CN109327478B - A secure access method for chaotic physical layer - Google Patents

Abstract

The invention discloses a chaotic physical layer secret access method, which comprises the steps of firstly obtaining a data matrix of an OFDM signal, then carrying out partition division on the matrix to obtain two matrixes, respectively encrypting the two matrixes by adopting different methods, then restoring the two encrypted matrixes into one matrix according to a partition division reverse method, carrying out subsequent processing and sending on the matrix by a sending end, analyzing the matrix after receiving sent data by a receiving end to obtain the two matrixes, then carrying out decryption by adopting partition division in the same way, and restoring the two decrypted matrixes into one matrix according to the partition division reverse method, wherein the matrix is the recovered data matrix. The invention adopts information partition encryption, and can effectively improve the communication safety.

Description

A secure access method for chaotic physical layer

technical field

The invention belongs to the technical field of access network communication, and more particularly, relates to a chaotic physical layer security access method.

Background technique

显示，参与调查人群中遇到过个人信息泄露情况的人数占比为85.2％。因此，如何保证数据和个人信息在网络上安全地存储、传输、管理与共享成为人们的关注热点问题之一。网络信息安全问题不仅影响着个人，还会涉及到企业的运营管理。自2018年3月起，全球化社交网站Facebook共遭遇了两次大规模的用户数据泄露，近5000万用户的账户遭遇黑客入侵、甚至盗用。此类事件的发生直接导致Facebook股票报价持续下跌及受到英国监管部门处以的罚款，国内的微信、阿里、京东等众多全球性平台公司应引以为戒、提高警惕。

报告显示，中国内地与香港的企业在网络安全方面的平均投入高出全球数值的近四分之一，72％的中国内地与香港受访企业表示其针对物联网安全的战略已经就位。此外，网络的开放性给不法分子在网络上传播恐怖、色情、反动、分裂等有害信息提供了便利，直接威胁到国家的政治与国防建设等领域。因此，网络信息安全与保密问题已经引起了国家领导的高度重视。2014年2月，成立中央网络安全和信息化领导小组。2016年3月，将“构建泛在高效的信息网络、强化信息安全保障、全面保障信息系统安全”三大重点任务列入了我国十三五规划的纲要中。2016年11月，全国人民代表大会常务委员会发布了《中华人民共和国网络安全法》以保障网络安全，维护网络空间主权和国家安全、社会公共利益，保护公民、法人和其他组织的合法权益，促进经济社会信息化的健康、安全发展。此后，我国政府还发布了《国家网络空间安全战略》和《网络空间国际合作战略》。With the continuous advancement of the "Internet +" strategy and the rapid development of cloud computing, big data, industrial Internet and other industries, more data and user personal information have become business shared resources, promoting the process of social and economic globalization. But at the same time, various information security incidents are also showing a large-scale outbreak. The latest released by the China Consumers Association

It shows that 85.2% of the people who participated in the survey have encountered personal information leakage. Therefore, how to ensure the safe storage, transmission, management and sharing of data and personal information on the network has become one of the hot issues that people pay attention to. Network information security issues not only affect individuals, but also involve the operation and management of enterprises. Since March 2018, the global social networking site Facebook has suffered two large-scale user data leaks, and nearly 50 million user accounts have been hacked or even stolen. The occurrence of such incidents directly led to the continuous decline of Facebook's stock price and the fines imposed by the British regulatory authorities. Many global platform companies such as WeChat, Ali, and JD.com in China should take precautions and be more vigilant.

