Grating public key encryption method and device based on super-large-scale MIMO

Abstract

The invention provides a lattice public key encryption method and device based on super-large-scale MIMO. The method is composed of a physical layer public key encryption part and a private key decryption part. And the base station completes encryption and SVD precoding operation by combining the channel matrix and the public key. And the legal user side completes key generation and decryption operation. The legal user side generates a private key based on the orthogonal basis of the lattice; and based on the private key and the orthogonal basis, carrying out nearest plane algorithm operation on the noisy encrypted information, and finally realizing decryption. When the number of antennas of an eavesdropper is infinite and far larger than the number of legal antennas, and the distance between the eavesdropper and a legal end is smaller than one half of the wavelength, or when the eavesdropper and the legal end directly break through the channel estimation process to obtain legal channel information, the method is safe. The method can be simultaneously suitable for time division duplex and frequency division duplex channels, does not need to depend on channel reciprocity, is based on lattice cryptography, can resist currently known quantum attacks, and meets the requirement of future 6G for communication security.

Description

Technical Field

[0001] The present invention relates to information security technology and data encryption communication technology, and in particular to a very large-scale MIMO (multiple-input multiple-output) secure communication, a physical layer grid public key encryption scheme and an algorithm design. Background Art

[0002] Considering the trend of the Internet of Everything and the explosive growth of data scale in the future, the research on the sixth generation mobile communication system has begun to rise. In the future, 6G may adopt the millimeter wave frequency band (26.5GHz~300GHz) or even the higher terahertz frequency band (0.1THz~10THz), thus bringing a brand new network architecture system. Heterogeneity and full coverage are one of the visions of 6G networks, requiring various communication technologies to cooperate with each other to increase communication capacity and reduce cell interference. Among them, the multiple input multiple output (MIMO) communication technology is to equip multiple antennas at the transmitting and receiving ends. It was first proposed by Marzetta, a researcher at Bell Labs (Marzetta T L. Noncooperative Cellular Wireless with Unlimited Numbers of Base Station Antennas [J]. IEEE Transactions on Wireless Communications, 2010, 9 (11): 3590-3600). This technology can greatly enhance antenna gain. The number of antennas in large-scale MIMO can reach hundreds or even thousands, which can increase the spatial freedom of the communication system in a certain time and frequency resources. Chinese patent invention CN205104610U designs a MIMO antenna system and mobile terminal. The patent shows that when the interval between antennas is greater than half the wavelength, the channels between different MIMO antennas are independent of each other. The transmitter can use beamforming technology to adjust the amplitude and phase of the transmitted signal, so as to transmit it directionally to the receiving end, ultimately increasing the communication capacity and reducing the interference between different channels. In the future, ultra-large-scale MIMO is expected to be deployed on skyscrapers in cities, crowded shopping malls, high-speed rail stations and walls of large concerts to enhance the spatial multiplexing gain of the communication system, improve spectrum efficiency and speed up the transmission rate. In future 6G applications, the security of MIMO data link transmission is particularly important. If the communication security in the 6G era relies solely on traditional upper-layer encryption mechanisms, it will be difficult to resist eavesdropping attacks as the computing power of eavesdroppers increases. Physical layer security utilizes the randomness of the channel to establish an advantage between legitimate channels and eavesdropping channels. The literature (Ren Pinyi, Tang Xiao. A review of physical layer security technologies for 5G [J]. Journal of Beijing University of Posts and Telecommunications, 2018, 41(5): 69-77) shows that this technology can achieve perfect security in the sense of information theory.

[0003] Public key cryptography schemes need to be based on one-way trapdoor functions to achieve computational security. Traditional public key methods are based on discrete logarithm problems over finite fields, large integer factorization problems, and discrete logarithm problems over elliptic curve groups. In communication systems, if eavesdroppers can use quantum computers with the help of quantum technology, they can break traditional public key cryptography systems such as RSA (Rivest Shamir Adleman), ECC (Ellipse Curve Cryptography), and ElGamal in polynomial time algorithms. In order to protect information security in the future 6G era, it is particularly important to study post-quantum public key cryptography schemes. Currently, candidate post-quantum cryptography schemes include multivariate public key cryptography systems, encoding-based cryptography schemes, hash-based cryptography systems, and lattice cryptography. Among them, lattice cryptography can reduce the worst case to the average case, has high security and fast encryption and decryption rates, which is particularly eye-catching. Lagrange and others began to study lattice problems in the 18th century. The emergence of the LLL lattice basis reduction algorithm (Lenstra AK, Lenstra HW, Lovász L. Factoring polynomials with rational coefficients [J]. Mathematische annalen, 1982, 261 (ARTICLE): 515-534) officially opened the era of lattice public key cryptography. The LLL lattice basis reduction algorithm can be used to attack the knapsack cryptography scheme and the RSA public key cryptography system. The general method is to transform it into a difficult problem on the lattice and output the corresponding solution in polynomial time. In addition, the lattice-based one-way trapdoor function can reduce the worst case of the difficult problem in the lattice to the average case and realize the provable security of the lattice public key cryptography scheme. When designing a lattice public key cryptography scheme, the lattice-based difficult problems that can be considered include the nearest vector problem, the shortest lattice basis problem, the small integer solution problem, the shortest vector problem, and the fault-tolerant learning problem. The lattice-based public key cryptography scheme has a fast linear operation rate and cannot be broken by the currently known quantum polynomial time algorithm.

