A physical layer key generation method and system based on gray-cdf quantization and adaptive LDPC syndrome negotiation

Abstract

The application discloses a physical layer key generation method and system based on Gray-CDF quantization and adaptive LDPC syndrome negotiation. The legal communication parties acquire channel characteristic sequences in reciprocal wireless channels, determine multi-level equal probability quantization thresholds according to empirical cumulative distribution functions of local channel characteristics, and adopt Gray codes to map adjacent quantization intervals into code words with only one different bit, so as to generate original key sequences; subsequently, LDPC syndrome lengths are adaptively determined according to current channel quality or initial bit inconsistency rate estimation values, the syndromes are disclosed through a public channel to complete key error correction, and retry or discard processing is performed on decoding failure frames; after successful negotiation, privacy amplification is performed according to disclosed leakage, and a consistent key is obtained. The application can improve original key generation rate, reduce negotiation disclosure, and improve the reliability of physical layer key generation and the available key rate.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication security, physical layer key generation, and information negotiation, and in particular to a Gray-CDF quantization and adaptive LDPC syndrome negotiation method and system oriented towards reciprocal wireless channel characteristics. Background Technology

[0002] Physical layer key generation technology leverages the reciprocity, randomness, and spatial decorrelation properties of wireless channels to enable legitimate communicating parties to extract a shared random key from their respective channel observations. Its typical process includes channel sounding, channel feature extraction, quantization, information negotiation, and privacy amplification. These technologies reduce reliance on pre-set keys and complex key distribution infrastructure, making them suitable for scenarios such as the Internet of Things (IoT), short-range wireless communication, and dedicated wireless links.

[0003] In existing schemes, channel feature quantization often employs methods such as single-threshold, double-threshold, or level-crossing. These methods are relatively simple to implement, but common problems include a small number of output bits per channel sample, and some samples being used, discarded, or filtered out because they fall into the uncertainty region, resulting in a low original key rate. At the same time, when the signal-to-noise ratio is low or the channel estimation deviation is large, the inconsistency rate of quantization results between legitimate parties increases, leading to increased negotiation overhead.

[0004] Information negotiation is a critical step in physical layer key generation that affects the final usable key rate and security. Negotiation methods based on publicly disclosed position sequences may leak a significant amount of information about channel characteristic distribution or local stable regions, while fixed-redundancy error correction negotiation struggles to adapt to different signal-to-noise ratios and initial bit inconsistency rates. Insufficient redundancy increases the decoding failure rate, while excessive redundancy increases public leakage, and privacy amplification reduces the usable key length.

[0005] Therefore, there is an urgent need for a physical layer key generation method with quantization and negotiation as its core, which can enable the original key to have a high generation rate and an error structure suitable for error correction, and can adaptively adjust the negotiation redundancy according to the channel quality, while explicitly measuring public leakage, thereby improving the final usable key rate and key consistency. Summary of the Invention

[0006] The purpose of this invention is to provide a physical layer key generation method and system based on Gray-CDF quantization and adaptive LDPC syndrome negotiation, so as to solve the problems of limited key generation rate, large amount of negotiated public information, and difficulty in adapting error correction redundancy to channel changes in existing quantization methods.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: During the channel coherence time, both parties in legitimate communication perform channel probing and extract channel feature sequences; each party determines a multi-level equal-probability quantization threshold based on the empirical cumulative distribution function of its local channel feature sequences, and maps adjacent quantization intervals to Gray codewords with a Hamming distance of 1 to generate the original key sequence. Preferably, four-level Gray-CDF quantization is used, with the 25%, 50%, and 75% quantiles as thresholds, corresponding to codewords 00, 01, 11, and 10 respectively.

[0008] During the negotiation phase, this invention adaptively determines the LDPC syndrome length based on the current channel quality index or the initial bit inconsistency rate estimate. One party in legitimate communication discloses the LDPC syndrome, while the other party calculates the error syndrome based on its own original key sequence and the disclosed syndrome, and estimates the error pattern through LDPC decoding. If decoding fails, the current frame is discarded, or the syndrome length is increased and the negotiation is renegotiated. Upon successful negotiation, the system amplifies privacy based on the disclosed amount to obtain the final key.

