Key Generation Method Based on Space-Filling Curve Mapping and Nonlinear Correlation Matching

Abstract

The present application discloses a key generation method based on space-filling curve mapping and non-linear correlation matching, which relates to the technical field of physical layer security. The present application generates keys through steps such as channel detection and synchronous ciphertext transmission, distribution transformation of the collected channel sample sequence, index mapping based on space-filling curve, segmented random non-linear transformation and permutation, and segmented matching based on non-linear correlation measurement; among them, channel detection and synchronous ciphertext transmission collect channel sample sequences by terminals exchanging detection packets, and synchronously transmit encrypted data to improve communication efficiency; distribution transformation is used to convert the channel sample sequence with normal distribution into a two-dimensional channel sample sequence with uniform distribution, making the distribution of its channel samples more dispersed, which is convenient for subsequent generation of a more uniform index mapping; segmented matching performs segmented matching by measuring the non-linear correlation between each index segment to enhance the robustness of the matching and improve the accuracy and generation rate of key generation.

Description

Technical Field

[0001] The present application relates to the field of physical layer security technology, and in particular to a key generation method based on space filling curve mapping and nonlinear correlation matching. Background Art

[0002] With the rapid development and widespread deployment of new generation wireless communication technologies such as B5G (Beyond 5G), 6G and satellite communications, these technologies have become an important strategic support for promoting industrial control innovation, industrial transformation and national security. Although wireless networks provide the advantages of low cost and high bandwidth for data communication, the complex wireless environment brings complex coupling of spectrum, intelligent interference forms and diverse security threats, such as eavesdropping, signal interference, data injection, man-in-the-middle attacks, etc., which seriously threaten users' property safety and privacy protection. Therefore, with the widespread application of wireless communication technology in people's lives, facing the increasingly complex wireless environment and escalating security challenges, wireless communication security issues have become a key issue that needs to be solved urgently.

[0003] Traditional encryption schemes usually rely on pre-shared information to generate keys to prevent illegal access by malicious devices. However, the application of these methods in wireless environments is limited due to the inadequate key management infrastructure and limited mobile device resources. In particular, with the development of quantum computing technology, quantum algorithms pose a serious challenge to traditional public key encryption schemes. Therefore, in view of the limitations and potential threats of traditional encryption schemes, wireless communication security technology is urgently needed as an important support and effective supplement.

[0004] In order to overcome the shortcomings of traditional encryption schemes, in recent years, researchers have explored physical layer security technologies that use the inherent physical characteristics of wireless channels and wireless devices to ensure communication security. Physical layer security technology provides a new security guarantee for wireless communications by realizing functions such as information-theoretic security key generation, encrypted communication, and identity authentication. As a core component of this system, physical layer key generation uses the time-varying and reciprocal properties of wireless channels to generate shared keys between the communicating parties to support encrypted communication. Unlike traditional encryption methods, physical layer key generation relies on the channel itself, avoiding key distribution and management issues, and does not require a large amount of computing resources, thereby reducing the network burden. Therefore, physical layer key generation is particularly suitable for distributed, heterogeneous wireless networks, providing effective support for resource-constrained wireless devices and diverse network environments.

[0005] Traditional physical layer key generation methods usually use quantization algorithms to convert channel samples into initial key bits. However, due to the asynchrony during channel probing by half-duplex devices and the interference of environmental noise, the channel sample sequences of the two communication parties may lose correlation, resulting in quantization inconsistency. This problem has prompted researchers to propose matching-based key generation methods in recent years. These methods randomly permute the channel sample sequences, measure the similarity between channel samples to establish matches, and derive random permutation sequences for key generation based on the matching relationships. However, most matching-based key generation methods rely only on the single-dimensional features of the channel sample sequences and measure the similarity of channel samples through distance metrics, which often leads to a reduction in the robustness of sample matching, thus affecting the performance of key generation in complex wireless environments. For example, in a quasi-static or slowly varying channel environment, the statistical characteristics of local channel samples may be highly similar, resulting in ambiguity during the matching process and thus affecting the accuracy of key generation. In addition, in high-noise scenarios, outliers may appear in the channel sample sequences, thereby impairing the channel reciprocity on which physical layer key generation depends, greatly affecting the reliability of distance metrics, and ultimately leading to a decrease in the consistency of matching and key generation.

