CN105846947B - A kind of encryption in physical layer method introducing Latin battle array - Google Patents

Abstract

The present invention relates to a kind of encryption in physical layer methods introducing Latin battle array.Key of good performance is generated using chaos system and Latin battle array; then key scramble planisphere is utilized; the distribution of the constellation point of different modulating mode on a complex plane is set to tend to be uniform; and then personal characteristics parameter possessed by different modulating mode tends to be identical, achievees the purpose that set about protecting modulation system and modulation intelligence from physical layer.Complex plane information after mapping is made full use of, achievees the purpose that greatly extended secret key space.By introducing Extract functions, the relevance between chaos sequence is fully eliminated, under the premise of ensureing key space and a large amount of keys need not be generated, substantially reduce hardware realization complexity, and NIST Randomness tests are carried out to the key of generation, verify its unpredictability.

Description

A Physical Layer Encryption Method Introducing Latin Matrix

technical field

The invention relates to a physical layer encryption method, in particular to a physical layer encryption method based on Latin matrix and amplitude-to-phase transformation.

Background technique

With the increasing degree of informatization in today's society, traditional business activities, transaction processing, and government services have been increasingly implemented and provided through open computer and communication networks, especially tools based on the World Wide Web. Information security It has become an important guarantee condition for people to survive and develop in the information space. From the perspective of security, the main characteristics of information security include confidentiality, integrity, authentication and non-repudiation. At this stage, ensuring information security based on cryptography is still the main security strategy. But in the communication network, the upper layer encryption mechanism based on traditional cryptography faces some new challenges.

The flat development of wireless mobile communication systems, the open nature of wireless links, the dynamic topology of mobile networks, and the miniaturization of nodes have brought some new challenges to the traditional security strategies based on cryptography for encryption at the upper communication layers such as the link layer. On the one hand, the rapid development of supercomputers makes it possible for the traditional encryption mechanism based on large calculations to be deciphered; the idea of increasing the key length and expanding the key space to resist exhaustive cracking will be affected by key management and broadband transmission. System high transfer rate limitation. On the other hand, with the rapid development of cognitive radio technology, eavesdroppers can use some eavesdropping techniques to intercept information that is not protected by traditional security strategies such as the frequency, bandwidth, and modulation mode of wireless channels.

Based on the current situation of the above-mentioned communication network, some eavesdropping behaviors have gradually evolved into the fact that the eavesdroppers do not steal information that is difficult to decipher, such as communication data, but instead use unprotected physical layer information to eavesdrop on who the two communication parties are, their respective geographical locations, etc. Information that is relatively less difficult to decipher is called a traffic analysis attack (Traffic analysis attack). Although the information stolen by eavesdroppers through traffic analysis attacks is not communication data, it can reflect the communication status, which still poses a great threat in military communication. Therefore, how to ensure the security of the modulation mode and modulation information at the physical layer has become an important aspect in the current research on the security of mobile communications.

There are two main directions to achieve communication security from the physical layer. One is to use the physical characteristics of the wireless channel to generate, manage and distribute keys and physical layer authentication based on the wireless channel; the other is to use the physical layer security based on the eavesdropping channel model. That is, the concept of secrecy capacity proposed by Wyner based on Shannon information theory. The physical layer security technology based on secret capacity requires that the channel quality of the main channel is better than that of the eavesdropping channel, and there is a secret code that not only ensures the reliable communication of legitimate users, but also makes it impossible for eavesdroppers to obtain information, so that secret communication can be realized without the use of keys The purpose, including physical layer security transmission technologies such as artificial noise and beamforming. But this kind of physical layer security technology based on information theory depends on channel information, and the security cannot be guaranteed when the eavesdropper and legitimate party have similar channels. Therefore, at the physical layer, the present invention proposes an encryption method that utilizes a Latin matrix and a chaotic sequence to scramble a constellation diagram based on a chaotic system.

Contents of the invention

The technical problem to be solved by the present invention is to provide a key with good performance using the chaotic system and the Latin matrix, and then use the key to scramble the constellation diagram, so that the distribution of the constellation points of different modulation methods on the complex plane tends to be uniform, Furthermore, the individual characteristic parameters of different modulation methods tend to be the same, so as to achieve the purpose of protecting the modulation method and modulation information from the physical layer. In order to solve the above problems, the present invention proposes a physical layer encryption method combining Latin matrix and amplitude-phase transformation, and generates a key set through a chaotic system to achieve the purpose of encrypting a constellation diagram.

