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摘要:
基于信道随机特征的共享密钥提取是实现大气光信道物理层安全的一种有效手段。密钥生成速率和不一致率是关注焦点。利用大气湍流光信道随机特征作为共享随机源，提出多输入-多输出(Multiple-Input Multiple-Output, MIMO)大气光信道环境下的密钥提取方案；采用另类奇异值分解法来分解信道矩阵，通过简单移动平均提升合法双方获得的信道特征序列间的相关性，并对移动平均后的信道特征序列进行单门限交错量化；合法双方基于分集差分值生成编码映射控制随机序列，实现对信道特征序列的单门限交错量化结果的编码映射。实验结果表明，本文方案的原始密钥不一致率在信噪比为30 dB时能够达到5.2×10−4，且生成的随机比特序列可通过美国国家标准与技术研究院(NIST)的随机性测试。本文结果对MIMO大气光信道密钥提取有一定参考价值。
Abstract:Shared secret-key extraction from random channel characteristics is an effective approach to ensuring the physical layer security of atmospheric optical channels. The secret-key generation rate and disagreement rate are two issues that attract a lot of attention. Using the random characteristics of atmospheric turbulent optical channels as a shared source of randomness, a secret-key extraction scheme for multiple-input multiple-output (MIMO) atmospheric optical channels is proposed. The alternative singular value decomposition is used to decompose the channel matrix; the correlation between the two channel characteristic sequences obtained by the two legitimate parties is enhanced by carrying out a simple moving average; a channel quantization alternating scheme with a single threshold is used to quantize the resultant channel characteristic sequences. The two legitimate parties generate random controlling sequences for coding mapping based on differential diversity values, which are used in performing coding mapping of the quantized bits of the channel characteristic sequences generated by the channel quantization alternating scheme with a single threshold. The experimental results show that our scheme’s initial key disagreement rate can reach 5.2×10−4 at a signal-to-noise ratio of 30 dB, and that the generated random bit sequences have passed the National Institute of Standards and Technology (NIST) randomness test. This paper’s results are useful in the implementation of secret-key extraction from atmospheric MIMO optical channels.
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Key words:
- MIMO /
- optical channel /
- atmospheric turbulence /
- secret-key extraction /
- quantization
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图 4 不同移动平均窗口大小下
$ {\boldsymbol{r}}_{A,i}^{\left(1\right)} $ 与$ {\boldsymbol{r}}_{B,i}^{\left(1\right)} $ 的皮尔逊相关系数Figure 4. Pearson correlation coefficient between
$ {\boldsymbol{r}}_{A,i}^{\left(1\right)} $ and$ {\boldsymbol{r}}_{B,i}^{\left(1\right)} $ with different moving average window sizes
图 6 不同方案的原始密钥不一致率对比图
Figure 6. Comparison chart of initial key disagreement rate for different schemes
表 1 NIST随机性测试结果
Table 1. NIST Randomness Test Results
Test Average P-value 频率 0.066882 块内频率 0.058146 游程 0.350485 最大游程 0.213309 二进制矩阵秩 0.065429 离散傅里叶变换 0.534971 非重叠字匹配 0.739913 重叠字匹配 0.911413 线性复杂度 0.739918 串行 0.122325 0.035174 累积和 0.064229 0.067324 
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