According to the report, companies in mainland China and Hong Kong spend on average nearly a quarter higher on cybersecurity than the global figure, and 72% of companies surveyed in mainland China and Hong Kong say their IoT security strategies are in place. In addition, the openness of the Internet provides convenience for lawbreakers to spread harmful information such as terror, pornography, reaction, and separatism on the Internet, which directly threatens the country's political and national defense construction and other fields. Therefore, the issue of network information security and confidentiality has attracted great attention from national leaders. In February 2014, the Central Network Security and Informatization Leading Group was established. In March 2016, the three key tasks of "building a ubiquitous and efficient information network, strengthening information security, and comprehensively ensuring the security of information systems" were included in the outline of my country's 13th Five-Year Plan. In November 2016, the Standing Committee of the National People's Congress promulgated the Cybersecurity Law of the People's Republic of China to ensure cybersecurity, safeguard cyberspace sovereignty and national security, social and public interests, protect the legitimate rights and interests of citizens, legal persons and other organizations, and promote The healthy and safe development of economic and social informatization. Since then, the Chinese government has also issued the National Cyberspace Security Strategy and the Cyberspace International Cooperation Strategy.

As the "last mile" of network service access, the access network has a large quantity and a wide range, and has become one of the most important parts affecting network construction. Among them, the Orthogonal Frequency Division Multiplexing Passive Optical Network (OFDM-PON) can flexibly allocate resources in the time/frequency domain, has high spectrum utilization, and has a strong tolerance to fiber dispersion. Features such as capability are widely used and are considered a promising way to provide broadband and low-cost access services. However, due to the huge number of users, frequent service interaction and the broadcast structure of PON, information security transmission faces great challenges. To sum up, the research on access network security and its security enhancement technology has important academic value and social significance.

The encryption technology to enhance the security of the access network is usually implemented at the media access control layer and the application layer. The main idea is to add authentication and encryption standards to the layered protocol. Although some methods guarantee high-performance secure communication, their key space is limited, and these methods do not provide security protection for data control information and headers. Compared with the upper layer protocol encryption method, the physical layer encryption technology can not only effectively ensure the security of the control protocol data, but also resist attacks from the bottom layer of the access network. In recent years, physical layer encryption algorithms related to chaotic technology have stimulated a research upsurge. The ergodicity, pseudo-randomness, sensitivity to initial conditions and control parameters of chaotic technology are just similar to the chaotic and diffusion properties of cryptosystems. At the same time, the generation of chaotic sequences is convenient and the number is huge, which can provide a better means of realizing covert communication. In October 2018, the 11th International Symposium on Chaos, Fractal Theory and Application was held in Chongqing, China. With the theme of "Developing Chaos and Fractal Science, Empowering the Information Security Industry", it closely followed the development trend of information security and helped the information security industry. develop.

Chosen Plaintext Attack (CPA) refers to an attack method in which the attacker first selects part of the plaintext and obtains the corresponding ciphertext through the encryption system, and then obtains the relevant information by analyzing and comparing the relationship between the two. . Most of the existing chaotic encryption schemes cannot resist chosen-plaintext attacks, and the schemes that can resist chosen-plaintext attacks have disadvantages such as high computational complexity and performance degradation. In November 2016, a research team from Shanghai Jiao Tong University proposed a dynamic phase rotation scheme that combines random features of input data, which can resist chosen-plaintext attacks. However, in the process of encryption and decryption, due to the accumulation of data noise due to the repeated use of some wrong OFDM data, the performance degradation of the bit error rate of 1 dB is introduced. In February 2017, they encrypted the data using chaotic binary sequences, nonlinear permutation boxes, and chaotic constant-amplitude zero-autocorrelation matrices. This scheme has a strong ability to resist selected plaintext attacks, but it needs to perform multiple cyclic XOR operations and generate a chaotic constant amplitude zero autocorrelation matrix, and the computational complexity is high.

SUMMARY OF THE INVENTION

The purpose of the present invention is to overcome the deficiencies of the prior art, and to provide a chaotic physical layer security access method, which can effectively improve communication security by adopting information partition encryption.

