database at the transmitting end, and encrypt the signal to be sent during the UFMC modulation process through the unused quantum random numbers QRN for encryption to obtain an encrypted UFMC signal;

[0078] Step S4: Transmit the encrypted UFMC signal and the quantization bits to the receiving end through the optical network;

[0079] Step S5: At the receiving end, send the received quantization bits into the database of the receiving end and further process them to generate the same quantum random number QRN as that of the database of the receiving end, and extract the corresponding quantum random number QRN to demodulate the received encrypted UFMC signal.

[0080] The following is a detailed introduction to this embodiment:

[0081] Figure 2 The schematic diagram of the proposed multi-carrier secure transmission scheme based on quantum random numbers is given. At the sending end, the original data is generated by the ASE-based QRNG, and after quantization, the quantization bits (a binary sequence composed of 0 and 1) are obtained and sent to the database of the receiving end and the optical network at the same time. Specifically, the database of the receiving end further processes the quantization bits to become a quantum random number QRN with high randomness, and the quantum random number QRN is used to encrypt the signal to be transmitted; another string of quantization bits is sent to the seven-core optical fiber (i.e., the optical network) together with the encrypted UFMC signal through the space division multiplexing technology. A string of QRN not used for encryption randomly selected by the database at the transmitting end encrypts 5 dimensions of the 64-QAM UFMC signal.

[0082] The present invention uses the traditional high-speed optical fiber channel to transmit a large number of QRNs, and transmits the processing driving key n (equivalent to every n bits in the following SHA-512 processing to ensure the timing of the bits) and the synchronization information through the low-speed quantum channel by the BB84 protocol. The synchronization information helps the receiver successfully locate the starting position of the quantization bits, and the driving key n is the key to processing the bits. Even if the quantization bits in the optical fiber channel are illegally stolen, without the driving key n and the synchronization information, the transmitted signal cannot be correctly demodulated. In short, the database at the receiving end performs SHA-512 processing according to the driving key n and the synchronization information to ensure the generation of the same QRN as that of the database at the transmitting end.

[0083] The receiving end respectively obtains the quantization bits and the encrypted signal. Through the analog-to-digital conversion module, the quantized bits are sent into the database of the receiving end and processed in the same way as the database of the transmitting end to obtain the same QRN. The encrypted signal enters the UFMC demodulation module, and the corresponding QRN sequence at the receiving end is extracted to decrypt the encrypted UFMC signal.

[0084] (1) Quantum random number processing method

[0085] The Lorenz chaotic model is a classic chaotic model, which consists of three coupled non-linear differential equations, and each differential equation can generate a pseudo-random number sequence. Since the pseudo-random numbers are generated based on an algorithm, for the same seed, the generated sequences will be exactly the same. As Figure 3 shown ((a) original data; (b) fractional part of the original data), the generated pseudo-random numbers exhibit a high degree of autocorrelation. Figure 3 (a) shows that the autocorrelation coefficient of the original pseudo-random numbers is 0.8, while in Figure 3 (b), only the decimal part is retained, so the autocorrelation coefficient is slightly lower, at 0.6. Therefore, the randomness and confidentiality of such pseudo-random numbers cannot be compared with the properties of true random numbers.

[0086] Although Figure 2 the quantum random number generator QRNG based on ASE of broadband light sources mentioned in Figure 4 (a) usually exhibits implicit correlation. The highest autocorrelation of the original data is only 0.2, far lower than that of the pseudo-random numbers. Then, quantization is performed according to the mean value of the original data to obtain quantization bits, and its autocorrelation is as shown in Figure 4 (b). Compared with the original data, the autocorrelation coefficient of the quantization bits drops to 0.1, but there is still a certain degree of correlation. Therefore, it is necessary to further process the quantization bits to eliminate the implicit correlation. Figure 4 (c) is the autocorrelation of the processed quantum random number QRN. Compared with the original data and the quantization bits, the autocorrelation of QRN almost drops to zero. Compared with the pseudo-random numbers, its autocorrelation is reduced by 98.2%. The extremely low autocorrelation of QRN allows for higher randomness and confidentiality.