[0004] MIMO physical layer security technology is usually implemented in three ways: physical layer key generation, physical layer authentication, and physical layer precoding secure transmission. The literature (T. Kebede, Y. Wondie, J. Steinbrunn, HB Kassa and K. T. Kornegay, "Precoding and Beamforming Techniques in mmWave-Massive MIMO: Performance Assessment" in IEEE Access, vol. 10, pp. 16365-16387, 2022) divides the existing large-scale MIMO precoding technology into four categories, including linear precoding, power allocation-based precoding, nonlinear precoding, and machine learning-based precoding. Studies have shown that when the number of antennas of the eavesdropper is large enough, the security of these precoding schemes will be greatly threatened. Shen et al. used a path tracing algorithm to find the optimal precoding scheme (Sheng Z, Tuan HD, Duong TQ, et al. Beamforming Optimization for Physical Layer Security in MISO Wireless Networks [J]. IEEE Transactions on Signal Processing, 2018, 66 (14) 3710–3723). This technology can maximize security capacity, power and efficiency, but it is only applicable to multiple-input single-output communication systems. In order to solve this problem, the literature (Jiang M, Li Y, Zhang Q, et al. Robust Secure Beamforming in MIMO Wiretap Channels With Deterministically Bounded Channel Errors [J]. IEEE Transactions on Vehicular Technology, 2018, 67 (10): 9775–9784) applied a batch optimization technique to the MIMO system and theoretically derived a suboptimal precoding matrix. This method points out that even if the eavesdropping channel matrix is ​​unknown, the MIMO security capacity can be maximized.In order to further adapt to the requirements of MIMO security in the 6G era, Yang et al. combined Taylor approximation with second-order cone optimization algorithm to design MIMO precoding (Z. Yang, D. Li, N. Zhao, Z. Wu, Y. Li and D. Niyato, "Secure Precoding Optimization for NOMA-Aided Integrated Sensing and Communication," in IEEE Transactions on Communications, vol. 70, no. 12, pp. 8370-8382, Dec. 2022), thereby maximizing the total confidentiality rate of MIMO multi-users. The literature (QiX, Chen Y, Jian R, et al. Two-level-enforced security with hybrid precoding for multicast massive MIMO wiretap systems [J]. Physical Communication, 2022, 54: 101817) proposes a hybrid precoding for large-scale MIMO multicast scenarios. The analog precoding is designed based on the singular value decomposition (SVD) and semidefinite program (SDP) of the legal channel matrix. The complexity of the algorithm is proportional to the square of the number of antennas. This technology can be used to optimize the MIMO physical layer security transmission rate. Subsequently, Marwan et al. pointed out that the zero forcing algorithm (Zero Forcing, ZF) can be used to reduce interference between MIMO users (Krunz M, Siyari P. Secure Linear Precoding in Overloaded MU-MIMO Wireless Networks[J]. IEEE Transactions on Communications, 2023), and then mixed multiple precoding technologies in the downlink to increase security. This technology can also solve the problem of user overload, but this scheme requires that the number of antennas at the transmitting end is greater than the number of antennas at the eavesdropping end and the legitimate receiving end.The literature (Jian J, Wang WQ, Chen H, et al. Physical-Layer Security for Multi-User Communications with Frequency Diverse Array-Based Directional Modulation [J]. IEEE Transactions on Vehicular Technology, 2023) uses directional modulation and precoding technology based on frequency diversity array (FDA) in both uplink and downlink. This scheme can not only enhance the security of MIMO, but also eliminate interference reaching different receiving antennas. Experiments show that this scheme is better than using the zero-forcing algorithm and singular value decomposition method alone. The literature (Liu Niansheng. Design and Implementation of MIMO Lattice Cryptography [J]. Computer Engineering and Applications, 2018, 54 (12): 10-13) found that if Gaussian random noise is introduced into the model, the MIMO channel can show irregular random changes, making it equivalent to solving a lattice-based problem for eavesdroppers to decode the ultra-large-scale multiple-input multiple-output problem. Since the security of this scheme is based on the lattice-based problem, it can resist quantum attacks and selective ciphertext attacks. Although this scheme omits the key management process, it needs to share the key through random channel matrix characteristics. The premise of this scheme is that it needs to be based on a legitimate channel estimation process that cannot be hacked by eavesdroppers.

[0005] In summary, current research on MIMO physical layer security needs to be based on the assumption that the eavesdropper has limited computing power, a limited number of eavesdropping antennas, or that the eavesdropper cannot obtain legitimate channel state information. These assumptions may not hold true in some cases, and they are not suitable for the security requirements of the future 6G era. There are relatively few studies on the security design of large-scale MIMO physical layer precoding combined with lattice public keys, and there is a lack of comprehensive security and correctness analysis.

[0006] Thomas et al. (Dean TR, Goldsmith AJ. Physical-layer cryptography through massive MIMO [J]. IEEE Transactions on Information Theory, 2017, 63 (8): 5419-5436) defined the MIMO-Search and MIMO-Decision problems. At the same time, they proved through the reduction process that the eavesdropper decoding the MIMO system signal is equivalent to solving the grid difficulty problem. This solution provides a certain security analysis idea for the present invention.