In order to achieve the above object of the invention, the chaotic physical layer security access method of the present invention comprises the following steps:

S1: The data matrix M of a×b is obtained by subcarrier allocation of the OFDM signal modulated by QAM, where a represents the number of subcarriers of an OFDM signal, b represents the number of symbols in a single subcarrier, a<b;

S2: Partition the matrix M to obtain the matrix P and the matrix Q. The specific method of partitioning is as follows:

Calculate the total number of columns c=b-a of the data extracted from the data matrix M, extract the data in column c from the data matrix M according to the predetermined partition rule, and splicing the data in the c column according to the column number in the data matrix M to obtain a × c The matrix P of , the remaining data is spliced according to the column number in the data matrix M to obtain a matrix Q of a × a;

S3: Based on the chaotic system, the matrix P and the matrix Q are encrypted in different ways, and the encrypted matrix P' and matrix Q' are obtained;

S4: According to the inverse method of partition division in step S2, the matrix P' and the matrix Q' are restored into a matrix M';

S5: The sender performs subsequent processing on the matrix M' and sends it;

S6: After the receiving end receives the transmitted data, it analyzes and obtains the matrix M', and then divides the matrix M' according to the partitioning method in step S2 to obtain the matrix P' and the matrix Q', and then uses the corresponding decryption method to decipher the matrix respectively. Decrypt P' and matrix Q' to obtain matrix P and matrix Q, and then use the reverse method of partition division to restore matrix M.

The chaotic physical layer security access method of the present invention firstly obtains the data matrix of the OFDM signal, then partitions the matrix to obtain two matrices, adopts different methods to encrypt the two matrices respectively, and then according to the reverse method of partition division, The two encrypted matrices are restored into one matrix. The sender performs subsequent processing on this matrix and sends it. After the receiver receives the sent data, it parses the matrix to obtain the matrix, and then divides the two matrices by partition to obtain two matrices. Decryption is performed, and then the decrypted two matrices are restored into a matrix according to the reverse method of partition division, and the matrix is the recovered data matrix.

The present invention has the following beneficial effects:

(1) The present invention adopts the data matrix partition division, which can reduce the cross-correlation relationship between the information, reduce the probability that the signal peaks are combined in the same phase, and can reduce the peak-to-average power ratio (PAPR) of the signal;

(2) The present invention can increase the key space and improve the difficulty of brute force cracking by illegal attackers by partitioning and using two different encryption means for separate encryption;

(3) The present invention can effectively resist the attack of selected plaintext, and the attacker cannot decipher all the information by using this attack method, and the following scenarios are analyzed:

①The selected part of the plaintext is encrypted by only one method. The attacker can know the encryption method according to the relevant information obtained, but cannot decipher the remaining information, because the partition of the data and another encryption method cannot be known;

②The selected part of the plaintext is encrypted using two methods at the same time, which increases the difficulty for the attacker to obtain relevant information. Even if the two encryption methods are obtained through multiple analysis, the remaining information cannot be deciphered because the partition of the information cannot be known;

(4) The partitioning method adopted in the present invention is relatively simple, and the operational complexity of the present invention is directly related to the two different encryption methods selected, and the encryption method with better performance and lower work complexity can avoid spectrum resources. The reduction of the utilization rate makes up for the deficiencies of the existing technical solutions.

Description of drawings

1 is a flow chart of a specific implementation manner of a chaotic physical layer secure access method of the present invention;

Fig. 2 is the schematic diagram of data matrix partition division in the present embodiment;

FIG. 3 is a flow chart of data transmission and reception decryption in this embodiment.

Detailed ways

The specific embodiments of the present invention are described below with reference to the accompanying drawings, so that those skilled in the art can better understand the present invention. It should be specially reminded that, in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

Example

FIG. 1 is a flow chart of a specific implementation manner of a chaotic physical layer secure access method according to the present invention. As shown in Figure 1, the specific steps of the chaotic physical layer security access method of the present invention include:

S101: OFDM signal matrixing:

A data matrix M of a×b is obtained by subcarrier allocation of the QAM modulated OFDM signal, where a represents the number of subcarriers of an OFDM signal, b represents the number of symbols in a single subcarrier, a<b. That is, an OFDM signal is represented as a data matrix, and each OFDM symbol is regarded as an element in the data matrix M.

