Difference-based shared key extraction scheme via multi-level quantization

doi:10.11772/j.issn.1001-9081.2025030297

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (3): 839-846.DOI: 10.11772/j.issn.1001-9081.2025030297

• Cyber security • Previous Articles Next Articles

Difference-based shared key extraction scheme via multi-level quantization

Qiong LI¹, Chunyi CHEN¹^,²(), Zhenzhong ZHANG¹, Bo YU¹, Haiyang YU¹, Xiaojuan HU¹

^1.School of Computer Science and Technology，Changchun University of Science and Technology，Changchun Jilin 130022，China
^2.Key Laboratory of Photoelectric Measurement and Control and Optical Information Transfer Technology，Ministry of Education （Changchun University of Science and Technology），Changchun Jilin 130022，China

Received:2025-03-24 Revised:2025-05-08 Accepted:2025-05-12 Online:2025-05-19 Published:2026-03-10
Contact: Chunyi CHEN
About author:LI Qiong， born in 1997， Ph. D. candidate. Her research interests include wireless channel key extraction.
ZHANG Zhenzhong， born in 1998， Ph. D. candidate. His research interests include wireless channel communication security.
YU Bo， born in 1990， Ph. D. candidate. Her research interests include computer simulation applications.
YU Haiyang， born in 1989， Ph. D.， associate professor. His research interests include optical transmission simulation.
HU Xiaojuan， born in 1985， Ph. D.， lecturer. Her research interests include wireless signal processing.
Supported by:
National Natural Science Foundation of China(62275033);Science and Technology Development Program of Jilin Province(20240602123RC)

基于差分的多级量化共享密钥提取方案

李琼¹, 陈纯毅¹^,²(), 张振忠¹, 于波¹, 于海洋¹, 胡小娟¹

^1.长春理工大学计算机科学技术学院，长春 130022
^2.光电测控与光信息传输技术教育部重点实验室（长春理工大学），长春 130022

通讯作者: 陈纯毅
作者简介:李琼（1997—），女，河南周口人，博士研究生，CCF会员，主要研究方向：无线信道密钥提取
张振忠（1998—），男，山西忻州人，博士研究生，主要研究方向：无线信道通信安全
于波（1990—），女，内蒙古通辽人，博士研究生，CCF会员，主要研究方向：计算机仿真应用
于海洋（1989—），男，吉林长春人，副教授，博士，主要研究方向：光传输仿真
胡小娟（1985—），女，山东淄博人，讲师，博士，CCF会员，主要研究方向：无线信号处理。
基金资助:
国家自然科学基金资助项目(62275033);国家自然科学基金资助项目(62305030);吉林省科技发展计划项目(20240602123RC)

Abstract

Abstract:

Legitimate communicating parties can leverage the randomness of wireless channel state to extract shared key sequences that are information-theoretically secure. To enhance the efficiency of wireless channel key extraction， a difference-based shared key extraction scheme via multi-level quantization was proposed. In the scheme， random modulation was employed to perform high-frequency sampling of the wireless channel， and two quantization algorithms integrated with random sampling difference — Adaptive Symbol Quantization （ASQ） and Balanced Multi-bit Modified Quantization （BMMQ） — were introduced to process the first-order differential sequence， so as to obtain the original key sequence. On this basis， an information negotiation algorithm was applied to correct inconsistent bits in the original key， and the signal was reconstructed using the original key and the first-order differential sequence， and then the signal was requantized， ultimately achieving key synchronization between legitimate communicating parties. Experimental results demonstrate that random sampling difference reduces the correlation coefficient between adjacent sample points to below e?1， thereby decreasing statistical dependence in the key sequence effectively； under a Signal-to-Noise Ratio （SNR） of 25 dB， the ASQ algorithm reduces the Key Disagreement Rate （KDR） to 3.8×10?? while maintaining an Original Key Extraction Rate （OKER） of 0.86； under lossless quantization conditions， the BMMQ algorithm reduces the KDR to 7×10?3. The finally generated shared key sequences pass the NIST （National Institute of Standards and Technology） randomness test， validating the security and effectiveness of the keys.

Key words: wireless channel, key extraction, multi-level quantization, random sampling, signal reconstruction

摘要：

合法通信双方可以利用无线信道状态的随机特性提取符合信息论安全的共享密钥序列。为了提高无线信道提取密钥的效率，提出一种基于差分的多级量化共享密钥提取方案。该方案采用随机调制对无线信道进行高频采样，并引入融合随机抽样差分的自适应符号量化（ASQ）和均衡化多比特修正量化（BMMQ）这2个算法处理一阶差分序列，以获得原始密钥序列。在此基础上，应用信息协商算法纠正原始密钥中不一致的比特，并使用原始密钥及一阶差分序列重构信号，再对该信号进行二次量化，最终实现合法通信双方的密钥同步。实验结果表明，随机抽样差分能够将相邻样本点之间的相关系数降低至e?1以下，有效降低密钥序列中的统计依赖性；在信噪比（SNR）为25 dB的条件下，ASQ算法可在保持原始密钥提取率（OKER）为0.86的同时，将密钥不一致率（KDR）降低至3.8×10??；在无损量化的条件下，BMMQ算法可以把KDR降低至7×10?3。最终生成的共享密钥序列通过了NIST（National Institute of Standards and Technology）随机性测试，验证了密钥的安全性和有效性。

关键词: 无线信道, 密钥提取, 多级量化, 随机抽样, 信号重构

CLC Number:

TN918.91

Qiong LI, Chunyi CHEN, Zhenzhong ZHANG, Bo YU, Haiyang YU, Xiaojuan HU. Difference-based shared key extraction scheme via multi-level quantization[J]. Journal of Computer Applications, 2026, 46(3): 839-846.