The physical layer encryption algorithm includes:

S1: Set various parameters of the system: carrier frequency, modulation mode, etc.;

S2: The system inputs the binary information sequence, converts it into a complex vector C through serial-to-parallel transformation and constellation mapping, where C=[c ₁ ,c ₂ ,c ₃ ,…c _n ] ^T , where [] ^T represents the transformation of the matrix Set, then obtain the information to be encrypted plain_data, wherein plain_data=C;

S3: Use the chaotic sequence to generate the key set {K1, K2, Latin matrix}, add K1 to the phase of the information to be encrypted plain_data to obtain the ciphertext E1; use K2 to multiply the corresponding elements of the ciphertext E1 to obtain the ciphertext E2 ; Finally, according to the element values in the Latin matrix, the ciphertext E2 is transformed accordingly to obtain the final ciphertext E;

The generation process of the key set {K1, K2, Latin matrix} is as follows:

1) Select a chaotic system and initial value start_data to generate chaotic sequence x _i ;

2) Although the chaotic sequence has long-term unpredictable characteristics, its short-term behavior has a certain correlation. To solve this problem, this paper introduces the Extract function and the Latin matrix, and innovates in the key generation and the construction of the Latin matrix to achieve complex control Under the premise of high degree, further improve the security;

_Dxi = mod(Extract( _xi ,12,13,14),256)/512

The Extract function is to extract the 12th, 13th, and 14th digits of the decimal part of the input value x _i , so as to obtain good unpredictability of the key. According to the above formula, a group of random data D _xi between [0, 0.5] can be obtained, and the key K1 for phase rotation can be obtained from K1=D _xi ×4π and K2=D _xi +0.75 (0≤K1≤ 2π) and the key K2 for amplitude transformation (0.75≤K2≤1.25);

3) In order to eliminate the correlation between the data, _xi is processed as follows to obtain _yi ;

y _i =10 ⁶ x _i -floor(10 ⁶ x _i )i=1,2...n

Arrange y _i in ascending order to obtain the arrangement information of y _i corresponding to serial number i, which is the Latin matrix. The main feature of the Latin matrix is that the elements of each row or column are randomly distributed from 1 to the number of rows or columns of the matrix;

S4: Parallel-to-serial conversion is performed on the ciphertext E, and then processed by D/A conversion, and sent to the wireless channel for transmission;

The physical layer decryption method is the reverse process of the encryption method. The last encrypted one is decrypted first, and the original plaintext information is obtained by decrypting layer by layer.

Adopting the above-mentioned technical solution, the beneficial effect of the present invention is: the essence of modulation is to map information from the binary bit field to the complex field, this process brings some redundant information, and the traditional encryption method does not make full use of the additional information brought by the mapping . The algorithm proposed in this paper makes full use of the mapped complex plane information to greatly expand the key space. By introducing the Extract function, the correlation between chaotic sequences is fully eliminated. On the premise of ensuring the key space without generating a large number of keys, the complexity of hardware implementation is greatly reduced, and the generated keys are tested for NIST randomness. , verifying its unpredictability. Introduce the Latin matrix, completely disrupt the coordinate information of the constellation points, and analyze the security of this algorithm from the aspects of key space, key sensitivity and identification modulation mode. The analysis results show that this algorithm has a large key space , nearly impossible to brute force. The algorithm has strong security under the premise of requiring little additional calculation, and has broad application prospects in the secure transmission of physical layer.

Description of drawings

Fig. 1 is the flow chart of the physical layer encryption method that the Latin matrix proposed by the present invention combines with amplitude-phase transformation;

Figure 2 is a constellation diagram before encryption at the sending end;

Figure 3 is a constellation diagram after encryption at the sending end;

Fig. 4 is a legal person constellation diagram;

Fig. 5 is the eavesdropper constellation diagram;

Fig. 6 is when the legitimate person and the eavesdropper's key difference are very small, the comparison chart of the bit error rate;

Fig. 7 is before and after applying the present invention, bit error rate comparison chart;

Fig. 8 is a comparison chart of the success rate based on the high-order cumulant recognition algorithm.