In this embodiment, 16-QAM modulation is used as an example for description. When the modulation mode adopts 16-QAM, the number of bits occupied by a single OFDM symbol is log ₂ (16) = 4, so the signal to be sent needs to be divided into a row vector of 1 row a×b×4 columns, through the serial/parallel ( S/P) conversion, convert the data from binary to decimal, then perform 16-QAM mapping, and finally obtain the data matrix M through subcarrier allocation. In this embodiment, a=120 and b=200 are set.

S102: Data matrix partition division:

The data matrix M is partitioned to obtain the matrix P and the matrix Q. The specific method of partitioning is as follows:

Calculate the total number of columns c=b-a of the data extracted from the data matrix M, this is to ensure that the remaining data after extraction can be combined into a square matrix. It is found through research that if the total number of extracted data is too small, the practical significance of using the encryption method of the present invention is not significant, so it is preferable to set 1/5≤c/b≤4/5, that is, b/5≤b-a≤4b/5 . Extract the data in column c from the data matrix M according to the predetermined partitioning rules, splicing the data in column c according to the column serial number in the data matrix M to obtain a matrix P of a×c, and the remaining data is spliced according to the column serial number in the data matrix M Get an a×a matrix Q.

The specific method of partition division can be adjacent partition method, staggered partition method and random partition method. The three methods are detailed as follows:

·Adjacent partition method

Let the number of partitions d of the data matrix M be the common divisor of the parameters b and c. If there are too many partitions, the complexity of subsequent processing will increase, and if too few partitions, it is difficult to achieve a relatively ideal technical effect. After research, it is found that the value range of d is 4≤d≤12. The effect is better. When a=120 and b=200, it can be known that c=80, then the possible values of the number of partitions d are 4, 5, 8, and 10. Then, the data matrix M is divided into d partitions on average by column, each partition contains e column, obviously e=b/d, and consecutive f columns of data are extracted from the same position of each partition, f=c/d, Note that the column number of the starting column of the data in column f in the partition is g. Since it is continuous extraction, there are e-f+1 extraction methods. The extracted c-column data is spliced according to the column sequence number in the data matrix M to obtain a matrix P of a×c, and the remaining data is spliced according to the column sequence number in the data matrix M to obtain the a×a matrix Q.

In this embodiment, the adjacent partition method is used for partition division. FIG. 2 is a schematic diagram of partitioning a data matrix based on the adjacent partitioning method in this embodiment. As shown in Figure 2, in this embodiment, the number of partitions is set to d=10, then obviously e=20, f=8, that is to say, the data matrix M is divided into 10 partitions, and each partition has 120 rows of 20 Column data, 8 columns of continuous data in every 20 columns of data are arbitrarily extracted, and it can be seen that there are 13 ways of extraction in this embodiment. In FIG. 2, g=5 is taken as an example, that is, the positioning of the 8-column continuous data is from the 5th column to the 12th column in each partition. By partitioning according to the above method, a matrix P of 120×80 and a matrix Q of 120×120 can be obtained.

· Staggered partition method

表示向下取整，第c个分区的列数为b-(c-1)d，分别从每个分区的相同位置提取出1列数据，将提取的c列数据按照在数据矩阵M中的列序号拼接得到a×c的矩阵P，剩余数据按照在数据矩阵M中的列序号拼接得到a×a的矩阵Q。若需要将数据矩阵M按列均匀划分为c个分区，可以通过参数设置令b为c的整数倍。Divide the data matrix M into c partitions by column, where the number of single partition columns for the first c-1 partitions is

Indicates rounding down, the number of columns in the c-th partition is b-(c-1)d, and 1 column of data is extracted from the same position in each partition, and the extracted data in column c is based on the data in the data matrix M. The column number is spliced to obtain a matrix P of a × c, and the remaining data is spliced according to the column number in the data matrix M to obtain a matrix Q of a × a. If the data matrix M needs to be evenly divided into c partitions by column, you can set b to be an integer multiple of c through parameter settings.