李琼, 陈纯毅, 张振忠, 于波, 于海洋, 胡小娟. 基于差分的多级量化共享密钥提取方案[J]. 《计算机应用》唯一官方网站, 2026, 46(3): 839-846.

Figures/Tables 11

Tab. 1 Description of variable symbols

变量符号	含义
y_X	Alice/Bob接收到的光信号序列，其中X=A代表Alice方，X=B代表Bob方
P_t	激光器发出光信号的功率
h_AB	Alice到Bob大气湍流引起的瞬时无线信道系数波动
h_BA	Bob到Alice大气湍流引起的瞬时无线信道系数波动
n_X	均值为0、方差为 $σ n X 2$ 的加性高斯白噪声
ϕ_X	Alice和Bob重构后的直接观测序列
N	合法双方直接观测序列的长度
D_X	直接观测序列随机抽样差分序列
k_X	ASQ/BMMQ算法量化得到的原始密钥序列
R	PRNG生成的长度为N的随机数序列
I	序列R中所有元素有序排列前的索引位置
$q X +$	ASQ量化算法中较大的量化门限
$q X -$	ASQ量化算法中较小的量化门限
θ	可调节参数，用来调节ASQ量化保护带的宽度
Q_X	BMMQ中的量化门限集合
n	BMMQ量化门限的个数，能够将样本空间划分为n+1个区域
m，s，ε	$m, s, ε ∈ [1, n + 1]$
E_X_，_m	第m个量化区域的中心点
v_A，_i	具有方向的单位向量
δ	可调节参数，用来调节BMMQ量化保护带的宽度
K_X	原始密钥序列经信息协商后的密钥序列
C_X	D_X 经信号重构后的序列
ρ	自相关系数
γ	信噪比

Tab. 1 Description of variable symbols

变量符号	含义
y_X	Alice/Bob接收到的光信号序列，其中X=A代表Alice方，X=B代表Bob方
P_t	激光器发出光信号的功率
h_AB	Alice到Bob大气湍流引起的瞬时无线信道系数波动
h_BA	Bob到Alice大气湍流引起的瞬时无线信道系数波动
n_X	均值为0、方差为 $σ n X 2$ 的加性高斯白噪声
ϕ_X	Alice和Bob重构后的直接观测序列
N	合法双方直接观测序列的长度
D_X	直接观测序列随机抽样差分序列
k_X	ASQ/BMMQ算法量化得到的原始密钥序列
R	PRNG生成的长度为N的随机数序列
I	序列R中所有元素有序排列前的索引位置
$q X +$	ASQ量化算法中较大的量化门限
$q X -$	ASQ量化算法中较小的量化门限
θ	可调节参数，用来调节ASQ量化保护带的宽度
Q_X	BMMQ中的量化门限集合
n	BMMQ量化门限的个数，能够将样本空间划分为n+1个区域
m，s，ε	$m, s, ε ∈ [1, n + 1]$
E_X_，_m	第m个量化区域的中心点
v_A，_i	具有方向的单位向量
δ	可调节参数，用来调节BMMQ量化保护带的宽度
K_X	原始密钥序列经信息协商后的密钥序列
C_X	D_X 经信号重构后的序列
ρ	自相关系数
γ	信噪比

Fig. 1 Structure of optical wireless channel transmission model

Fig. 2 Steps of proposed scheme

Fig. 3 Schematic diagram of quantizer threshold and quantization guard band setting in ASQ algorithm

Fig. 4 Schematic diagram of quantization guard band setting and correction in BMMQ algorithm

Fig. 5 Comparison before and after first-order differential signal reconstruction

Fig. 6 Time series of directly observed signals and relationship between DA autocorrelation time tρDA and S

Fig. 7 ASQ quantization results under varying γ and θ

Fig. 8 Performance comparison between lossless ASQ and single-threshold lossless CQ

Fig. 9 IKDR of keys generated by legitimate parties using BMMQ and CQ

Tab. 2 NIST randomness test results

测试项	P-value
Frequency	0.122 3
Block Frequency	0.350 5
Cumulative Sums	0.534 1
Runs	0.122 3
Longest Run	0.739 9
Rank	0.534 1
FFT	0.534 1
Nonoverlapping Template	0.506 6
Overlapping Template	0.122 3
Approximate Entropy	0.911 4
Serial	0.066 9
Linear Complexity	0.350 5

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Difference-based shared key extraction scheme via multi-level quantization

基于差分的多级量化共享密钥提取方案

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