[0006] Therefore, how to extract the multi-dimensional features of the channel sample sequences and perform channel sample matching based on these features to enhance the reliability of channel sample matching has become the key to improving the consistency and robustness of key generation. In addition, relying solely on traditional distance metric-based matching methods may not be able to effectively handle complex wireless environments. To solve this problem, non-linear transformation of channel samples is required, and non-linear correlation measurement methods are used for sample matching, so as to ensure accurate and robust key generation in complex wireless environments. Summary of the Invention

[0007] In view of the deficiencies of the prior art, the present application provides a key generation method based on space-filling curve mapping and non-linear correlation matching, which uses steps such as channel probing and synchronous ciphertext transmission, adaptive segmented rearrangement optimization, random segmented non-linear transformation and permutation, and segmented matching based on non-linear correlation measurement for key generation to improve the accuracy and generation rate of key generation.

[0008] The technical solution adopted by the present application is as follows:

[0009] A key generation method based on space-filling curve mapping and non-linear correlation matching, the method comprising the following steps:

[0010] Step 1: Channel probing and synchronous ciphertext transmission;

[0011] Terminal A and Terminal B sample the channel between them to obtain the channel sample sequences of Terminal A and B;

[0012] Terminal A generates a random permutation sequence as the secret key, encrypts the plaintext with the secret key to generate the ciphertext, and synchronously transmits the ciphertext during channel probing;

[0013] Step 2: Terminal A / B respectively performs distribution transformation on its channel sample sequence;

[0014] Terminal A / B converts its channel sample sequence into a standard normal distribution to obtain the standardized channel sample sequence of Terminal A / B;

[0015] Then, based on the inverse process of the selected distribution transformation algorithm that follows a normal distribution, the standardized channel sample sequence of Terminal A / B is converted into a uniform distribution to obtain the two-dimensional channel sample sequence after conversion of Terminal A / B;

[0016] Step 3: Index mapping based on the space-filling curve;

[0017] Terminal A / B converts the two-dimensional channel sample sequence after conversion of Terminal A / B into the two-dimensional coordinate lattice sequence of Terminal A based on the common space-filling curve parameters, and then maps it to the one-dimensional space index to obtain the one-dimensional index sequence after mapping of A / B;

[0018] Step 4: Piecewise random non-linear transformation and permutation;

[0019] Terminal A uses the method of equal-length segmentation to perform fixed-length segmentation on the one-dimensional index sequence after mapping of Terminal A to obtain the index segmentation sequence of Terminal A, and performs random non-linear transformation on each index segmentation therein to obtain the index segmentation sequence after non-linear transformation of Terminal A;

[0020] Terminal A performs random permutation on the index segmentation sequence after non-linear transformation thereof based on the random permutation sequence generated in Step 1 to obtain the index segmentation sequence after permutation of Terminal A and sends it to Terminal B;

[0021] Terminal B performs fixed-length segmentation on the one-dimensional index sequence after mapping of Terminal B using the same segmentation length as Terminal A to obtain the index segmentation sequence of Terminal B;

[0022] Step 5: Piecewise matching based on non-linear correlation measurement;

[0023] Terminal B uses the non-linear correlation coefficient as a metric to perform matching between index segments of the index segmentation sequence of Terminal B and the index segmentation sequence after permutation of Terminal A, and takes the obtained matching sequence as the key.

[0024] Furthermore, in Step 1, Terminal A and Terminal B sample the channel between the two, and the specific generation of the channel sample sequences of Terminal A and B respectively is:

[0025] Terminal A and Terminal B sample the channel between them within the channel coherence time of Terminal A and Terminal B, and stop until both Terminal A and Terminal B have collected a specified number of channel samples; and record the channel sample sequences collected by Terminal A and Terminal B as and ; where is the channel sample sequence of Terminal A, is the channel sample sequence of Terminal B, , respectively represent the th channel sample in the channel sample sequences of Terminals A and B, and , N is the length of the channel sample sequence, that is, the specified number of channel samples.

[0026] Furthermore, in step 1, the random permutation sequence is a random permutation sequence from to , where is the set length of the random permutation sequence.

