国家重点研发计划(2017YFB0801903)
国家自然科学基金(61601514)
国家自然科学基金(61501516)
国家自然科学基金(61521003)
国家自然科学基金(61471396)
中国博士后科学基金(2016M592990)
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Figure 1
SKG model. (a) Source-type; (b) channel-type
Figure 2
SKG procedures based on SSS and SPC
Figure 3
(Color online) DBER versus KOP $L_{\rm~K}=~128$
Figure 6
SPC model
Transmitted power at Alice | Received noise power at Bob | Received SNR threshold at Bob | Key length |
$P~=~500$ | $\sigma~_{\rm~B}^2~=~1$ | $\rho~_{\rm~B}^\tau~=~10$ dB | ${L_{\rm~K}}~=~128$ |
Received noise power at Eve | $P_{\rm~cop}$ threshold | Population number | SPC length |
$\sigma~_{\rm~E}^2~=~0$ | $P_{\rm~cop}^\tau~=~10^{-6}$ | ${N_{\rm~P}}~=~200$ | $N~=~512$ |
Maximum generation | Crossover probability | Mutation probability | |
${G_{\rm~max}}~=~100$ | ${P_{\rm~crossover}}~=~0.6$ | ${P_{\rm~mutation}}~=~0.02$ |
Compute $P_{\rm~e}^{\rm~AB}(~{W_N^{(i)}}~)$ and $P_{\rm~e}^{\rm~AE}(~{W_N^{(i)}}~)$ by Gaussian approximation and ${\rho~_{\rm~B}},~{\rho~_{\rm~E}}$; |
Sort $P_{\rm~e}^{\rm~AB}(~{W_N^{(i)}}~)$ to screen the polarized sub-channels by ( |
Solve ( |
Return the SPC $({K_{\rm~M}},{{I}_{\rm~M}},{K_{\rm~R}},{{I}_{\rm~R}},{K_{\rm~F}},{{I}_{\rm~F}})$ and $\eta$, $L_{\rm~I}$; |
Estimate the legitimate channel ${~\boldsymbol{\hat~h}}$ using the received signal ${{\boldsymbol{y}}_{\rm~pilot}}$ and the public pilot ${{\boldsymbol{x}}_{\rm~pilot}}$; |
Compute the SSS parameters $\phi,\alpha,{\rho~_{\rm~B}},{\rho~_{\rm~E}}$ by ( |
Construct the SPC $({K_{\rm~M}},{{I}_{\rm~M}},{K_{\rm~R}},{{I}_{\rm~R}},{K_{\rm~F}},{{I}_{\rm~F}})$ and obtain the parameter $\eta$, ${L_{\rm~I}}$ with GA$^2$SPCC algorithm; |
Secure polar encoding ${{\boldsymbol{u}}_{\rm~M}}$ and then BPSK modulation to obtain ${v_1}(t)$; |
Generate the signal-like noise ${v_i}(t),i~=~2,3,~\ldots~,{N_{\rm~A}}$ and send out with the desired signal together; |
Obtain the secret keys $K$ by Hash function with the input length ${L_{\rm~I}}$. |
Frequency | Block frequency (128) | Cumulative sums (Fwd) | Cumulative sums (Rev) | Runs |
0.472894 | 0.483268 | 0.479731 | 0.582617 | 0.318374 |
Longest run | Rank | Approximate entropy | Linear complexity | Serial |
0.028386 | 0.526912 | 0.046022 | 0.953862 | 0.903275 |
FFT | Non overlapping template | Overlapping template | ||
0.673452 | 0.927958 | 0.207544 |
BPSK demodulate the received signal $y_{\rm~B}$; |
Secure polar decode to get ${\boldsymbol{\hat~u}}_{\rm~M}^{\rm~B}$ by $({K_{\rm~M}},{{I}_{\rm~M}},{K_{\rm~R}},{{I}_{\rm~R}},{K_{\rm~F}},{{I}_{\rm~F}})$; |
Obtain the secret keys $K$ by Hash function with the input length $L_{\rm~I}$. |