[0009] Compared with existing technologies, the present invention has the following advantages: First, Gray-CDF multilevel quantization increases the number of output bits per channel sample through equal-probability binning and makes the output bits more evenly distributed; Second, Gray code mapping makes misjudgments in adjacent quantization intervals mainly manifest as single-bit errors, which is more suitable for LDPC syndrome error correction; Third, adaptive syndrome length can improve error correction capability at low channel quality and reduce public leakage at high channel quality; Fourth, failure frame processing avoids the misuse of inconsistent keys; Fifth, privacy amplification length deducts the negotiated public leakage, making the final key length have a clearer security interpretation.

[0010] Figure 1 This is a schematic diagram of the overall process for generating physical layer keys according to an embodiment of the present invention.

[0011] Figure 2 This is a schematic diagram of the Gray-CDF four-level quantization process according to an embodiment of the present invention.

[0012] Figure 3 This is a schematic diagram of the adaptive LDPC syndrome negotiation process according to an embodiment of the present invention.

[0013] Figure 4 This is a schematic diagram of the public disclosure measurement and privacy amplification process according to an embodiment of the present invention.

[0014] Figure 5 This is a schematic diagram illustrating the application of the final key to secure physical layer transmission in an embodiment of the present invention.

[0015] The embodiments of the present invention will be further described below in conjunction with the accompanying drawings. It should be understood that the following embodiments are used to explain the present invention rather than limit the present invention. Without departing from the idea of the present invention, the channel estimation method, the form of channel characteristics, the number of quantization levels, the type of error correction code, and the final key usage can all be equivalently replaced.

[0016] As Figure 1 shown, the embodiments of the present invention include channel detection, channel feature extraction, Gray-CDF quantization, adaptive LDPC syndrome negotiation, failed frame processing, privacy amplification, and final key output. The two legitimate communication parties can be Alice and Bob, and the eavesdropping end Eve is in a passive eavesdropping state, capable of receiving wireless signals and public channel public information, but unable to obtain channel observations that are exactly the same as those of the two legitimate parties.

[0017] In the channel detection stage, Alice and Bob exchange pilots or training sequences within the same channel coherence time to estimate the wireless channel respectively. The channel characteristics can be the amplitude of the channel impulse response, the amplitude of the frequency-domain subcarriers, the received signal strength, or the combination of multipath amplitudes. To reduce the influence of noise, the results of multiple pilot estimations can be averaged or smoothed.

[0018] As Figure 2 shown, in the Gray-CDF four-level quantization embodiment, the legitimate communication parties sort the local channel feature sequence x and calculate the empirical quantiles q25, q50, and q75. When x i < q25, Gray code 00 is output; when q25 ≤ x i < q50, Gray code 01 is output; when q50 ≤ x i < q75, Gray code 11 is output; when x i ≥ q75, Gray code 10 is output. This quantization method outputs two original key bits for each feature sample.

[0019] The above quantization thresholds are calculated locally by each legitimate communication party and do not need to be publicly disclosed through the public channel. Since the channel observations of Alice and Bob are highly correlated, their empirical quantiles are usually close; due to the different spatial positions of Eve, its channel observations are decorrelated from those of the two legitimate parties, and it is difficult to obtain the same original key even if it knows the quantization rule. After using Gray code mapping, the misjudgment of adjacent intervals caused by noise between the two legitimate parties only results in one error, which is beneficial for subsequent LDPC error correction.

[0020] In other embodiments, Gray-CDF quantization can be extended to 2 r level quantization. The legitimate communication parties form 2 rThere are quantization intervals, which are mapped according to r-bit Gray codes. When the channel quality is good, the quantization level can be increased to improve the original key rate; when the channel quality is poor, the quantization level can be decreased to reduce the initial bit inconsistency rate.