Detailed ways

The present invention is further described by examples below, but it should be noted that the purpose of announcing the embodiments is to help further understand the present invention, but those skilled in the art can understand: without departing from the spirit of the present invention and the appended claims Various substitutions and modifications are possible within the scope. Therefore, the present invention should not be limited to the content disclosed in the examples, and the protection scope of the present invention is subject to the scope defined in the claims.

The technical scheme of the present invention is, on the OFDM system, a kind of constellation scrambling method that introduces Latin matrix, the concrete sending end encryption process comprises the following steps:

S1: Set various parameters of the system: number of subcarriers N, cyclic prefix CP, modulation mode, etc.;

S2: The system inputs the binary information sequence, converts it into a complex vector C through serial-to-parallel transformation and constellation mapping, where C=[c ₁ ,c ₂ ,c ₃ ,…c _n ] ^T , where [] ^T represents the transformation of the matrix Set, then obtain the information to be encrypted plain_data, wherein plain_data=C;

S3: Use the chaotic sequence to generate the key set {K1, K2, Latin matrix}, add K1 to the phase of the information to be encrypted plain_data to obtain the ciphertext E1; use K2 to multiply the corresponding elements of the ciphertext E1 to obtain the ciphertext E2 ; Finally, according to the element values in the Latin matrix, the ciphertext E2 is transformed accordingly to obtain the final ciphertext E; the key set generation process is as follows:

1) Select a chaotic system and initial value start_data to generate chaotic sequence x _i ;

2) Although the chaotic sequence has long-term unpredictable characteristics, its short-term behavior has a certain correlation. To solve this problem, this paper introduces the Extract function and the Latin matrix, and innovates in the key generation and the construction of the Latin matrix to achieve complex control Under the premise of high degree, further improve the security;

_Dxi = mod(Extract( _xi ,12,13,14),256)/512

The Extract function is to extract the 12th, 13th, and 14th digits of the decimal part of the input value x _i , so as to obtain good unpredictability of the key. According to the above formula, a group of random data D _xi between [0, 0.5] can be obtained, and the key K1 for phase rotation can be obtained from K1=D _xi ×4π and K2=D _xi +0.75 (0≤K1≤ 2π) and the key K2 for amplitude transformation (0.75≤K2≤1.25);

3) In order to eliminate the correlation between the data, _xi is processed as follows to obtain _yi ;

y _i =10 ⁶ x _i -floor(10 ⁶ x _i ) i=1,2…n

Arrange y _i in ascending order to obtain the arrangement information of y _i corresponding to serial number i, which is the Latin matrix. The main feature of the Latin matrix is that the elements of each row or column are randomly distributed from 1 to the number of rows or columns of the matrix.

The coordinate information after amplitude-phase transformation is scrambled by Latin matrix. The scrambling process takes the following matrix as an example: matrix A is the plaintext matrix, matrix B is the Latin matrix, and matrix C is the ciphertext after the Latin matrix is scrambled. For each element of the plaintext array A, the corresponding element value of the Latin array B is the transformation of the corresponding element, such as B (2,1)=4 in the Latin array B, then the A (2,4) element in the matrix A Put in C(2,1), so that each line is transformed in turn to obtain the ciphertext array C;

plaintext array to be encrypted

latin matrix

Ciphertext matrix encrypted by Latin matrix

S4: Carry out parallel-to-serial conversion on the ciphertext E, and then send it to the wireless channel for transmission after processing such as adding pilot frequency, peak-to-average ratio reduction, cyclic prefix, and D/A conversion.

The following is a theoretical analysis of the anti-attack capability of the algorithm of the present invention:

Cryptographic Characteristic Test of A Chaotic Sequence as Key

The chaotic sequence can be used as a key, which must meet the randomness requirements of cryptography for keys. In this paper, the binary quantization method is used to quantify the generated chaotic sequence, and then the NIST randomness test is carried out to test its unpredictability;

The NIST test is a set of standards for testing randomness that includes 16 indicators developed by the National Institute of Standards and Technology. This standard compares the degree of deviation between the detection sequence and the ideal random sequence from different angles through different indicators. The results of each indicator in this standard are reflected by the P-value of each indicator obtained through a certain test algorithm as the test result. P-value∈[0,1], if P-value≥0.01, the test is passed, and the larger the P-value, the better the pseudo-randomness of the tested sequence. The following table shows the NIST test results of the quantized chaotic key sequence. This test selects several typical indicators, and it can be seen that all the P-value values meet the randomness standard, that is, the key generated by the chaotic sequence meets the good of unpredictability.