·Random partition method

Randomly extract data in column c from the data matrix M, and record their column serial numbers, splicing the extracted data in column c according to the column serial numbers in the data matrix M to obtain a matrix P of a×c, and the remaining data according to the data matrix M The column numbers in s are concatenated to obtain a matrix Q of a×a.

S103: Partition encryption:

The matrix P and the matrix Q are encrypted by different methods, and the encrypted matrix P' and matrix Q' are obtained.

In practical application, the encryption method can be selected according to actual needs. In this embodiment, a chaos-based partition encryption method is proposed, and the specific method is as follows:

Generate four chaotic sequences X, Y, Z, U, where the length of the chaotic sequence X is a, the length of the chaotic sequence Y is c, and the lengths of the chaotic sequences Z and U are a. The matrix P' is obtained by encryption, and the matrix Q' is obtained by encrypting the matrix Q by using the chaotic sequences Z and U.

The generation method of the chaotic sequence can be selected as required. In this embodiment, a 4D hyper-chaotic system is used to generate the chaotic sequence. In practice, a low-dimensional chaotic system can also be used to run multiple times to generate 4 chaotic sequences. The 4D hyperchaotic system can be expressed by the following formula:

δ为产生数字混沌序列的参数，x、y、z、u分别为变量，

分别为混沌系统的输出。Among them, γ, μ, ε,

δ is the parameter to generate the digital chaotic sequence, x, y, z, u are variables respectively,

are the outputs of the chaotic system, respectively.

在混沌序列

中截取长度为a的序列作为混沌序列X，在混沌序列

中截取长度为c的序列作为混沌序列Y，在混沌序列

中截取长度为a的序列作为混沌序列Z，混沌序列

中截取长度为a的序列作为混沌序列U。Set parameters to ensure that the system works in a good chaotic state. In this embodiment, input the initial values of chaotic sequence x ₀ , y ₀ , z ₀ , u ₀ , and use Runge-Kutta in MATLAB The algorithm solves the above differential equation to get the chaotic sequence

in chaotic sequence

intercept the sequence of length a as the chaotic sequence X, in the chaotic sequence

intercept the sequence of length c as the chaotic sequence Y, in the chaotic sequence

intercept the sequence of length a as the chaotic sequence Z, the chaotic sequence

The sequence of length a is intercepted as the chaotic sequence U.

As far as the specific encryption method is concerned, it can also be selected as required, and the encryption methods of the two matrices will be described in detail below.

Matrix P encryption:

和

表示排列后序号为i的元素在原混沌序列X中的序号，i＝1,2,…,a，

表示排列后序号为j的元素在原混沌序列Y中的序号，j＝1,2,…,c。采用索引向量D_X对矩阵P进行行扰乱，即将第

行数据移动至第i行，然后采用索引向量D_Y对经行扰乱处理后的矩阵进行列扰乱，即将第

列数据移动至第j列，得到矩阵P′。Arrange the elements in the chaotic sequence X and Y respectively to get the index vector

and

Indicates the sequence number of the element with sequence number i in the original chaotic sequence X, i=1,2,...,a,

Represents the sequence number of the element with sequence number j in the original chaotic sequence Y, j=1,2,...,c. Use the index vector D _X to scramble the matrix P, that is, the first

The row data is moved to the ith row, and then the index vector D _Y is used to perform column scramble on the matrix after row scramble processing.

The column data is moved to the jth column, and the matrix P' is obtained.

The arrangement method can be set according to actual needs, and an arrangement method based on a quick sort algorithm is adopted in this embodiment. The arrangement method based on the quick sort algorithm can be briefly described as follows: First, determine the critical point C, the midpoint of the data is the critical point C, and the value of this point is used as the arrangement benchmark. Do not change the position of the critical point C first, place the data smaller than the critical point C in front of the critical point, and place the data larger than the critical point C behind the critical point, and then place the adjacent point C at the front of the sequence to complete the data arrangement. If the row sequence is {0.8, 0.6, 0.5, 0.1, 0.7, 0.3}, and 0.5 is selected as the critical point, after scrambling with this scheme, the sequence becomes {0.5, 0.1, 0.3, 0.8, 0.6, 0.7}, then according to This resulting index vector changes from [1 2 3 4 5 6] to [34 6 12 5]. Assuming row shuffling with this index vector, the data in row 3 is placed in row 1, the data in row 4 is placed in row 2, and so on.