[0087] As mentioned above, the quantization bit stream is sent to the database and the optical network simultaneously. The quantization bit stream put into the database is further processed to enhance randomness and becomes the true quantum random number QRN; the other quantization bit stream is sent to the optical network together with the signal. That is, the two databases at the sending end and the receiving end receive the same quantization bits. The database at the receiving end can obtain the same QRN based on the driving key n and the synchronization information and using the same processing method as the database at the sending end.

[0088] In this embodiment, every n bits (equivalent to the driving key n) of the data stream are put into the database and processed by the secure hash algorithm SHA-512 to eliminate the implicit correlation and enhance randomness. Take out n bits from the data and calculate its SHA-512 value to obtain a hexadecimal string, as shown by the light gray line in Figure 5 . Then assign values to the hexadecimal string: assign 0 for values from 0 to 7, and assign 1 for others. After processing, it becomes the true quantum random number QRN, as shown by the dark gray line in Figure 5 , and its autocorrelation is asFigure 4 (c) as shown. This indicates that the processing method has eliminated the hidden correlation. The randomness of QRN passes the NIST randomness test, which is a series of tests developed by the National Institute of Standards and Technology (NIST) of the United States to evaluate and verify the quality and randomness of random number generators. Figure 6 For the NIST randomness test results of QRN, where the p - value represents the likelihood of the observed data in a hypothesis test. Generally speaking, the closer the p - value is to 1, the stronger the randomness and statistical properties of the sequence. The significance level is usually set to 0.01, that is, if the p - value is less than the given significance level, the null hypothesis is rejected, and it is considered that the sequence does not have the expected randomness.

[0089] In the encryption algorithm proposed in this embodiment, what really needs to be kept secret are the driving key n and synchronization information of the quantization bits transmitted in the optical fiber. These data will notify the receiver in the quantum channel and periodically change the driving key n and synchronization information. Then QRN is divided into the required length and stored in the database together with the corresponding SHA - 256 value. The SHA - 256 value serves as an index for QRN, pointing to the position of the correct QRN sequence in the database, and reducing the computational complexity of finding the sequence. The database will randomly select a QRN string not used for encryption to encrypt the 64 - QAM UFMC signal data, and the index SHA - 256 value is transmitted together with the encrypted UFMC signal.

[0090] In addition, due to the sensitivity of the SHA - 512 algorithm to the input, in order to correctly demodulate, the bit error rate (BER) of the quantization bits transmitted in the channel should be as low as possible. Under the same received power, the bit error rate increases with the increase of the modulation order. Therefore, through on - off keying (OOK) modulation, the quantization bit stream sent into the optical network is modulated to improve the transmission performance.

[0091] According to the driving key n and synchronization information sent in the quantum channel, the receiving end can use the same processing method as the sending end to regain the QRN and the index SHA - 256 value. In the case where there is a SHA - 256 index value in the signal, the encrypted UFMC signal can be restored through the corresponding QRN. So far, the reception and transmission of QRN are completed.

[0092] (2) UFMC modulation principle

[0093] UFMC has the advantages of flexible spectrum, anti - interference, low latency, strong compatibility, etc., and is superior to traditional single - carrier modulation. Figure 7This is the block diagram of UFMC modulation (FFT represents Fourier Transform, and IFFT represents Inverse Fourier Transform). Suppose there are B subbands (i.e., frequency bands), and each subband has M subcarriers. Then the information symbols are allocated to the subbands C = [C1; C2;...; C b ;...; C B , where C b contains M complex Quadrature Amplitude Modulation (QAM) symbols on the b-th subband (b ∈ [1, 2,..., B]).