Table 1 Chaotic sequence NIST test results

B key sensitivity analysis

A perfect encryption algorithm should have strong key sensitivity, that is, when the eavesdropper's key is very slightly different from the legal key, the eavesdropper cannot recover the source information. In the algorithm proposed in this paper, when the legal key K1 is [1,1,1], and the Eve key is [1,1,1+1×10 ^-14 ], the constellation diagram and erroneous Bit rate comparison diagrams are shown in Figures 6, 7, and 8 respectively. Similarly, it can be obtained that the key accuracy when generating the Latin matrix is 10 ^-8 . Even if the key difference is small, the eavesdropper cannot get any valuable information, so the key has strong sensitivity;

C key space analysis (calculation analysis)

In the face of brute-force attack, the key used for information encryption should have a large enough key space. Considering that the amplitude transformation only confuses the shape of the constellation diagram, but does not change the quadrant where the constellation points are located in the complex domain, the amplitude transformation key K2 does not participate in the key space analysis. Assume that the value range of the key is (0,20], of course it is far beyond this range. Under the three-dimensional Lorentzian chaotic sequence, the key space is (3×20×10 ⁸ )×(3×20×10 ¹⁴ )= 3.6×10 ²⁵ . Taking a computer that operates 10 billion times per second as an example, if the eavesdropper deciphers one-third of the information, the eavesdropping is considered successful, and the time required for deciphering is 3.8×10 ⁷ years, which is far beyond the calculable time , it can be seen that the key space of the algorithm is very large, so it is very difficult to crack the key;

D modulation identification analysis

Modulation recognition based on reconstructed constellation diagrams. The k-means clustering algorithm is to select the cluster center, and the non-cluster center objects are divided into the cluster center with the highest similarity according to the similarity degree, and then take the average value of all objects to obtain a new cluster center. Continue in turn until the measure function converges. However, as shown in Figure 2, after this encryption algorithm, the constellation points are within the plane range, which basically conforms to random distribution, and the phase information of the constellation points is also irregular, which cannot match the constellation template of the existing modulation method. That is, the information cannot be recovered by reconstructing the constellation diagram.

Modulation Recognition Based on Higher Order Cumulants

Higher order statistics are abbreviated as HOS (Higher order statics), which are mainly used for digital signal modulation identification. Using the absolute value of the high-order cumulant can eliminate the influence of phase jitter; using its ratio as the identification parameter can also eliminate the influence of the amplitude on the parameter. Compared with instantaneous statistics, high-order cumulants have good anti-fading properties; compared with high-order moments, they also have the advantage of suppressing Gaussian noise. The zero-mean stationary complex stochastic process is denoted as y(k), and its p-order mixed moment is defined as:

M _pq = E(y(k) ^(pq) y ^* (k) ^q )

Regarding the content of cumulants, here are the definitions of cumulants of each order used:

C ₂₀ =Cum(y(k),y(k))=M ₂₀

C ₂₁ =Cum(y(k),y ^* (k))=M ₂₁

C ₄₀ =Cum(y(k),y(k),y(k),y(k))=M ₄₀ -3(M ₂₀ ) ²

Under the conditions of no noise, equal probability of symbol emission, and normalized average power, the theoretical values of high-order cumulants under different modulation modes are obtained, as shown in the table below. To remove the effect of phase jitter, the absolute value of the higher-order cumulant is used. Where E is the average signal power;

Table 2 Theoretical values of higher order cumulants

Using the above table to construct the MPSK signal characteristic invariant F _M can be used to identify the modulation mode:

From the theoretical value of formula (10), the modulation mode judgment standard can be obtained, as shown in formula (11):

Under different signal-to-noise ratios, 500 independent simulations were carried out, and the recognition success rate under this judgment standard is shown in Figure 8. It can be seen that the identification method based on the high-order cumulant can effectively identify the unencrypted modulation mode, and when the signal-to-noise ratio is greater than 4dB, the success rate of identifying the unencrypted modulation mode is as high as 95%. However, the recognition success rate of this algorithm has been lower than 5%. It can be seen that without the correct key, the recognition method based on high-order cumulants cannot recognize the modulation method encrypted by this algorithm. That is to say, the algorithm in this paper has a strong anti-identification advantage.