[0027] Furthermore, in step 1, synchronously transmitting the ciphertext during the channel sounding specifically means: embedding the ciphertext as the data payload into the data field of the channel sounding packet, and transmitting it together with the pilot signal during the channel sounding.

[0028] Furthermore, in step 2, the distribution transformation algorithm that follows the normal distribution and is selected is the Box-Muller algorithm.

[0029] Further, step 3 specifically includes:

[0030] Step 3.1: Terminal A and Terminal B set the same order of the space-filling curve ;

[0031] Step 3.2: Terminal A converts the two-dimensional channel sample sequence after conversion by Terminal A into a two-dimensional coordinate lattice point sequence of Terminal A, where the th two-dimensional coordinate lattice point pair is specifically: ; where the two-dimensional coordinate lattice point index satisfies , , is the length of the two-dimensional channel sample sequence, and = , the symbol represents the floor operation; , respectively represent the th two-dimensional channel sample in the two-dimensional channel sample sequence ;

[0032] The terminal B, according to the order converts the two-dimensional channel sample sequence after the conversion of the terminal B into a two-dimensional coordinate lattice point sequence of the terminal B , where the th two-dimensional coordinate lattice point pair is specifically: ; , respectively represent the th two-dimensional channel sample in the two-dimensional channel sample sequence ;

[0033] Step 3.3: The terminal A uses a two-dimensional space-filling curve with an order of to map the two-dimensional coordinate lattice point sequence of the terminal A into a one-dimensional index sequence after the mapping of the terminal A, where each one-dimensional index satisfies , ;

[0034] The terminal B uses a two-dimensional space-filling curve with an order of to map the two-dimensional coordinate lattice point sequence of the terminal B into a one-dimensional index sequence after the mapping of the terminal B, where each one-dimensional index satisfies , .

[0035] Furthermore, in Step 3, the Hilbert curve is selected as the space-filling curve.

[0036] Furthermore, in Step 4, the random non-linear transformation includes but is not limited to: exponential transformation, logarithmic transformation, sine-cosine transformation, hyperbolic tangent function (Tanh) transformation, etc.

[0037] Furthermore, in Step 5, the terminal B uses the non-linear correlation coefficient as a metric to perform the matching between the index segmented sequences of the terminal B and the permuted index segmented sequence of the terminal A as:

[0038] ;

[0039] where is the th segment in the permuted index segmented sequence of the terminal A, is the th segment in the index segmented sequence of the terminal B, represents the adopted non - linear correlation coefficient, represents the matching order between index segments, is the set length of the random permutation sequence.

[0040] Further, in step 5, the non - linear correlation coefficient adopts the Chatterjee correlation coefficient.

[0041] The technical solution provided by this application has at least the following beneficial effects:

[0042] (1) By combining the space - filling curve mapping and non - linear correlation matching, this application overcomes the limitation of only using one - dimensional sample features in traditional matching - based key generation methods, thus achieving more accurate and efficient physical - layer key generation;

[0043] (2) By introducing the channel probing and synchronous ciphertext transmission mechanism, this application realizes the synchronous transmission of encrypted data during the channel probing process, reduces the additional packet exchanges in secure communication, and thus effectively improves the communication efficiency;

[0044] (3) This application adopts a distribution transformation method based on the Box - Muller algorithm to convert the original normal - distribution channel sample sequence into a uniform - distribution channel sample sequence, which overall enhances the difference between channel samples and promotes the matching - based key generation; in this process, the terminals can complete the distribution transformation without exchanging data, significantly reducing the communication volume and potential data leakage risk during the key generation process;

[0045] (4) Through the index mapping method based on the space - filling curve, this application maps the channel sample sequence to a one - dimensional space index according to the construction method of the space - filling curve, and avoids the limitation of only relying on the features of single - dimension channel samples; this method also enhances the robustness of the index matching process under extreme channel sample conditions, and ensures the locality of the mapping between different dimensions by selecting an appropriate space - filling curve (such as the Hilbert curve), thus improving the reliability of the subsequent index segmentation and matching process;

[0046] (5) This application performs index segment matching based on non - linear correlation measurement. By adopting the method of segmented random non - linear transformation, it confuses the correlation between index segments before and after transformation, reducing the risk of index segments leaking keys after public permutation; compared with the traditional method that only matches through index segment distance measurement, this application significantly enhances the robustness of the matching process by measuring non - linear correlation, ensuring the accuracy and generation rate of key generation in complex wireless environments. Detailed implementation manners

[0047] To enable those skilled in the art to better understand the technical solutions in this specification, the technical solutions of this application will be described in detail and completely below in combination with the embodiments of this application.