[0094] In the present invention, a time-domain Finite Impulse Response (FIR) Dolph-Chebyshev filter is utilized. Therefore, first, the subband symbols C b are transformed into a time-domain signal c b through an N-point IFFT (N ≥ B × M), and the impulse response of the FIR filter is f b = [f b (1), f b (2),..., f b (L)], where L is the length of the filter. In addition, the coefficients of the subband filter are normalized to Adding all the filtered subband signals, the k-th UFMC symbol x (k) transmitted in the time domain can be expressed as:

[0095]

[0096] In the formula, b is the subband index, k is the UFMC symbol index (k ∈ [1, 2,..., K]), is convolution. When the number of UFMC symbols is K, the transmitted signal x is:

[0097] x = {x (1) , x (2) , …, x (K)}

[0098] (3) UFMC Encryption Principle

[0099] Figure 8Shows the five-dimensional UFMC encryption scheme proposed based on QRN. Extract the unused QRN in the database to generate the corresponding matrix, and encrypt the UFMC signal in five dimensions: constellation, subcarrier, subband (frequency band), symbol, and phase. After the signal to be transmitted undergoes serial-to-parallel conversion, the bit stream is subjected to 64-QAM constellation mapping. Based on the QRN, a phase perturbation sequence is generated, and the constellation dimension is encrypted by rotating the constellation phase. Then, the constellation signal is subjected to UFMC modulation, where the dimensions of subcarrier, frequency band, and symbol are masked with the permutation matrix generated by QRN. Next, the phase of the UFMC signal is encrypted using the QRN-based Selective Mapping (SLM) algorithm to enhance security while suppressing the Peak-to-average Power Ratio (PAPR) of the multi-carrier signal. Finally, the index SHA-256 of the QRN sequence corresponding to the encrypted UFMC is placed at the end of the encrypted signal. The receiver finds the corresponding QRN in the database according to the index SHA-256 value to recover the signal.

[0100] At the transmitter, any unused QRN sequence extracted from the database is converted into a permutation matrix for encryption in five dimensions. Then, the index SHA-256 value of the QRN sequence is modulated and appended to the encrypted signal as the transmitted signal.

[0101] At the receiver, the received signal is divided into two parts. First, the index SHA-256 value is extracted, which points to the required QRN sequence in the database. This sequence is the same as the sequence at the transmitter to generate the corresponding decoding matrix. The remaining encrypted signal will be decoded by the decoding matrix.

[0102] Next, the generation of the permutation matrix using QRN will be explained in detail. First, convert the binary QRN into a decimal sequence y of every A bits, ranging from 0 to 2 A -1. Then, according to the symbol length of UFMC, the sequence y is divided into the required length (taking Figure 9 as an example, the required length is the length of each subsequence after dividing the sequence y). Figure 9 is the matrix structure in the database regarding the sequence y. Based on the matrix of the sequence y, set y C 、y Sc 、y Sb 、y SymQRN matrices for encrypting UFMC signals in the constellation, subcarrier, frequency band, and symbol dimensions respectively. It is worth mentioning that in this embodiment, the SHA-256 value of sequence y (specifically, the SHA-256 value of each subsequence after dividing sequence y) is also calculated, and the corresponding SHA-256 value is used as the index of the corresponding quantum random number QRN. The indexed SHA-256 value is stored at the head of sequence y. After obtaining the encrypted UFMC signal, the indexed SHA-256 value corresponding to sequence y is extracted, and the corresponding indexed SHA-256 value and the encrypted UFMC signal are transmitted to the receiving end, where the encrypted UFMC signal is accurately located through the indexed SHA-256 value.

[0103] Matrix y C =[y C(1) ; y C(2) ; …; y C(k) ; …; y C(K) is a QRN-based matrix for encrypting UFMC signals in the constellation dimension, where y C(k) is the constellation masking sequence of the k-th UFMC symbol with a length of B×m, B is the number of frequency bands, and M is the number of subcarriers in each frequency band. The masking factor of the i-th constellation point constellation phase θ i (k) is expressed as:

[0104]

[0105] where i ∈ [0, B×M]. Then the masked constellation point C’ (k) , phase rotation θ (k) , can be expressed as:

[0106] C' (k) = C (k) ·exp(jθ (k) )

