Objective The key distribution method based on atmospheric random fading perturbation provides a low-cost implementation scheme for information theory-secure key sharing by using classical atmospheric optical channels. During this process, the inconsistency rate and randomness of the generated keys are the concerns of the scheme. Aiming at the above problems, a fault-tolerant region mapping quantization method integrating gradient features is proposed. The two methods, FTZMQ and Alternating Quantization with Fault-Tolerant Interval Mapping (AQ-FTIM), can both be used to quantify and generate the initial key.

Methods  First, the quantization boundaries are constructed using the channel measurement sequence and the corresponding gradient information. Fixed proportion tolerance bands are introduced on both sides of each quantization interval boundary to determine whether the current sample falls within the critical region. The FTZMQ method eliminates legal sequences that belong to the tolerance region and its opposite tolerance region, while the remaining sequences are encoded according to their respective Gray coding rules. The AQ-FTIM method combines Gray Code to reduce bit transitions and dynamically adjusts the quantization interval index based on the tolerance frequency band mapping of the legitimate parties. When Alice's feature value falls into the left tolerance band and Bob's corresponding value falls into the right, Bob's quantization interval index is shifted left to avoid boundary discrepancies; conversely, a right shift operation is performed.

Results and Discussions  The results show that the initial keys generated by the legitimate parties using the above quantization method have high consistency. When the signal-to-noise ratio is 15 dB and the quantization bit count is 1 for FTZMQ, there is no need for key negotiation, and the legitimate parties generate completely consistent keys. The AQ-FTIM method can reduce the key inconsistency rate to 1.2×10⁻³ under lossless conditions. Compared with the situation without interval alternation, the key inconsistency rate can be reduced by up to 80%. Ultimately, the key generated by both legitimate parties was able to pass the NIST (National Institute of Standards and Technology) test, verifying the validity of the generated key.

Conclusions  The FTZMQ method and the AQ-FTIM method are proposed to address the issue of reducing the key inconsistency rate in the quantization process of random fading channels. By dynamically dividing the quantization boundary using the gradient values of the signal observation sequence and simultaneously adopting the fault-tolerant band cooperative correction strategy, the initial key is obtained for the fuzzy samples within the fault-tolerant band using the FTZMQ method or the lossless method AQ-FTIM. The FTZMQ method can change the values of relevant parameters to reduce the inconsistency rate. For the analog signal receiving process in an environment with a signal-to-noise ratio of 5 to 30 dB, the initial key generated after FTZMQ quantization obtained a completely consistent key when the signal-to-noise ratio was 15 dB. Especially in a low signal-to-noise ratio environment, the key matching rate was improved by 59% compared to the segmented quantization method, making it difficult for Eve to obtain the relevant information. In addition, the lossless method AQ-FTIM has higher data integrity, can make full use of the relevant information of the observation sequence, and has a higher key generation rate. At a signal-to-noise ratio of 30 dB, the inconsistency rate can be as low as 1.2×10⁻³, which is 54% lower than that of the CQA method. Be capable of adapting to channel conditions. In practical applications, the FTZMQ method or AQ-FTIM method can be adopted according to specific circumstances. Finally, the randomness test of the generated keys was conducted using the NIST test. The results showed that the P-value of the keys generated by the method proposed was all greater than 0.01, which proved the validity of the generated keys. In the future, the trade-off between the accuracy of the gradient feature estimation quantization threshold and the coverage range of the fault-tolerant zone can be further explored.