[0048] The embodiment of this application provides a key generation method based on space-filling curve mapping and non-linear correlation matching. It uses steps such as channel detection and synchronous ciphertext transmission, distribution transformation based on the Box-Muller algorithm, index mapping based on space-filling curves, segmented random non-linear transformation and permutation, and segmented matching based on non-linear correlation measurement to generate keys. Among them, channel detection and synchronous ciphertext transmission collect channel sample sequences by the terminals exchanging detection packets, and synchronously transmit encrypted data to improve communication efficiency. The distribution transformation based on the Box-Muller algorithm converts the channel sample sequence of the normal distribution into a two-dimensional channel sample sequence of the uniform distribution by using the inverse process of the Box-Muller algorithm, making the distribution of its channel samples more dispersed, which is convenient for generating a more uniform index mapping subsequently. The index mapping based on space-filling curves maps the two-dimensional channel sample sequence to a one-dimensional space index. Compared with the traditional single coordinate mapping method, the space-filling curve can better combine the multi-dimensional characteristics of channel samples and provide stronger discrimination, making the generated index mapping more consistent in the matching process. The segmented random non-linear transformation and permutation segment the index and use random non-linear transformation to enhance the non-linear characteristics of the index segments, further improving the anti-passive attack performance of key generation. The segmented matching based on non-linear correlation measurement performs segmented matching by measuring the non-linear correlation between each index segment, which can enhance the robustness of segmented matching and effectively improve the accuracy and generation rate of key generation.

[0049] As a possible implementation, a key generation method based on space-filling curve mapping and non-linear correlation matching provided by the embodiment of this application includes the following steps:

[0050] Step 1: Channel detection and synchronous ciphertext transmission. Terminal A and Terminal B sample the channel between them, respectively generate the channel sample sequence of Terminal A and the channel sample sequence of Terminal B. At the same time, Terminal A generates a random permutation sequence as the secret key, encrypts the plaintext with the secret key to generate ciphertext, and synchronously transmits the ciphertext during the channel detection process.

[0051] Step 2: Perform distribution transformation on the sampled channel sample sequence. Terminal A approximately converts the channel sample sequence of Terminal A into a standard normal distribution through standardization, obtaining the standardized channel sample sequence of Terminal A, and approximately converts the standardized channel sample sequence of Terminal A into a uniform distribution based on the inverse process of the selected distribution transformation algorithm that follows a normal distribution (such as the Box-Muller algorithm), obtaining the two-dimensional channel sample sequence of Terminal A after conversion; Similarly, Terminal B approximately converts the channel sample sequence of Terminal B into a standard normal distribution through standardization, obtaining the standardized channel sample sequence of Terminal B, and uses the inverse process of the Box-Muller algorithm to approximately convert the standardized channel sample sequence of Terminal B into a uniform distribution, obtaining the two-dimensional channel sample sequence of Terminal B after conversion;

[0052] Step 3: Based on the index mapping of the space-filling curve, Terminal A uses the common space-filling curve parameters to convert the two-dimensional channel sample sequence of Terminal A after conversion into the two-dimensional coordinate lattice point sequence of Terminal A, and uses the space-filling curve to map the two-dimensional coordinate lattice point sequence of Terminal A to a one-dimensional space index, obtaining the one-dimensional index sequence of Terminal A after mapping; Similarly, Terminal B uses the common space-filling curve parameters to convert the two-dimensional channel sample sequence of Terminal B after conversion into the two-dimensional coordinate lattice point sequence of Terminal B, and uses the same space-filling curve as Terminal A to map the two-dimensional coordinate lattice point sequence of Terminal B to a one-dimensional space index, obtaining the one-dimensional index sequence of Terminal B after mapping;