[0107] Matrix y Sc =[y1 Sc ; y2 Sc ; …, y k Sc ; …; y K Sc is a QRN-based matrix for encrypting UFMC signals in the subcarrier dimension, where y k Sc is the subcarrier masking sequence of the k-th UFMC symbol with a length of B×m. The subcarrier masking matrix P Sc(k) of the k-th UFMC symbol is:

[0108] P Sc(k) = Mat{sort[ySc(k) T ×reciproc[y Sc(k)}

[0109] where the value range of k is from 1 to K, and sort[] represents the operation of sorting the row sequence. T is the transpose operation, and reciproc[] is the operation of calculating the reciprocal of each element of the matrix. Mat{} is the operation of setting the elements in the matrix that are not 1 to zero. Then, a permutation matrix for subcarrier encryption is obtained.

[0110] Similarly, the frequency band masking matrix P Sb(k) is:

[0111] P Sb(k) = Mat{sort[y Sb(k) T ×reciproc[y Sb(k)}

[0112] In the formula, the value range of k is from 1 to K, and y Sb(k) represents a frequency band masking sequence with a length of B. The matrix y Sb = [y Sb(1) ; y Sb (2) ; …, y Sb(k) ; …; y Sb(K) is a QRN-based matrix for encrypting the UFMC signal in the subband dimension. The sequence y Sym = [y1 Sym , y2 Sym , …, y k Sym , …, y K Sym is a QRN-based sequence for encrypting the UFMC signal in the symbol dimension. The symbol masking matrix P Sym can be expressed as:

[0113] P Sym = Mat{sort[y Sym T ×reciproc[y Sym}.

[0114] Therefore, in the time domain, the UFMC signal x' encrypted in the constellation, subcarrier, subband, and symbol dimensions can be expressed as:

[0115]

[0116] where f b represents the impulse response of the FIR filter, ​​​is convolution, and IFFT represents the inverse Fourier transform.

[0117] The above equation involves the permutation matrix of the encrypted UFMC signal in four dimensions. The decoding matrix at the receiving end is the transpose of the corresponding matrix.

[0118] The encryption principle of the phase dimension is as Figure 10 shown, where the SLM algorithm is used to suppress the PAPR of the encrypted UFMC signal. The number of phase factors is set to b, and the phase factors are normalized to 1. Therefore, the phase is written as where j is the unit imaginary number. Convert every b bits of the binary QRN into a decimal number, and the generated decimal number sequence is ψ, whose value ranges from 0 to 2 b -1 is not equal, where ψ = [ψ 1 ; ψ 2 ; ψ s ; …; ψ S , ψ s is a subsequence of ψ (equivalent to obtaining ψ s ) by equally length intercepting ψ, and the range of s is 1~S. In this embodiment, calculate the index SHA-256 value of each subsequence ψ s , and place the index SHA-256 value of ψ s at the front of the corresponding subsequence, as Figure 9 shown. The phase masking sequence Q is:

[0119]

[0120] Next, multiply the frequency-domain encrypted UFMC signal X encrypted in the constellation, subcarrier, sub-band, and symbol dimensions by the phase masking sequence Q to obtain a set of signals:

[0121]

[0122] Then, inverse Fourier transform all the signals X 1 , X 2 ,... X S in the group to the time domain, and calculate its peak-to-average power ratio PAPR:

[0123]

[0124] Take the index s* of the signal x s* with the minimum PAPR corresponding to the sequence ψ s* . Therefore, the signal x s* to be transmitted after phase encryption is:

[0125]

[0126] This embodiment also calculates the sequence ψ s*The SHA-256 value is used as an index and placed at the head.

[0127] Finally, the UFMC encryption sequences y and ψ are extracted separately s* The index SHA-256 value is placed at the tail of the encrypted signal x s* and transmitted to the receiving end along with the signal, as Figure 8 shown.