[0021] like Figure 3 As shown, adaptive LDPC syndrome negotiation includes syndrome length determination, syndrome transmission, error syndrome calculation, LDPC decoding, and success determination. Let the original key sequence length be n, and the initial bit inconsistency rate estimate be p. hat Then the syndrome length m can be calculated as m = clip(ceil(β·n·h2(p)). hat )),m min ,m max ) Determine. Where n is the length of the original key sequence, p hat Here, h2 is the initial bit inconsistency rate estimate, h2 is the binary entropy function, β is the redundancy coefficient, and m is the initial bit inconsistency rate estimate. min To preset the minimum syndrome length, m max The maximum syndrome length is preset.

[0022] p hat The LDPC parity-check matrix H can be estimated from the signal-to-noise ratio, channel estimation error variance, pilot repetition measurement difference, historical frame decoding results, or a small number of reserved sample verification results. The LDPC parity-check matrix H can be determined by the public seed, frame number, key length n, and parity length m; the two parties do not need to transmit the complete matrix. Alice calculates... A =H·k A mod 2 and published, Bob calculates s B =H·k B mod2, and by s A XOR s B The error syndrome is obtained, and the error pattern e is estimated by LDPC decoding.

[0023] If Bob decodes successfully, then calculate k. B '=k B XOR e yields the negotiated key sequence consistent with Alice's. If decoding fails, the system can either discard the current frame directly or resend the incremental or updated key sequence by increasing the key sequence length by a preset step size. This failure frame handling mechanism prevents incorrect keys from entering subsequent privacy amplification or business encryption processes due to negotiation failures.

[0024] like Figure 4 As shown, negotiated public information is included in the amount of public leaks. pub The privacy amplification stage can employ Toeplitz universal hashing to compress the negotiated key sequence into the final key. The output length ell can be determined according to ell = floor(n). s-leak pub -p eve ·n s -2log2(1 / epsilon)) is determined, where n s Leak is the length of the negotiated key sequence. pub p represents the total number of bits disclosed during the information negotiation phase. eve `ell` represents the channel correlation estimate from the eavesdropping endpoint, and `epsilon` is a security parameter. When `ell` is less than or equal to zero, the final key is not output in the current frame.

[0025] like Figure 5 As shown, the final key can serve as an upper-layer encryption key, authentication key, session key, or driving key for physical layer secure transmission parameters. In one application embodiment, the final key is used to generate the order parameters and weighting parameters of the MP-WFRFT, and maps the order parameters to a secure region far from integer degeneracy points to drive the physical layer weighted transformation. This application embodiment is used to illustrate the use of the final key and does not change the core technical solution of this invention, which is based on Gray-CDF quantization and adaptive LDPC syndrome negotiation.

[0026] Simulation results show that with Gray-CDF four-level quantization, each channel sample can generate two original key bits. As the signal-to-noise ratio increases, the initial bit inconsistency rate decreases, the decoding success rate of adaptive LDPC syndrome negotiation improves, and the usable key length after privacy amplification increases. Compared with methods relying solely on level crossing or fixed redundancy negotiation, this invention has advantages in key generation rate, negotiation reliability, and measurability of public disclosure.

Claims

1. A physical layer key generation method based on Gray-CDF quantization and adaptive LDPC syndrome negotiation, characterized in that, include: During the channel coherence time, the two parties in legitimate communication perform channel probing and obtain channel observations of the reciprocal wireless channel respectively. Channel feature sequences are extracted from the channel observations; The multi-level equal-probability quantization threshold is determined based on the empirical cumulative distribution function of the local channel feature sequence, and adjacent quantization intervals are mapped to Gray codewords with a Hamming distance of 1 to generate the original key sequence. The LDPC syndrome length is adaptively determined based on the current channel quality index or the initial bit inconsistency rate estimate. One legitimate communication terminal calculates the LDPC syndrome based on its original key sequence and publishes it through a public channel. The other legitimate communication terminal corrects its original key sequence based on the LDPC syndrome. When the error correction is successful, the negotiated key sequence is output. When the error correction fails, the current frame is discarded or the syndrome length is increased and renegotiation is performed. Privacy amplification is performed on the negotiated key sequence based on the amount of information disclosed during the negotiation, resulting in a consistent final key.