Matrix Q encryption:

For the encryption of the matrix Q in this embodiment, the chaotic sequences Z and U are used to generate a reconfigurable matrix based on discrete Fourier transformation (Discrete Fourier Transformation, DFT), and the matrix Q is implemented by precoding.

Let F be a standard DFT matrix of a × a whose expression is as follows:

Among them, F _{α, β} represent the elements of the standard DFT matrix F, α, β represent the row number and column number of the element, respectively, α, β=0,1,...,a-1.

Let F' be a DFT-based reconfigurable matrix of a × a, whose expression is as follows:

Among them, F' _{α, β} represent the elements of the DFT-based reconfigurable matrix F', Z[α] represents the α-th element in the chaotic sequence Z, and U[β] represents the β-th element in the chaotic sequence U.

The matrix Q is precoded by the DFT-based reconfigurable matrix F′, which can be expressed by the following formula:

Q'=F'·Q

where · represents the dot product of the matrix.

In practical applications, since the elements in the chaotic sequences Z and U have many digits after the decimal point, it is not easy to calculate, and in order to improve the randomness of the elements, the chaotic sequences Z and U can also be preprocessed, and the preprocessing can be expressed by the formula as follows:

Among them, k represents the number of digits after the decimal point, k=1,2,…,K, K is set according to actual needs, ω[α] _k represents the kth number after the decimal point of the αth element in the original chaotic sequence Z, υ[ β] _k represents the kth digit after the decimal point of the βth element in the original chaotic sequence U, and λ _k and ρ _k represent the coefficients corresponding to the kth digit after the decimal point when the chaotic sequences Z and U are preprocessed respectively. Generally speaking , λ _k and ρ _k are integers, which can be set according to actual needs.

S104: Encrypted information synthesis:

According to the inverse method of partition division in step S102, the matrix P' and the matrix Q' are restored into a matrix M', which is the encrypted matrix.

Taking a=120, b=200, c=80, d=10, e=20, f=8, and g=5 in this embodiment as an example for illustration: divide the matrix P' and matrix Q' into equal columns respectively. The method is divided into 10 partitions, and then based on matrix Q', the 8-column data of partition ① in matrix P' is inserted between the 4th and 5th columns of partition ① in matrix Q', and so on. Finally, the encrypted data matrix M' is obtained.

Generally speaking, the size of the key space can be used to quantitatively evaluate the robustness of the encryption scheme. The larger the key space, the stronger the ability of the encryption algorithm to resist exhaustive attacks. For the present invention, different partition parameters d and g will generate key spaces of different sizes, and selecting optimal d and g values will result in a larger key space.

Taking the parameters in this embodiment as an example, the size of the key space obtained based on a chaotic physical layer security access method of the present invention is 13×120! ×80! ×10 ¹⁵ ×10 ¹⁵ ×10 ¹⁵ ×10 ¹⁵ to 10 ³⁷⁹ . Among them, 13 represents the number of ways to take 8 columns of continuous data, 120! ×80! It represents the key space generated by independent row and column scrambling of matrix P, and the conservative key space provided by each chaotic sequence is 10 ¹⁵ . It can be seen that the present invention has good performance in key space.

S105: Data sending:

The sending end performs subsequent processing on the matrix M' and sends it. The specific processing process of data transmission can be set according to actual needs. At present, the common processing process of OFDM-PON is as follows:

Step 1: The matrix M' is transformed by Hermitian conjugate to obtain a conjugate matrix M" of the same size.