[0128] At the receiving end, first the index SHA-256 value is demodulated and then compared with the SHA-256 values of the sequences y and ψ in the database. Then the corresponding QRN sequence is extracted and the decoding matrix is calculated to decrypt the signal.

[0129] Figure 11 The experimental setup diagram of the multi-carrier secure transmission scheme based on quantum random numbers is given. The detailed structures of the Digital Signal Processing (DSP) encryption module and the DSP decryption module are as Figure 8 shown. At the sending end, the encrypted UFMC signal is generated by the DSP encryption module. The number of UFMC subbands, the number of subcarriers per subband, and the number of symbols are set to 8, 16, and 64 respectively, and the total number of subcarriers is 512. The sampling rate of the Arbitrary Waveform Generator (AWG) is 12.5 GSa / s and is used for the digital-to-analog conversion of the encrypted UFMC signal. A continuous wave laser with a wavelength of 1550 nm and a power of 13 dBm is used as the optical signal source. After intensity modulation by the Mach-Zehnder Modulator (MZM), the signal is transmitted through 6 of the 7 cores in a 10-kilometer 7-core optical fiber, and the key is transmitted through the 7-core optical fiber. The raw data generated by the QRNG is processed into quantization bits and transmitted to the database and the optical fiber channel. These quantization bits are modulated by OOK and transmitted to the remaining 1 core of the 7-core optical fiber at a sampling rate of 25 GSa / s.

[0130] The legitimate receiver obtains the driving key n = 1000 and receives the synchronization information in the quantum channel. The quantization bits received through the 7-core optical fiber are formed into QRNs through the driving key n and the same QRN generation scheme. Thus, a receiving database identical to the transmitter's database is established. The receiver extracts the index SHA-256 value from the back of the encrypted signal, and the index points to the correct QRN sequence in the database. Then the encrypted signal can be decrypted using the decoding matrix generated by this QRN sequence.

[0131] The illegal receiver intercepts the encrypted signal and quantization bits in the 7-core optical fiber, but cannot access the key elements transmitted through the quantum channel: the driving key n and the synchronization information. Therefore, the illegal receiver cannot correctly demodulate the encrypted information.

[0132] The performance of this embodiment is analyzed as follows:

[0133] (1) Analysis of key transmission performance

[0134] The random numbers generated by the QRNG are modulated by the OOK signal and transmitted through one of the seven cores in the optical fiber. Figure 12 The measured bit error rate curves of the OOK signal at different received power levels are shown. The eye diagrams of the OOK signal at received powers of -20dBm, -24dBm, and -28dBm. As the received power increases, the eye diagram becomes clearer, thus improving the bit error rate performance. When the received power is -27dBm, the bit error rate of the OOK signal reaches the forward error correction (FEC) decision threshold (3.8×10 -3 ).

[0135] (2) Performance of the SLM algorithm

[0136] To evaluate the effectiveness of the SLM algorithm based on QRN in reducing the PAPR of the UFMC signal, Figure 13 the cumulative distribution function (CCDF) curves of the PAPR of the UFMC signal are given. The number of phase factors is set to 4, i.e., [+1, -1, +j, -j], and the number of phase mask sequences S are 16, 8, and 4 respectively. As the number of phase mask sequences S increases, the PAPR decreases. When S = 4, a PAPR reduction of 2.0dB can be achieved; when S = 8, a PAPR reduction of 2.4dB can be achieved; when S = 16, the PAPR of the signal is reduced by 2.6dB. Although increasing the number of phase sequences can improve the performance of the SLM algorithm, it also introduces additional computational complexity without significant performance improvement. Considering the trade-off between computation and performance, choosing S = 4 can reduce the PAPR by up to 2.0dB while reducing the computational complexity.

[0137] It is worth mentioning that the traditional SLM algorithm needs to transmit the phase sequences used. Or the signal transmission needs to transmit the phase sequences, which may lead to a loss of signal capacity. However, in the method described in the invention, the phase sequences are generated using QRN. This eliminates the need to transmit additional phase sequences in the channel.