[0007] In addition, in practical applications, there are many scenarios where the ideas of the present invention can be applied. For example: in the 6G era, base stations may collapse completely due to natural disasters and other reasons. Temporary emergency base stations can be equipped with hundreds or thousands of antennas, and the ideas of the present invention can be used for secure communications between them. On the other hand, if terahertz electromagnetic waves (0.1THz~10THz) are used for future communications, the signal wavelength will be further reduced, the antenna spacing will be smaller, and ultra-large-scale antennas can be integrated on a very small circuit board. It is expected that hundreds of antennas can be installed in mobile phones. At this time, the secure communication between mobile phones and base stations can also use the ideas of the present invention. Summary of the invention

[0008] In order to solve the above technical problems, the present invention discloses a lattice public key encryption scheme based on ultra-large-scale MIMO, which can effectively protect the privacy information between the sender and the receiver and achieve resistance to quantum attacks.

[0009] The technical solution of the present invention is as follows:

[0010] A lattice public key encryption method based on ultra-large-scale MIMO, the steps of which include:

[0011] 1) The legitimate user generates a public-private key pair and estimates the legitimate channel, and transmits the public key and channel state information to the base station in plain text;

[0012] 2) The base station uses MIMO precoding and public key to encrypt the plaintext, and transmits the obtained ciphertext to the legitimate user through a legitimate channel;

[0013] 3) The legitimate user decrypts the data using the private key and obtains the original plaintext.

[0014] Furthermore, the legitimate user generates a public-private key pair using a general hard problem on a lattice. Specifically, the legitimate user generates a public-private key pair based on the Shortest Basis Problem (SBP).

[0015] Furthermore, the public-private key pair and other public parameters are generated by the following steps:

[0016] 1) The legal user end is equipped with M antennas, and the base station is equipped with N antennas. The values ​​of M and N are made public. The number of antennas of the legal user end is large, which can be 512 in this scheme. Both are public parameters.

[0017] 2) The legal user generates an N-dimensional complex matrix R∈C N×N , all elements in this matrix are taken from the mean 0 and the variance σ 2 The complex Gaussian random distribution requires that the modulus of each element in the matrix R is less than or equal to T (the value of T is relatively small, for example, it can be 4 in one embodiment of the present invention).

[0018] 3) Calculation Then generate Σ′ as: Σ′=R+KI N ∈C N×N , where I N is the N-dimensional identity matrix.

[0019] 4) The legal user terminal randomly generates a unimodular matrix P of the complex field, the determinant modulus length of the matrix is ​​1, and the generation method of P is: P = L t U t . Where L t is an N-dimensional lower triangular matrix, U t are N-dimensional upper triangular matrices. The element moduli of the diagonal of these two matrices are both 1, and the element moduli of other non-zero positions can be 1 or 0.

[0020] 5) In the cryptographic scheme, the public key and the private key correspond to each other, referred to as a key pair. The public key is the part that is published to the public, and the private key is the part that needs to be kept secret. The message encrypted with the public key can only be decrypted using the private key. Therefore, according to the above key generation algorithm, Σ′P is the public key and (Σ′,P) is the private key.

[0021] Further, the legitimate user terminal obtains channel state information according to a minimum mean square error (MMSE) channel estimation method, the steps of which include:

[0022] 1) The base station sends a pilot signal s, which is transmitted to the receiving end, i.e., the legal user end, through a legal channel. The signal received by the legal user is Y. It can be obtained that Y=Hs+e, where H is the channel to be estimated and e is the noise.

[0023] 2) Legal client computing When the minimum mean square error estimation is achieved, the error vector is the same as the one calculated here Orthogonal, that is, it satisfies the orthogonality principle. Then calculate the statistical information E{HH H}, where E represents the calculation of mathematical expectation.

[0024] 3) Legal user terminal calculation matrix The cross-correlation matrix in represents the noise intensity, represents the pilot signal strength, Represents the inverse of the signal-to-noise ratio.

[0025] 4) The legitimate user end uses the same method to calculate the real channel matrix H and the matrix The cross-correlation matrix between Right now in Representative Matrix The complex conjugate transpose of .

[0026] 5) The channel gain matrix finally obtained by the MMSE channel estimation method is And pass this matrix to the base station in plain text. In the above, H is the real channel matrix, is the channel matrix obtained by the least squares method, is the channel matrix obtained by the MMSE channel estimation method. The MMSE algorithm can minimize the mean square error of the estimated channel matrix. In the subsequent scheme,

[0027] Furthermore, the base station uses the channel gain matrix H and the public key to jointly design a new precoding and physical layer encryption through the following steps:

[0028] 1) The base station uses the singular value decomposition (SVD) method to decompose the channel matrix H and obtains: H = U∑V H , where H∈C M×N , U∈C M×M ,∑∈C M×N , V∈C N×N , U and V are both unitary matrices, representing the generalization of orthogonal matrices in the complex domain;

[0029] 2) The base station originally sends a signal X, which is precoded into V∑′PX using SVD precoding technology and public key ∑′P, and the result is transmitted to the legitimate user through a legitimate channel.