[0053] Step 4: Piecewise random non-linear transformation and permutation. Terminal A uses the method of equal-length segmentation to perform fixed-length segmentation on the one-dimensional index sequence of Terminal A after mapping, obtaining the index segmentation sequence of Terminal A, and performs random non-linear transformation on each index segment in the index segmentation sequence of Terminal A, obtaining the index segmentation sequence of Terminal A after non-linear transformation, and performs random permutation on the index segmentation sequence of Terminal A after non-linear transformation using the random permutation sequence generated in Step 1, obtaining the index segmentation sequence of Terminal A after permutation; Terminal A sends the index segmentation sequence of Terminal A after permutation to Terminal B; Terminal B uses the same segmentation length as Terminal A to perform fixed-length segmentation on the one-dimensional index sequence of Terminal B after mapping, obtaining the index segmentation sequence of Terminal B;

[0054] Step 5: Piecewise matching based on non-linear correlation measurement. Terminal B uses the non-linear correlation coefficient as a measurement to perform matching between the index segmentation sequences of Terminal B and the index segmentation sequence of Terminal A after permutation, and obtains the matching sequence as the key.

[0055] In one embodiment, the channel detection and synchronous ciphertext transmission in Step 1 of the embodiments of the present application includes:

[0056] Step 1.1: Terminal A and terminal B sample the channel between them within the channel coherence time of terminal A and terminal B, and end when both terminal A and terminal B have collected a certain number of channel samples, and the channel sample sequences collected by terminal A and terminal B are recorded as and ;in, is the channel sample sequence of terminal A, is the channel sample sequence of terminal B, , Respectively represent the first channel samples, N is the channel sample sequence length;

[0057] Step 1.2: Terminal A generates a slave arrive Random permutation sequence As a secret key shared between terminal A and terminal B, Corresponding to the length of the index segment sequence of terminal A in step 4.1, and using the secret key to encrypt the plaintext of terminal A, to obtain the ciphertext of terminal A;

[0058] Step 1.3: Terminal A embeds the ciphertext of terminal A as a data payload in the channel detection packet and transmits it together with the pilot signal in the channel detection to reduce the data packet exchange for confidential communication.

[0059] In one embodiment, step 2 of the embodiment of the present application specifically includes:

[0060] Step 2.1: Terminal A obtains the channel sample sequence from terminal A Estimate the sample mean of the channel sample sequence of terminal A and the sample standard deviation , respectively:

[0061] ;

[0062] ;

[0063] And according to the sample mean of the channel sample sequence of terminal A and the sample standard deviation Channel sample sequence for terminal A Standardize and obtain the standardized channel sample sequence of terminal A , where each element ( ) is as follows:

[0064] ;

[0065] The standardized channel sample sequence of terminal A obtained approximately follows the standard normal distribution ; Similarly, terminal B estimates the sample mean and the sample standard deviation of the channel sample sequence of terminal B from the channel sample sequence of terminal B as follows: respectively:

[0066] ;

[0067] ;

[0068] and standardizes the channel sample sequence of terminal B according to the sample mean and the sample standard deviation of the channel sample sequence of terminal B to obtain the standardized channel sample sequence of terminal B where each element ( ) is standardized as follows: ;

[0069] ;

[0070] The standardized channel sample sequence of terminal B obtained also approximately follows the standard normal distribution ;

[0071] Step 2.2: Terminal A splits the dimensions of the standardized channel sample sequence of terminal A to obtain the two-dimensional channel sample sequence of terminal A where = and the symbol represents the floor operation; Similarly, terminal B splits the dimensions of the standardized channel sample sequence of terminal B to obtain the two-dimensional channel sample sequence of terminal B ;

[0072] Step 2.3: Terminal A approximately converts the two-dimensional channel sample sequence of terminal A into a uniform distribution through the inverse process of the Box-Muller algorithm to obtain the converted two-dimensional channel sample sequence of terminal A ; Specifically, for the th two-dimensional channel sample pair ( ) in the two-dimensional channel sample sequence of terminal A , terminal A calculates the auxiliary quantity and based on this auxiliary quantity The converted two-dimensional channel sample sequence of computing terminal A , where the ( ) two-dimensional channel sample pair is :

[0073]

[0074]

[0075] Among them, is the arctangent function with the value range defined in , and e is the natural base; similarly, terminal B also approximately converts the two-dimensional channel sample sequence of terminal B into a uniform distribution through the inverse process of the Box-Muller algorithm, and obtains the converted two-dimensional channel sample sequence of terminal B.