[0138] (3) Analysis of UFMC transmission performance

[0139] Figure 14The fitted BER curves of UFMC signals with or without SLM in back-to-back (BTB), 7-core fiber and illegal channels are described.

[0140] In the case of illegal reception where the receiver lacks the correct key, the constellation diagram shows a cluster pattern even at high reception power. The BER of the signal through various channels always hovers around 0.5, indicating that the signal cannot be correctly decrypted. This observation emphasizes the excellent security performance of the encryption key.

[0141] When receiving legally, it is observed that the bit error rate increases with the decrease of the received optical power. When the SLM algorithm is used to process the UFMC signal, the bit error rate performance of the 7-core fiber is comparable to that of the BTB. When the received laser power is -19dBm, the UFMC signal with SLM reaches the FEC limit threshold. On the other hand, if the UFMC signal is used without the SLM algorithm, the bit error rate performance of the BTB is slightly better than that of the 7-core fiber. In this case, the FEC limit threshold is reached when the received laser power is -18dBm.

[0142] In the BTB transmission experiment, the SLM algorithm improved the sensitivity of the FEC limit threshold by about 0.8dB, allowing the system to reach the FEC limit threshold more efficiently. In the 7-core fiber transmission experiment, the SLM algorithm showed a greater sensitivity improvement of about 1.0dB. This demonstrates the effectiveness and potential of the SLM algorithm in optical communication systems. In addition, at the FEC threshold, the 7-core fiber showed a smaller sensitivity loss compared to the BTB. This highlights the superior transmission performance of the 7-core fiber, as it can maintain better sensitivity even under challenging conditions.

[0143] (4) Key performance analysis

[0144] For unsynchronized quantized bits, it is impossible to generate the same QRN sequence using the same drive key n. Likewise, even if correctly synchronized, the same QRN sequence cannot be generated using different drive keys n.

[0145] Assuming that the illegal receiver intercepts the quantization bit and the driving key n asynchronously, the bit error rate distribution of different timing errors is as follows: Figure 15 (a) (5 dimensions) shows that the bit error rate is about 0.5. This means that without the correct timing synchronization data, there is no correct demodulated signal. In addition, this embodiment also discusses scenarios with or without SLM, where four dimensions of the UFMC signal are masked: constellation, symbol, subcarrier, and subband. Figure 15(b) (4 dimensions) shows the bit error rate distribution for different timing synchronization errors, with its value hovering around 0.5. This observation indicates that the encryption scheme using 4 dimensions has robust security features. When only using QRN-based SLM to mask the phase dimension of the UFMC signal, Figure 15 (c) (only the signal phase dimension) depicts the bit error rate distribution in the range of 0.49 - 0.5. This shows that the QRN-based SLM algorithm not only effectively reduces the PAPR but also has strong encryption capabilities.

[0146] The driving key n and synchronization information are transmitted in the quantum channel, changing once per second. The legitimate receiver is authorized to synchronize in the quantum channel. Assume that the illegal receiver only intercepts the quantized bits in the channel within that second without being authorized for the driving key n and synchronization information. At 25×10 9 quantized bits per second, the value range of the driving key n is at least 10 3 ~10 4 , and each driving key n needs to calculate at least 2.5×10 6 SHA-512 hash values, involving at least 4×10 11 operations. Relying on brute-force cracking, the total number of operations required is 8.1×10 26 times, and a supercomputer would take 128 years to calculate (at a speed of 200 million trillion calculations per second). Importantly, these are only the bits transmitted within one second. As the number of bits increases, the requirements for cracking computing power also become higher. Therefore, the encryption algorithm is powerful enough to resist brute-force cracking by supercomputers. The results show that the encryption algorithm is robust against brute-force cracking attacks based on supercomputers, verifying its encryption effectiveness.