Step 2: Arrange the matrices M' and M" in rows, that is, the data of the matrix M' is arranged in the first row a, the data of the matrix M" is arranged in the last row a, and then fill the B-2a row with all zero data to obtain the matrix N . Wherein, B represents the number of rows of an Inverse Fast Fourier Transform (IFFT) matrix. At this time, the number of subcarriers is extended from 2a to B, and the OFDM symbol matrix N is converted from the frequency domain to the time domain by using the inverse fast Fourier transform method, and the matrix N' is obtained.

The third step: After the parallel/serial (P/S) conversion of the matrix N', the data sequence becomes a row vector of 1 row B×b column.

The fourth step: adding a cyclic prefix (Cyclic Prefix, CP).

S106: Receive decryption:

After the receiving end receives the transmitted data, it analyzes and obtains the matrix M'. The analysis process includes de-CP, serial/parallel (S/P) conversion, fast Fourier transform (FFT) processing and sub-carrier allocation, and the matrix M' can be extracted. Then, according to the partitioning method in step S102, the matrix M' is divided to obtain the matrix P' and the matrix Q'. Obviously, the sender and the receiver need to share the partition division and the relevant parameters of the chaotic system in advance to achieve decryption. Then the corresponding decryption method is used to decrypt the matrix P' and the matrix Q' respectively to obtain the matrix P and the matrix Q, and then the reverse method of partition division is used to restore the matrix M.

FIG. 3 is a flow chart of data transmission and reception decryption in this embodiment. As shown in Figure 3, matrix division, partition encryption, and matrix reorganization are the process of data matrix partition division and encryption in the present invention, and matrix division, partition decryption, and matrix reorganization are the data decryption process in the present invention.

As far as the encryption method based on chaos adopted in this embodiment is concerned, the same chaotic system and initial value of chaotic sequence are used to generate 4 chaotic sequences X, Y, Z, U during decryption, and then the chaotic sequences X and Y are respectively analyzed. Arrange the elements of , to obtain two index vectors, and recover the row and column disturbances of the matrix P' according to the index vectors. If the row index vector obtained according to the chaotic sequence X is [3 4 6 1 2 5], it means that the data in the first row in the current matrix P' should be located in the third row in the original matrix P, and the second row in the current matrix P' The data for the row should be in row 4 in the original matrix P, and so on.

Then the chaotic sequence Z, U is used to generate the matrix F", and its expression is as follows:

Among them, F″ _{α, β} represent the elements of the matrix F″. F"·F'=E, where E represents the identity matrix.

The decryption process is to multiply the square matrix Q' precoded by the matrix F' with the matrix F". The decryption expression is as follows:

F″·Q′=F″·F′·Q=Q

Although the illustrative specific embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, As long as various changes are within the spirit and scope of the present invention as defined and determined by the appended claims, these changes are obvious, and all inventions and creations utilizing the inventive concept are included in the protection list.

Claims (6)

1. a chaotic physical layer security access method, is characterized in that, comprises the following steps: S1: The data matrix M of a×b is obtained by subcarrier allocation of the OFDM signal modulated by QAM, where a represents the number of subcarriers of an OFDM signal, b represents the number of symbols in a single subcarrier, a<b; S2: Partition the matrix M to obtain the matrix P and the matrix Q. The specific method of partitioning is as follows: Calculate the total number of columns c=b-a of the data extracted from the data matrix M, extract the data in column c from the data matrix M according to the predetermined partition rule, and splicing the data in the c column according to the column number in the data matrix M to obtain a × c The matrix P of , the remaining data is spliced according to the column number in the data matrix M to obtain a matrix Q of a × a; S3: Based on the chaotic system, the matrix P and the matrix Q are encrypted in different ways to obtain the encrypted matrix P' and the matrix Q'; the encryption methods of the matrix P and the matrix Q are as follows: Generate four chaotic sequences X, Y, Z, U, where the length of the chaotic sequence X is a, the length of the chaotic sequence Y is c, and the lengths of the chaotic sequences Z and U are a. The matrix P' is obtained by encryption, and the matrix Q is encrypted by using the chaotic sequences Z and U to obtain the matrix Q'; Among them, the encryption method of the matrix P is as follows: Arrange the elements in the chaotic sequences X and Y respectively to obtain the index vector

and

Indicates the sequence number of the element with sequence number i in the original chaotic sequence X, i=1,2,...,a,

Represents the sequence number of the element with sequence number j in the original chaotic sequence X after arrangement, j=1,2,...,c; the matrix P is scrambled by the index vector D _X , that is, the first

The row data is moved to the ith row, and then the index vector D _Y is used to perform column scramble on the matrix after row scramble processing.