[0076] In one embodiment, step 3 of the embodiment of the present application specifically includes:

[0077] Step 3.1: Terminal A and terminal B select a two-dimensional Hilbert curve as the space-filling curve, and set the same curve parameter order , indicating that the number of iterations required in the construction of the Hilbert curve is times (similarly, Hilbert curves or other space-filling curves with other dimensions and orders can also be selected for index mapping);

[0078] Step 3.2: Terminal A converts the two-dimensional channel sample sequence of terminal A after conversion into the two-dimensional coordinate lattice point sequence of terminal A according to the order , where the ( ) two-dimensional coordinate lattice point pair is ; similarly, terminal B converts the two-dimensional channel sample sequence of terminal B after conversion into the two-dimensional coordinate lattice point sequence of terminal B according to the order , where the ( ) two-dimensional coordinate lattice point pair is ;

[0079] Step 3.3: Terminal A uses the two-dimensional Hilbert curve with the order of to map the two-dimensional coordinate lattice point sequence of terminal A into the one-dimensional index sequence after mapping of terminal A, where each one-dimensional index ( ), all satisfy ; Similarly, terminal B uses a two-dimensional Hilbert curve of order to map the two-dimensional coordinate lattice point sequence of terminal B to the one-dimensional index sequence after mapping of terminal B, where each one-dimensional index ( ) all satisfy .

[0080] In one embodiment, step 4 of the embodiment of the present application specifically includes:

[0081] Step 4.1: Terminal A performs fixed-length segmentation on the one-dimensional index sequence after mapping of terminal A according to a fixed length to obtain the index segmentation sequence of terminal A, where , ( ) is the th index segment, and the length of each index segment is ; Similarly, terminal B performs fixed-length segmentation on the one-dimensional index sequence after mapping of terminal B according to a fixed length to obtain the index segmentation sequence of terminal B, where ( ) is the th segment, and the length of each index segment is ;

[0082] Step 4.2: Terminal A uses a random non-linear transformation for each segment ( ) in the index segmentation sequence of terminal A to obtain the index segmentation sequence after non-linear transformation of terminal A, where ( ) is the index segment of the index segmentation sequence of terminal A after non-linear transformation , and these non-linear transformations can be selected from exponential transformation, logarithmic transformation, sine-cosine transformation, Tanh transformation, etc.;

[0083] Step 4.3: Terminal A uses the random permutation sequence described in step 1.2 to Perform a random permutation to obtain the index segment sequence of terminal A after permutation , where the th index segment ( ) is the index segment sequence of terminal A after non - linear transformation in the th ( ) index segment;

[0084] Step 4.4: Terminal A sends the index segment sequence of terminal A after permutation to terminal B.

[0085] In one embodiment, step 5 of the embodiments of the present application specifically includes:

[0086] Step 5.1: Terminal B establishes a segment - by - segment match between the index segment sequence of terminal B and the index segment sequence of terminal A after permutation , and derives the key therefrom; specifically, terminal B selects the Chatterjee correlation coefficient as the non - linear correlation measure between index segments, calculates the matching order between the index segments in the index segment sequence of terminal B and the index segment sequence of terminal A after permutation to minimize the matching error, and the matching order is used as the key of terminal B:

[0087] ;

[0088] Among them, ( ) is the th segment in the index segment sequence of terminal A after permutation , ( ) is the th segment in the index segment sequence of terminal B , is the Chatterjee correlation coefficient between segment and , and the specific calculation process is as follows;

[0089] Let and be two segments of equal length. For in pairs of sample values , arrange them in ascending order such that ; Let be the order of in , that is of quantity, the Chatterjee correlation coefficient is defined as:

[0090] .