[0147] Although the preferred embodiments of the present application have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0148] Obviously, the above embodiments are merely examples given for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to exhaustively list all implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A multi-carrier secure transmission method based on quantum random numbers, characterized in that: Including: Step S1: At the sending end, use a quantum random number generator QRNG based on a broadband light source ASE to generate raw data, quantize the raw data to obtain quantization bits, and send the quantization bits to the database at the sending end; Step S2: Further process the quantization bits through the database at the sending end to generate a quantum random number QRN; Step S3: Randomly select a quantum random number QRN that has not been used for encryption in the database at the sending end, and encrypt the signal to be sent with the quantum random number QRN that has not been used for encryption during the UFMC modulation process to obtain an encrypted UFMC signal; In step S3, randomly select a quantum random number QRN that has not been used for encryption in the database at the sending end, and perform UFMC modulation and encryption on the signal to be sent. The method includes: Use the quantum random number QRN that has not been used for encryption to encrypt the signal to be sent in the constellation, subcarrier, subband, and symbol dimensions during the UFMC modulation process. Specifically: Extract the quantum random number QRN that has not been used for encryption from the database at the transmitting end and convert it into a decimal sequence y of every A bits. The range of the sequence y is from 0 to 2 A -1; then divide the sequence y into several subsequences of equal length, and several subsequences of equal length form a matrix with respect to the sequence y; Based on the matrix of sequence y, set y C , y Sc , y Sb , y Sym are matrices for encrypting the signal to be transmitted in the constellation, subcarrier, subband, and symbol dimensions respectively; Through y C 、y Sc 、y Sb 、y Sym Generate an encryption matrix to encrypt the signal to be sent; Step S4: Transmit the encrypted UFMC signal and the quantization bits to the receiving end through an optical network; Step S5: At the receiving end, send the received quantization bits into the database at the receiving end and further process them to generate the same quantum random number QRN as the database at the receiving end, and extract the corresponding quantum random number QRN to demodulate the received encrypted UFMC signal.

2. The multi-carrier secure transmission method based on quantum random numbers according to claim 1, characterized in that: In step S2, further process the quantization bits through the database at the sending end to generate a quantum random number QRN. The method includes: For the quantization bits, put a data stream of every n bits into the database at the sending end, calculate its SHA-512 value through the hash algorithm SHA-512 to obtain a hexadecimal string, and assign values to the hexadecimal string: assign 0 to values from 0 to 7, and assign 1 to other values to generate a quantum random number QRN.

3. The multi-carrier secure transmission method based on quantum random numbers according to claim 1, characterized in that: Matrix y C = [y C(1) ; y C(2) ; …; y C(k) ; …; y C(K) is a QRN-based matrix for encrypting UFMC signals in the constellation dimension, where y C(k) is the constellation masking sequence of the k-th UFMC symbol with length B×M, B is the number of frequency bands, and M is the number of subcarriers in each frequency band; then the masking factor of the i-th constellation point constellation phase θ i (k) is expressed as: Where, i ∈ [0, B×M]; Then the mask constellation point C’ (k) , with a phase rotation θ (k) , is expressed as: C' (k) = C (k) ·exp(jθ (k) )。 4. The multi-carrier secure transmission method based on quantum random numbers according to claim 3, characterized in that: Matrix y Sc = [y1 Sc ; y2 Sc ; …, y k Sc ; …; y K Sc is a QRN-based matrix for encrypting UFMC signals in the subcarrier dimension, where y k Sc is the subcarrier masking sequence of the k-th UFMC symbol with length B×M, B is the number of frequency bands, and M is the number of subcarriers in each frequency band; Then the sub - carrier masking matrix \(P\) of the \(k\) - th UFMC symbol Sc(k) is as follows: P Sc(k) = Mat{sort[y Sc(k) T × reciproc[y Sc(k)}​ Among them, the value range of k is from 1 to K, and sort[] represents the operation of sorting the row sequence; T is the transpose operation; reciproc[] is the operation of calculating the reciprocal of each element of the matrix; Mat{} is the operation of setting the elements in the matrix that are not 1 to zero.