[0030] Furthermore, the legitimate user uses the Nearest Plane Algorithm and solves the equation. This process can recover X in polynomial time. The steps include:

[0031] 1) The signal received by the legitimate user end is y = HV∑′PX+e1 = U∑∑′PX+e1. Multiplying both sides of the equation by the conjugate transpose of the unitary matrix U yields U H y=U H U∑∑′PX+U H e1=∑∑′PX+e3,where U H e1 and e3 are noises of equal magnitude;

[0032] 2) The legal user terminal regards ∑∑′PX as a grid point in the complex domain, U H y is regarded as an arbitrary complex point in M-dimensional space, and then the process of eliminating e3 is equivalent to solving the Closest Vector Problem (CVP) on the lattice;

[0033] 3) The legitimate user knows the private key ∑′ and P, where the private key ∑′ is a lattice basis with good orthogonality. The corresponding lattice point ∑∑′PX can be solved using the Nearest Plane Algorithm, and the solution algorithm has a polynomial time complexity;

[0034] 4) After ∑∑′PX is obtained, ∑ is the result of SVD decomposition of the legal channel matrix and is public, ∑′ and P are private keys, which are also known to the legal user end, so the original transmitted signal X can be directly obtained by solving the equation and normal decoding.

[0035] Furthermore, the method for solving the shortest vector problem on the lattice is based on an orthogonal lattice basis and uses a nearest plane algorithm to solve the shortest vector problem, and the steps include:

[0036] 1) The algorithm inputs four matrices U H y∈C M×1 ,∑∈C M×N ,∑′∈C N×N , P∈C N×N ;

[0037] 2) It is known that ∑′ is the orthogonal lattice basis, so the algorithm does not need to perform the LLL lattice basis reduction process;

[0038] 3) Will U H y is assigned to b: b←U H y;

[0039] 4) Treat each column of ∑′ as an orthogonal lattice basis Traverse each dimension to calculate in Represents vector b and vector Do the inner product operation, It means taking the nearest integer;

[0040] 5) From M dimension to 1 dimension, traverse and calculate b←bc j b j ;

[0041] 6) The algorithm finally outputs U H yb, this value is ∑∑′PX.

[0042] A physical layer security communication device includes an encoder, a modulator, a transmitting device, a transmission channel connected in sequence at a transmitting end, and a receiving device, a demodulator, and a decoder connected in sequence at a receiving end. The encoder and the decoder as well as the transmitting device and the receiving device are configured to execute the above-mentioned method of the present invention.

[0043] Compared with the prior art, the present invention has the following advantages:

[0044] 1) The lattice public key encryption scheme based on ultra-large-scale MIMO proposed in the present invention significantly improves the security of communication, and the present invention is correct and feasible.

[0045] 2) When the number of antennas of the eavesdropper is infinite and far greater than the number of legal antennas, the present invention is also safe.

[0046] 3) When the eavesdropper is less than half of the wavelength away from the legitimate end, or directly breaks through the channel estimation process to obtain legitimate channel information, the present invention is also safe.

[0047] 4) The present invention is applicable to both time division duplex and frequency division duplex channels without resorting to channel reciprocity.

[0048] 5) The precoded public key encryption scheme proposed in the present invention is based on lattice cryptography, which can resist currently known quantum attacks and adapt to the future 6G requirements for communication security.

[0049] 6) When future communications use the terahertz frequency band (0.1THz to 10THz), a large number of antennas can be integrated on a very small circuit board, and the present invention is also applicable to communications between base stations and mobile phone users. If terahertz electromagnetic waves are used in future 6G communications, the signal wavelength will be further reduced, the antenna spacing will be smaller, and ultra-large-scale antennas can be integrated on a very small circuit board. At this time, the secure communication between mobile phones and base stations, as well as the emergency security communication between base stations, can use the ideas of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is an architecture diagram of the ultra-large-scale MIMO lattice public key encryption solution in the method described in an embodiment of the present invention.

[0051] Figure 2 It is a diagram of the MIMO.KeyGen algorithm for key generation in the method described in an embodiment of the present invention.

[0052] Figure 3 It is a flow chart of bilateral channel estimation and singular value decomposition in the method described in the embodiment of the present invention.

[0053] Figure 4 It is a schematic diagram of the shortest lattice basis ∑′ in the method described in the embodiment of the present invention.

[0054] Figure 5 It is a diagram of the MIMO.Dec algorithm for decryption by the receiver in the method described in the embodiment of the present invention.

[0055] Figure 6 It is a relationship diagram between the decoding bit error rate and the signal-to-noise ratio of the legitimate receiving end and the eavesdropping end in the method described in the embodiment of the present invention. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below through examples.

[0057] The present invention discloses a lattice public key encryption scheme based on ultra-large-scale MIMO, and the technology consists of two parts: public key encryption and private key decryption. Public key encryption includes: a legitimate user uses a pilot transmitted from a base station to complete channel estimation, and transmits the channel state information to the base station; the legitimate user generates a public key based on the shortest lattice basis theory, and directly transmits the public key through a channel; the base station completes the public key encryption of the original message and the precoding operation based on the SVD decomposition of the channel matrix based on the received public key and channel state information. Private key decryption includes: the legitimate user generates a private key based on an orthogonal basis; based on the private key and the orthogonal basis, the nearest plane algorithm operation is performed on the noisy encrypted information, and finally decryption is achieved. In the above steps, the key generation and decryption operations are completed at the legitimate user end.