[0091] In the description of this specification, the descriptions referring to terms such as "one embodiment", "some embodiments", "example", "specific example", or "some examples", etc., mean that the specific features, structures, materials, or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of this application. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, without contradiction, those skilled in the art can combine and combine the different embodiments or examples described in this specification and the features of different embodiments or examples.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the application and are not intended to limit them; although the application has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A key generation method based on space filling curve mapping and nonlinear correlation matching, characterized in that: The following steps are involved: Step 1: Channel detection and synchronous ciphertext transmission; Terminals A and B sample the channel between them respectively to obtain channel sample sequences of terminals A and B; Terminal A generates a random permutation sequence as a secret key, and uses it to encrypt plaintext to generate ciphertext, and transmits the ciphertext synchronously during channel detection; Step 2: Terminal A / B performs distribution transformation on its channel sample sequence respectively; After the terminal A / B converts its channel sample sequence into a standard normal distribution, based on the inverse process of the selected distribution transformation algorithm that obeys the normal distribution, the standardized channel sample sequence of the terminal A / B is converted into a uniform distribution to obtain a two-dimensional channel sample sequence after the terminal A / B is converted; Step 3: Index mapping based on space-filling curve; Terminal A / B converts the converted two-dimensional channel sample sequence into a two-dimensional coordinate grid point sequence based on the common space filling curve parameters, and then maps it to a one-dimensional space index to obtain a one-dimensional index sequence mapped by terminal A / B; Step 4: piecewise random nonlinear transformation and permutation; Terminal A segments the mapped one-dimensional index sequence with a fixed length based on the set segment length to obtain the index segment sequence of terminal A, and performs a random nonlinear transformation on each index segment to obtain the index segment sequence after the nonlinear transformation of terminal A; then, the index segment sequence is randomly permuted based on the random permutation sequence generated in step 1 to obtain the permuted index segment sequence of terminal A and send it to terminal B; Terminal B uses the same segment length as terminal A to perform fixed-length segmentation on the one-dimensional index sequence mapped by terminal B to obtain an index segment sequence of terminal B; Step 5: Segment matching based on nonlinear correlation metrics; Terminal B uses the nonlinear correlation coefficient as a metric to match the index segment sequence of terminal B with the index segment sequence after replacement by terminal A, and uses the obtained matching sequence as a key; Wherein, step 3 specifically includes: Step 3.1: Set the same order of space-filling curves for both terminal A and terminal B ; Step 3.2: Terminal A is based on the order The two-dimensional channel sample sequence converted by terminal A Transformed into a two-dimensional coordinate grid sequence of terminal A , among which 2D coordinate grid points Specifically: ; Among them, the two-dimensional coordinate grid index satisfy , is the length of the two-dimensional channel sample sequence, and = ,symbol Indicates floor operation; , Represent the two-dimensional channel sample sequence The Two-dimensional channel samples; Terminal B according to the order The two-dimensional channel sample sequence converted by terminal B Transformed into a two-dimensional coordinate grid sequence of terminal B , among which 2D coordinate grid points Specifically: ; , Represent the two-dimensional channel sample sequence The Two-dimensional channel samples; Step 3.3: Terminal A uses the order The two-dimensional space-filling curve of terminal A is Mapped to the one-dimensional index sequence after terminal A is mapped , where each one-dimensional index All meet , ; Terminal B uses the order The two-dimensional space-filling curve of terminal B is Mapped to the one-dimensional index sequence after terminal B mapping , where each one-dimensional index All meet , .

2. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 1, characterized in that: In step 1, the random permutation sequence is a sequence from arrive A random permutation sequence of The length of the random permutation sequence is set.

3. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 1, characterized in that: In step 1, synchronously transmitting the ciphertext during the channel detection process specifically includes: embedding the ciphertext as a data payload into the data field of the channel detection packet, and transmitting it together with the pilot signal during the channel detection.

4. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 1, characterized in that: In step 2, the distribution transformation algorithm selected to obey the normal distribution is the Box-Muller algorithm.

5. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 1, characterized in that: In step 3, the Hilbert curve is selected as the space filling curve.

6. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 1, characterized in that: In step 4, the random nonlinear transformation is an exponential transformation, a logarithmic transformation, a sine-cosine transformation or a hyperbolic tangent function.

7. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 1, characterized in that: In step 5, terminal B uses the nonlinear correlation coefficient as a metric to match the index segment sequence of terminal B with the index segment sequence after replacement of terminal A: ； in, The index segment sequence after the terminal A is replaced The Segments, is the index segment sequence of terminal B The Segments, represents the nonlinear correlation coefficient used, Indicates the matching order between index segments. The length of the random permutation sequence is set.

8. The key generation method based on space filling curve mapping and nonlinear correlation matching according to claim 7, characterized in that: In step 5, the nonlinear correlation coefficient adopts the Chatterjee correlation coefficient.

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