The column data is moved to the jth column, and the matrix P' is obtained; The encryption method of matrix Q is as follows: First, the chaotic sequences Z and U are preprocessed by the following methods:

Among them, k represents the number of digits after the decimal point, k=1,2,…,K, K is set according to actual needs, ω[α] _k represents the kth number after the decimal point of the αth element in the original chaotic sequence Z, υ[ β] _k represents the kth digit after the decimal point of the βth element in the original chaotic sequence U, and λ _k and ρ _k represent the coefficients corresponding to the kth digit after the decimal point when the chaotic sequences Z and U are preprocessed respectively; The chaotic sequence Z, U is used to generate a DFT-based reconfigurable matrix F', and its expression is:

Among them, F' _{α, β} represent the elements of the DFT-based reconfigurable matrix F', α, β represent the row number and column number of the element, respectively, α, β=0,1,...,a-1, Z[α ] represents the αth element in the chaotic sequence Z, and U[β] represents the βth element in the chaotic sequence U; The matrix Q' is calculated by the following formula: Q'=F'·Q S4: According to the inverse method of partition division in step S2, the matrix P' and the matrix Q' are restored into a matrix M'; S5: The sender performs subsequent processing on the matrix M' and sends it; S6: After the receiving end receives the transmitted data, it analyzes and obtains the matrix M', and then divides the matrix M' according to the partitioning method in step S2 to obtain the matrix P' and the matrix Q', and then uses the corresponding decryption method to decipher the matrix respectively. Decrypt P' and matrix Q' to obtain matrix P and matrix Q, and then use the reverse method of partition division to restore matrix M. 2 . The chaotic physical layer secure access method according to claim 1 , wherein the parameters a and b satisfy the following relationship: b/5≤b-a≤4b/5. 3 . 3. chaotic physical layer security access method according to claim 1, is characterized in that, in described step S2, partition is divided and adopts adjacent partition method, and concrete method is: make the number of partitions d of data matrix M be parameter b and The common divisor of c, the data matrix M is divided into d partitions on average by column, and the continuous f-column data is extracted from the same position in each partition, f=c/d, and the starting column of the f-column data is in the partition. The column serial number in the data matrix is g, and the extracted data in column c is spliced according to the column serial number in the data matrix M to obtain a matrix P of a × c, and the remaining data is spliced according to the column serial number in the data matrix M to obtain a matrix Q of a × a . 4. The chaotic physical layer security access method according to claim 1, characterized in that, in the step S2, the partition division adopts the staggered partition method, and the specific method is: the data matrix M is divided into c partitions by column, wherein The number of columns for a single partition of the first c-1 partitions is

Indicates rounding down, the number of columns in the c-th partition is b-(c-1)d, and 1 column of data is extracted from the same position in each partition, and the extracted data in column c is based on the data in the data matrix M. The column number is spliced to obtain a matrix P of a × c, and the remaining data is spliced according to the column number in the data matrix M to obtain a matrix Q of a × a. 5. The chaotic physical layer security access method according to claim 1, wherein in the step S2, the partitioning adopts a random partitioning method, and the specific method is: randomly extracting the data of column c in the data matrix M, and Record their column numbers, splicing the extracted c-column data according to the column numbers in the data matrix M to obtain an a×c matrix P, and splicing the remaining data according to the column numbers in the data matrix M to obtain a×a matrix Q. 6. The chaotic physical layer security access method according to claim 1, wherein the 4 chaotic sequences are generated by using a 4D hyperchaotic system.

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