[0058] Figure 1 The main framework of this scheme is described, which consists of two parts: public key encryption and private key decryption. The base station sends a pilot signal S to the legitimate user, and the legitimate user uses the pilot signal to estimate the channel and performs SVD decomposition of the channel matrix H = U∑V H , where H∈C M×N , U∈C M×M ,∑∈C M×N , V∈C N×N , U and V are both unitary matrices, representing the generalization of orthogonal matrices in the complex field. The legitimate user generates a public key ∑′P based on the shortest lattice problem and transmits the public key and channel state information to the base station. The base station encrypts the original message X based on the public key and the precoding matrix, and transmits V∑′PX to the other end. The legitimate user decrypts it using the private key, completing the entire process.

[0059] In general, the lattice public key encryption scheme based on ultra-large-scale MIMO proposed in this method significantly improves the security of communications. When the number of antennas of the eavesdropper is infinite and far greater than the number of legal antennas, the present invention is also safe. The present invention is also safe when the eavesdropper is less than half the wavelength away from the legal end, or directly breaks through the channel estimation process to obtain legal channel information. The present invention can be applied to both time division duplex and frequency division duplex channels without the need to rely on channel reciprocity; the precoding encryption scheme proposed in the present invention is based on lattice cryptography, which can resist currently known quantum attacks and can adapt to the future 6G requirements for communication security; when future communications use terahertz frequencies, a large number of antennas can be integrated on a very small circuit board, and the present invention is also applicable to communications between base stations and mobile phone users.

[0060] Figure 2The key generation algorithm MIMO.keyGen is described (see Table 1 for a detailed description of the symbols in the algorithm). The algorithm shows the generation process of the public key and the private key. The base station is equipped with M antennas and the legitimate user is equipped with N antennas. The values ​​of M and N are made public. Both M and N are large, and in this scheme, they can be 512. Both are public parameters. Then, the legitimate user generates an N-dimensional complex matrix R∈C N×N , all elements in this matrix are taken from the mean 0 and the variance σ 2 The modulus of each element of the matrix R is less than or equal to T (the value of T is relatively small, and can be 4 in the present invention). Then, calculate Then the legitimate user generates ∑′ as: ∑′=R+KI N ∈C N×N , where I N is an N-dimensional unit matrix. Then, the legitimate user randomly generates a unimodular matrix P of the complex field, the determinant modulus of which is 1, and P is generated as follows: P = LU. Where L is an N-dimensional lower triangular matrix, and U is an N-dimensional upper triangular matrix. The modulus of the elements on the diagonals of these two matrices is 1, and the modulus of the elements at other non-zero positions can be 1 or 0. Therefore, the public key pk = ∑′P, and the private key sk = (∑′, P).

[0061] Table 1 Explanation of symbols in the scheme

[0062]

[0063] Figure 3 The flowchart of channel estimation and singular value decomposition is shown. The base station sends a pilot signal s, which is transmitted to the receiving end through a legal channel. The signal received by the legal user is Y. Then, the legal user calculates It can be obtained that this matrix and the estimated channel error matrix are mutually orthogonal matrices, and the statistical information of the channel matrix E{HH H}. Then, the legitimate user calculates the matrix The cross-correlation matrix in represents the noise intensity, represents the pilot signal strength, Represents the inverse of the signal-to-noise ratio. The legitimate user uses the same method to calculate the real channel matrix H and the matrix The cross-correlation matrix between Finally, the channel gain matrix obtained by the MMSE (Minimum Mean Square Error) channel estimation method is And pass this matrix to the base station in plain text. Above, H is the real channel matrix, is the channel matrix obtained by the least squares method, is the channel matrix obtained by the MMSE channel estimation method. After receiving the channel state information, the base station uses the singular value decomposition (SVD) method to decompose the channel matrix H and obtain: H = U∑V H , where H∈C M×N , U∈C M×M ,∑∈C M×N , V∈C N×N , U and V are both unitary matrices, representing the generalization of orthogonal matrices in the complex domain.

[0064] The legitimate user transmits ∑′P to the base station through an open channel, and the eavesdropper can also obtain ∑′P. If it is difficult for the eavesdropper to deduce ∑′ and P from ∑′P, ∑′P can be used as the public key and ∑′ and P as the private key. This section will explain the difficulty of deriving ∑′ and P from ∑′P from the perspective of lattice cryptography. A lattice can be represented by different lattice bases. There is a relationship between the lattice base vectors being very close to orthogonal and the lattice base vector length being very short. Assume [b1, b2, …, b n ] is a lattice basis of the lattice L, [b1, b2, …, b n The orthogonal defect of ] can be defined as where det(L) represents the determinant of the lattice L. According to ∑′∈C N×N The generation method shows that the modulus length of the elements on the diagonal of the matrix is ​​much larger than the modulus length of the elements at other positions, so ∑′∈C N×N It can be used as a lattice basis with a small orthogonal defect. After the transformation of the unimodular matrix P, ∑′P becomes a bad basis, such as Figure 4 As shown in the figure, restoring ∑′ from a bad basis ∑′P is one of the difficult problems on the lattice, which can be understood as finding the shortest basis vector [b1, b2, …, b n ], so that they are the shortest under the specified length definition, e.g. This process is to solve the shortest basis problem (SBP).