2. The method according to claim 1, characterized in that, The channel feature sequence includes at least one of the following: channel impulse response amplitude sequence, frequency domain subcarrier amplitude sequence, received signal strength sequence, multipath amplitude combination sequence, or normalized sequence thereof; the empirical cumulative distribution function is calculated from the local channel feature sequence of the legitimate communication terminal, and the quantization threshold is not disclosed through the public channel.

3. The method according to claim 1, characterized in that, The multilevel equal probability quantization is 2. r Level Gray-CDF quantization, where r is an integer greater than or equal to 1, the 2 r Each quantization interval is determined by the equiprobability quantiles of the empirical cumulative distribution function, and each quantization interval is mapped according to the r-bit Gray code. When r=2, the two legitimate communicating parties respectively calculate the 25%, 50%, and 75% quantiles of the local channel feature sequence, and map the four quantization intervals to Gray codes 00, 01, 11, and 10 in sequence.

4. The method according to claim 1, characterized in that, The current channel quality metrics include at least one of the following: signal-to-noise ratio, channel estimation error variance, pilot repeat measurement difference, historical frame decoding results, or reserved sample verification results; the LDPC syndrome length m is calculated according to the formula m=clip(ceil(β·n·h2(p hat )),m min ,m max ) is determined, where n is the length of the original key sequence, p hat Here, h2 is the initial bit inconsistency rate estimate, h2 is the binary entropy function, β is the redundancy coefficient, and m is the initial bit inconsistency rate estimate. min To preset the minimum syndrome length, m max The maximum syndrome length is preset.

5. The method according to claim 1, characterized in that, The LDPC parity check matrix is ​​determined by the public seed, frame number, key length, and syndrome length, so that legitimate communicating parties do not need to transmit the complete parity check matrix through a public channel. The party receiving the syndrome calculates the local syndrome based on its own original key sequence, and obtains the error syndrome from the public syndrome and the local syndrome, so as to estimate the error pattern and correct its own original key sequence through LDPC decoding.

6. The method according to claim 1, characterized in that, The process of increasing the syndrome length and then renegotiating includes increasing the LDPC syndrome length by a preset step size or a preset ratio, and retransmitting the incremental syndrome or the updated syndrome until decoding is successful or the syndrome length reaches the upper limit. If decoding is still unsuccessful when the syndrome length reaches the upper limit, the current frame is marked as an invalid frame and discarded.

7. The method according to claim 1, characterized in that, The privacy amplification uses Toeplitz general hashing; the output length ell of the privacy amplification is based on ell=floor(n). s -leak pub -p eve ·n s -2log2(1 / epsilon)) is determined, where n s Leak is the length of the negotiated key sequence. pub p represents the total number of bits disclosed during the information negotiation phase. eve The channel correlation estimate is given by the eavesdropping device, and epsilon is a security parameter.

8. The method according to claim 1, characterized in that, The final key is used to generate at least one of the following: physical layer secure transmission parameters, upper-layer encryption key, authentication key, or session key; when the final key is used to generate the order parameters and weighting parameters of MP-WFRFT, the order parameters are mapped to a secure range far from the integer degeneracy point and then used for the physical layer secure transformation of the modulation symbols.

9. A physical layer key generation system based on Gray-CDF quantization and adaptive LDPC syndrome negotiation, characterized in that, include: The channel detection module is used to enable both parties in a legitimate communication to obtain channel observations of the reciprocal wireless channel. The feature extraction module is used to extract channel feature sequences from the channel observations; the Gray-CDF quantization module is used to determine the multi-level equal probability quantization threshold based on the local empirical cumulative distribution function and perform Gray code mapping to generate the original key sequence; the syndrome length determination module is used to adaptively determine the LDPC syndrome length based on the current channel quality index or the initial bit inconsistency rate estimate. The LDPC syndrome negotiation module is used to disclose the syndrome and perform error correction on the original key sequence; The failure frame processing module is used to discard or increase the syndrome length and renegotiate when decoding fails; the privacy amplification module is used to compress the negotiated key sequence according to the amount of public disclosure to generate the final key.

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