5. The multi-carrier secure transmission method based on quantum random numbers according to claim 4, characterized in that: Matrix y Sb = [y Sb(1) ; y Sb(2) ; …, y Sb(k) ; …; y Sb(K) is a QRN-based matrix for encrypting UFMC signals in the sub-band dimension, where y Sb(k) is a band masking sequence of length B; Then the sub-band masking matrix P of the k-th UFMC symbol Sb(k) is as follows: P Sb(k) = Mat{sort[y Sb(k) T × reciproc[y Sb(k)}​ Among them, the value range of k is from 1 to K, and sort[] represents the operation of sorting the row sequence; T is the transpose operation; reciproc[] is the operation of calculating the reciprocal of each element of the matrix; Mat{} is the operation of setting the elements in the matrix that are not 1 to zero.

6. The multi-carrier secure transmission method based on quantum random numbers according to claim 5, wherein: Matrix y Sym = [y1 Sym , y2 Sym , …, y k Sym , …, y K Sym is a QRN-based matrix for encrypting UFMC signals in the symbol dimension; Then the symbol masking matrix P Sym is expressed as: P Sym = Mat{sort[y Sym T × reciproc[y Sym}​ Among them, sort[] represents the operation of sorting the row sequence; T transpose is the transpose operation; reciproc[] is the operation of calculating the reciprocal of each element of the matrix; Mat{} is the operation of setting the elements in the matrix that are not 1 to zero.

7. The multi-carrier secure transmission method based on quantum random numbers according to claim 6, wherein: The signal x' encrypted in the constellation, subcarrier, subband, and symbol dimensions is represented in the time domain as: where f b represents the impulse response of the filter, is convolution, and IFFT represents the inverse Fourier transform.

8. The multi-carrier secure transmission method based on quantum random numbers according to claim 1, characterized in that: In step S3, randomly select a quantum random number QRN that has not been used for encryption in the database at the sending end, and encrypt the signal to be sent with the quantum random number QRN that has not been used for encryption during the UFMC modulation process. The method further includes: Extract the quantum random number QRN that has not been used for encryption in the database at the sending end to encrypt the signal to be sent in the phase dimension during the UFMC modulation process. Specifically: Use the SLM algorithm to suppress the PAPR of the encrypted UFMC signal. Set the number of phase factors to b, and normalize the phase factors to 1. Therefore, the phase is written as where j is the unit imaginary number; convert every b bits of the binary QRN into a decimal number, and generate a decimal number sequence ψ, whose values range from 0 to 2 b -1 is not equal, where ψ = [ψ 1 ; ψ 2 ; ψ s ; …; ψ S , ψ s is a subsequence of ψ, and the range of s is 1 to S; the phase masking sequence Q is: Multiply the frequency-domain UFMC signal X encrypted in the constellation, subcarrier, subband, and symbol dimensions by a phase masking sequence Q to obtain a set of signals: All signals X within the group 1 , X 2 ,... X S are inverse Fourier transformed to the time domain, and their peak-to-average power ratio PAPR is calculated: Select the signal \(x\) with the minimum peak-to-average power ratio (PAPR). s* The index \(s^*\) corresponding to the sequence \(\psi\). s* Therefore, the signal \(x\) to be transmitted after phase encryption s* is as follows:

9. The multi-carrier secure transmission method based on quantum random numbers according to claim 8, wherein: When using the quantum random number QRN that has not been used for encryption to encrypt the signal to be sent in the constellation, subcarrier, subband, symbol, and phase, it also includes setting an index for locating the quantum random number QRN: Calculate the SHA-256 values of the used encryption sequence y and sequence ψ respectively s* and use the corresponding SHA-256 values as the indices of the corresponding quantum random numbers QRN, and store the indexed SHA-256 values in the headers of sequence y and sequence ψ. After obtaining the encrypted UFMC signal, extract sequence y and sequence ψ s* and their corresponding indexed SHA-256 values, and transmit the corresponding indexed SHA-256 values together with the encrypted UFMC signal to the receiving end. At the receiving end, accurately locate the encrypted UFMC signal through the indexed SHA-256 values. s* ​

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