[0065] The base station originally sent a signal X, which is now precoded and encrypted into V∑′PX. The signal received by the legitimate receiving end is y=U∑∑′PX+e1, and the ciphertext is y∈C M×1 , the private key is ∑′∈C N×N With P∈C N×N , plaintext X∈C N×1 The following three situations will cause the eavesdropper to obtain the channel state information H and V:

[0066] (1) The distance between the eavesdropper and the legitimate receiver is less than half of the signal wavelength;

[0067] (2) When legitimate users transmit channel state information to the base station, this process can be eavesdropped;

[0068] (3) The base station and the legitimate users choose to proactively disclose channel status information.

[0069] The security of this scheme does not depend on the unknown channel state information, but only on computational complexity theory, so U∈C M ×M With ∑∈C M×N Can be used as a public parameter. The legitimate end uses the private key ∑′∈C N×N With P∈C N×N , we can see that the process of solving the signal X is solvable with polynomial time complexity.

[0070] At the same time, the signal received by the eavesdropping end is y e =GV∑′PX+e2, where G is the eavesdropping channel with good orthogonality, but GV∑′P will disrupt this orthogonality and stretch it in different dimensions. At this time, the ciphertext is y e , the public key is ∑′P, the known parameters are V and G, and the expected plaintext is X. Even if the eavesdropper can obtain V and G, it is equivalent to solving the CVP problem on a bad basis because it cannot separate ∑′ from P. This results in an exponential time complexity for the eavesdropper to solve X. Comparing the legitimate channel matrix with the equivalent eavesdropping channel matrix, this process is equivalent to establishing a certain channel advantage.

[0071] Analysis and evaluation:

[0072] 1) Correctness analysis:

[0073] The signal received by the legal receiving end is y=U∑∑′PX+e1. Multiplying both sides of the equation by the conjugate transpose of the unitary matrix U, we get U H y=U H U∑∑′PX+U H e1=∑∑′PX+e3, where e3 and e1 are both noise. Because U is a unitary matrix∈C M×M , we can get UU H =I M . e1 is the noise ∈C M×1 , U H The norm of e1 can be calculated by this process: From this we can get U H The norm of e1 is equal to the norm of e1. The unitary matrix U H The vector e1 is orthogonally transformed, and the orthogonal transformation does not change the length of the vector e1. This process reflects the norm preservation of the unitary matrix. Therefore, it can be obtained that both e3 and e1 are noises with equal size.

[0074] Consider ∑∑′PX as a lattice point in the complex field, U H y is regarded as any complex point in M-dimensional space. The process of eliminating noise e3 is essentially to solve the Closest Vector Problem (CVP) on the lattice. The problem is defined as given a lattice Λ and a point t in the space, the goal is to solve the lattice vector closest to t.

[0075] Since the lattice basis ∑′ has good orthogonality, the nearest plane algorithm can be used to directly solve the nearest lattice point, such as Figure 5 The receiver decrypts the MIMO.Dec algorithm shown. The specific solution algorithm is as follows:

[0076] (1) The algorithm inputs four complex matrices U H y∈C M×1 ,∑∈C M×N ,∑′∈C N×N , P∈C N×N ;

[0077] (2) It is known that ∑′ is an orthogonal basis of the lattice, so the algorithm does not need to perform the LLL lattice basis reduction process;

[0078] (3) Put U H y is assigned to b: b←U H y;

[0079] (4) Consider each column of ∑′ as a lattice basis Traverse each dimension to calculate in Represents vector b and vector Do the inner product operation, It means taking the nearest integer;

[0080] (5) From M dimension to 1 dimension, traverse and calculate b←bc j b j ;

[0081] (6) The algorithm finally outputs U H yb, this value is ∑∑′PX.

[0082] Recently, the planar algorithm is also called the Babai algorithm, and the final output result of the algorithm is ∑∑′PX, and then the original transmitted signal X can be directly obtained by solving the equation and the normal decoding process. Therefore, the present invention is correct, and the computational complexity is at the polynomial time level.

[0083] 2) Safety analysis:

[0084] The signal received by the eavesdropping end is y e=GV∑′PX+e2. The eavesdropper can also perform SVD decomposition based on the estimation of the eavesdropping channel matrix G, such as G=U e ∑ e V e H , where G∈C E×N , U e ∈C E×E ,∑ e ∈C E×N , V e ∈C N×N , U e With V e They are all unitary matrices, representing the generalization of orthogonal matrices in the complex field.

[0085] Similar to legitimate users, the eavesdropper further processes the signal and multiplies both sides of the equation by the unitary matrix U e The conjugate transpose of According to the norm preservation of unitary matrices, we can get and e4 are two noises of equal magnitude. PX hides the structure of X, even if the number of eavesdropping antennas is infinite to adjust V e H The value of V, but for the eavesdropping user, the process of solving X is equivalent to solving the CVP (Closest Vector Problem) problem on the bad basis ∑′P, which is difficult.