Below is the explanation to Fig. 1 encryption algorithm flowchart of the present invention:

This encryption algorithm is carried out on the constellation diagram after constellation mapping, and transforms the constellation diagram in the complex plane by using the chaotic sequence and the Latin matrix. Make full use of the redundant information brought by constellation mapping to expand the key space and achieve the purpose of secure communication.

The following is an analysis of the constellation diagram corresponding to the sending and receiving ends in Figure 2 and the bit error rate comparison chart in Figure 6 and 7

Figure 2 is a constellation diagram of the legal receiver and the eavesdropping terminal before and after encryption of the legal transmitter. Due to the sensitivity of the chaotic system to the initial value, that is, even if the initial value is set with a small difference, the results obtained after the long-term evolution of the chaotic system are completely different. Here, the key used by the eavesdropper is only ^10-14 different from the correct key, and the obtained constellation diagram does not show which modulation method it is, and the corresponding bit error rate is always around 0.5. However, the legal receiver with the correct key can recover the constellation information very well, and the bit error rate does not deteriorate significantly, which plays a very good encryption effect.

FIG. 8 is a comparison chart of the success rate of identifying modulation schemes using high-order cumulants. It can be seen from the figure that the recognition algorithm based on high-order cumulants is basically invalid for the information encrypted by this algorithm, and the recognition success rate is less than 5%, which can be considered as unrecognizable.

The above description is only one embodiment of the present invention, the present invention is not limited to the above embodiment, there may be local slight structural changes in the implementation process, if the various changes or modifications of the present invention do not depart from the spirit of the present invention and scope, and belong to the claims and equivalent technical scope of the present invention, the present invention also intends to include these changes and modifications.

Claims (1)

1. a kind of encryption in physical layer method introducing Latin battle array generates key set by chaos system, reach encryption planisphere Purpose, which is characterized in that the encryption in physical layer method is as follows：

S1：The various parameters of setting system：Such as carrier frequency, modulation system；

S2：System input binary information sequence is converted to complex vector located C, wherein C=[c through serial to parallel conversion, constellation mapping₁, c₂,c₃,…c_n]^T, wherein []^TIt indicates to the transposition of matrix, then to obtain confidential information plain_data to be added, wherein plain_data =C；

S3：Key set { K1, K2, Latin battle array } is generated using chaos sequence, with the phase of K1 and confidential information plain_data to be added It is added, obtains ciphertext E1；It is multiplied with ciphertext E1 corresponding elements with K2, obtains ciphertext E2；Finally according to the element value in Latin battle array, Ciphertext E2 is accordingly converted, final ciphertext E is obtained；

S4：Parallel serial conversion is carried out to ciphertext E, then through D/A conversion process, is sent into wireless channel and transmits,

Physical layer decryption method is the inverse process of encryption method, it is last it is encrypted decrypt at first, decrypted layer by layer one by one to get to original Beginning cleartext information；

The generating process of the key set { K1, K2, Latin battle array } is as follows：

1) a kind of chaos system of selection and initial value start_data, generate chaos sequence x_i；

2) Extract functions and Latin battle array are introduced,

D_xi=mod (Extract (x_i, 12,13,14), 256)/512

Wherein Extract functions are to extract input value x_i12nd, 13,14 data of fractional part, can not be pre- with obtain key The property surveyed, according to above formula, obtains one group of random data D between [0,0.5]_xi, by K1=D_xi× 4 π and K2=D_xi+0.75 Obtain the key K2 (0.75≤K2≤1.25) converted for the key K1 (π of 0≤K1≤2) and amplitude of phase place；

3) it is the correlation eliminated between data, to x_iIt is handled as follows to obtain y_i

y_i=10⁶x_i-floor(10⁶x_i) i=1,2 ... n

To y_iAscending order arrangement is carried out, obtains y_iThe arrangement information of corresponding serial number i, as Latin battle array, Latin battle array are every a line or every The element of one row is 1 to matrix line number or the random distribution of columns.