[0086] 3) Experimental performance evaluation:

[0087] The solution proposed in this invention is realized by using the MATLAB R2023a simulation platform, and the program running environment is Windows 11, 12 th Gen Intel(R) Core(TM) i5-12500 (12CPUs), ~3.0GHz and 8192MB RAM. This experiment constructs a two-dimensional spatial model, in which the values ​​of each element in the channel matrix are affected by large-scale fading and small-scale fading, the number of antennas is set to 512, and the modulation method is 16-QAM (Quadrature Amplitude Modulation). Figure 6The simulation results of the scheme proposed in the present invention are shown, and the decoding bit error rate of the receiving end and the eavesdropping end changes as the signal-to-noise ratio increases. The figure is divided into two parts, the upper part is the bit error rate when decrypting with a private key, and the lower part is the bit error rate when decrypting without a private key. In the upper part, the solid line represents that when the signal-to-noise ratio increases from -10dB to 10dB, the decoding bit error rate of the receiving end is significantly reduced from 0.15 to close to 0. When the signal-to-noise ratio continues to increase from 10dB to 80dB, the bit error rate tends to 0. This shows that when the receiving end knows the private key for decryption, the decoding accuracy will be significantly improved with the help of the nearest plane algorithm. The dotted line represents that when the eavesdropping end also has the private key, it will obtain a similar result to the receiving end (such as Figure 6 , the two curves are approximately overlapped in most areas). In the lower part, the dotted line represents that when the signal-to-noise ratio increases from -10dB to 10dB, the decoding bit error rate of the eavesdropping end is close to 0.5. This is the worst case for decoding, indicating that the eavesdropping end cannot obtain the original plaintext information in this scheme. When the signal-to-noise ratio continues to increase from 10dB to 80dB, the bit error rate has a certain downward trend, indicating that when the eavesdropping end directly decodes without knowing the private key, the bit error rate is high, which is much worse than the decoding performance of the legitimate receiving end that has the private key. The solid line shows that when the legitimate receiving end also does not know the private key, it will obtain a similar result to the eavesdropper. The comparison between the upper and lower parts shows that: (1) when the private key is possessed and combined with the nearest plane algorithm, the decoding bit error rate will be greatly reduced; (2) the security of this scheme does not require a confidential channel matrix, and the decoding correctness depends on the design of the scheme's precoding. Figure 6 In the figure, the eavesdropping channel G is different from the legitimate channel H. A total of four curves can control the influence of irrelevant variables. Regardless of which curve, when the signal-to-noise ratio increases to a certain extent, the bit error rate will tend to decrease, which is in line with the basic logic of communication.

[0088] In summary, the performance of the present invention is relatively excellent in terms of security and feasibility, and can provide a more secure communication system for legitimate users.

[0089] 4) Comparative analysis of solutions:

[0090] Traditional MIMO precoding schemes generally focus on how to eliminate interference. The security of MIMO precoding technology alone is weak. In order to achieve secure transmission, it is usually necessary to assume that the number of eavesdroppers' antennas is limited, the eavesdroppers are far enough away from the legitimate end (usually greater than half of the signal wavelength), the system is time-division duplex and satisfies channel heterogeneity. These requirements and assumptions are unreasonable in the future 6G security scenario and are difficult to resist quantum attacks. The literature (Liu Niansheng. Design and implementation of MIMO lattice cryptography [J]. Computer Engineering and Applications, 2018, 54(12): 10-13) found that if the MIMO channel can show irregular random changes, then the eavesdropper's decoding of ultra-large-scale multiple-input multiple-output (MIMO) is equivalent to solving a lattice-hard problem. The security of this literature (replaced by literature [1] in Table 2) is based on the lattice-hard problem, so it can resist quantum attacks and selective ciphertext attacks. Although this scheme omits the key management process, it needs to share the key through random channel matrix characteristics. The premise of this scheme is that the legitimate channel estimation process cannot be cracked by eavesdroppers.

[0091] In the present invention, a new precoding scheme is designed based on the shortest lattice basis problem on the lattice, that is, a lattice-based public key encryption scheme on the physical layer. This scheme does not need to assume any unreasonable preconditions. When the number of antennas of the eavesdropper is infinite and much larger than the number of legal antennas, when the eavesdropper is less than half of the wavelength away from the legal end, or when the channel estimation process is directly broken to obtain legal channel information, the present invention is also safe. The present invention can be applied to both time division duplex and frequency division duplex channels, does not require the use of channel reciprocity, and can meet the 6G security requirements even under quantum attacks.

[0092] The security comparison of the ultra-large-scale MIMO lattice public key encryption scheme proposed in this invention, the traditional MIMO precoding scheme and the reference [1] is shown in Table 2 below.

[0093] Table 2 Security comparison of precoding schemes

[0094]

[0095] Another embodiment of the present invention provides a physical layer security communication device, including an encoder, a modulator, a transmitting device, a transmission channel connected in sequence at a transmitting end, and a receiving device, a demodulator, and a decoder connected in sequence at a receiving end, wherein the encoder and the decoder as well as the transmitting device and the receiving device are configured to execute the above-mentioned method of the present invention.

[0096] Another embodiment of the present invention provides a computer device (computer, server, smart phone, etc.), which includes a memory and a processor, the memory stores a computer program, the computer program is configured to be executed by the processor, and the computer program includes instructions for executing each step in the method of the present invention.

[0097] Another embodiment of the present invention provides a computer-readable storage medium (such as ROM / RAM, magnetic disk, optical disk), wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a computer, the steps of the method of the present invention are implemented.

[0098] The above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. A person skilled in the art may modify or make equivalent substitutions for the technical solutions of the present invention without departing from the spirit and scope of the present invention. The protection scope of the present invention shall be subject to the claims.

Claims

1. A lattice public key encryption method based on ultra-large-scale MIMO, characterized in that: The following steps are involved: The legitimate user generates a public-private key pair and estimates the legitimate channel, and transmits the public key and channel state information to the base station in plain text; The base station uses MIMO precoding and public key to encrypt the plaintext, and transmits the obtained ciphertext to the legitimate user through a legitimate channel; The legitimate user decrypts the data using the private key and obtains the original plaintext.

2. The method according to claim 1, characterized in that The legitimate user generates the public-private key pair through the following steps: The legal user terminal is equipped with M antennas, and the base station is equipped with N antennas. The values ​​of M and N are made public. The legal user generates an N-dimensional complex matrix R∈C N×N , all elements in this matrix are taken from the mean 0 and the variance σ 2 The complex Gaussian random distribution requires that the modulus of each element in the matrix R is less than or equal to T; calculate Then generate ∑′ as: ∑′=R+KI N ∈C N×N , where I N is the N-dimensional identity matrix; The legitimate user terminal randomly generates a unimodular matrix P of the complex field, the determinant modulus length of the matrix is ​​1, and the generation method of P is: P = L t U t , where L t is an N-dimensional lower triangular matrix, U t is an N-dimensional upper triangular matrix; Among them, ∑′P is the public key and (∑′, P) is the private key.

3. The method according to claim 2, characterized in that The legitimate user obtains the channel state information according to the minimum mean square error MMSE channel estimation method through the following steps: The base station sends a pilot signal s, which is transmitted to the receiving end, i.e., the legal user end, through a legal channel. The signal received by the legal user end is Y, where Y = Hs + e, where H is the real channel matrix to be estimated and e is noise. Legal Client Computing is the channel matrix obtained by the least square method. When the minimum mean square error estimation is achieved, the error vector is Orthogonal, that is, satisfying the orthogonality principle, then calculate the statistical information E{HH H }, where E represents the calculation of mathematical expectation; Legal user terminal computing matrix The cross-correlation matrix in represents the noise intensity, represents the pilot signal strength, Represents the inverse of the signal-to-noise ratio; The legitimate user end calculates the real channel matrix H and the matrix The cross-correlation matrix between Right now in Representative Matrix The complex conjugate transpose of ; The channel gain matrix obtained by the MMSE channel estimation method And pass this matrix to the base station in plain text.

4. The method according to claim 3, characterized in that The base station uses the matrix H and the public key to jointly design a new precoding and physical layer encryption through the following steps: The base station uses the singular value decomposition method to decompose the matrix H and obtains: H = U∑V H , where H∈C M×N , U∈C M×M ,∑∈C M×N , V∈C N×N , U and V are both unitary matrices, representing the generalization of orthogonal matrices in the complex domain; The base station originally sends a signal X, which is precoded into V∑′PX using SVD precoding technology and public key ∑′P, and the result is transmitted to the legitimate user through a legitimate channel.

5. The method according to claim 4, characterized in that The legitimate user uses the nearest plane algorithm and solves the equation to recover X in polynomial time. The steps include: The signal received by the legitimate user end is y = HV∑′PX+e1 = U∑∑′PX+e1. Multiply both sides of the equation by the conjugate transpose of the unitary matrix U to obtain U H y=U H U∑∑′PX+U H e1=∑∑′PX+e3,where U H e1 and e3 are noises of equal magnitude; The legal user terminal regards ∑∑′PX as a grid point in the complex domain, U H y is regarded as an arbitrary complex point in M-dimensional space, and then the process of eliminating e3 is equivalent to solving the shortest vector problem on the lattice; The legitimate user knows the private key ∑′ and P, where the private key ∑′ is a lattice basis with good orthogonality, and the corresponding lattice point ∑∑′PX is solved using the nearest plane algorithm; After ∑∑′PX is obtained, ∑ is the result of SVD decomposition of the legal channel matrix and is public, ∑′ and P are private keys, which are known to the legal user end. The original transmitted signal X is directly obtained by solving the equation and decoding normally.

6. The method according to claim 5, characterized in that The method for solving the shortest vector problem on the lattice is based on an orthogonal lattice basis and uses a nearest plane algorithm to solve the shortest vector problem. The steps include: Input four matrices U H y∈C M×1 ,∑∈C M×N ,∑′∈C N×N , P∈C N×N ; It is known that ∑′ is an orthogonal lattice basis, so there is no need to perform the LLL lattice basis reduction process; Will U H y is assigned to b: b←U H y; Consider each column of ∑′ as an orthogonal lattice basis Traverse each dimension to calculate in Represents vector b and vector Do the inner product operation, It means taking the nearest integer; From M dimension to 1 dimension, traverse and calculate b←bc j b j ; Final output U H yb, this value is ∑∑′PX.

7. A physical layer security communication device, characterized in that: It includes an encoder, a modulator, a transmitting device, and a transmission channel connected in sequence at the transmitting end, and a receiving device, a demodulator, and a decoder connected in sequence at the receiving end. The encoder and the decoder as well as the transmitting device and the receiving device are configured to execute the method described in any one of claims 1 to 6.

8. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores a computer program, the computer program is configured to be executed by the processor, and the computer program comprises instructions for executing the method according to any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a computer, the method according to any one of claims 1 to 6 is implemented.

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