Secure Transmission of Identification Code in Loran C Station Based on EPR States

Luhan Zhao; Chunyan Yang; Chao Chen; Junwen Luo

doi:10.3788/LOP202158.0927002

Journals >Laser & Optoelectronics Progress >Volume 58 >Issue 9 >Page 0927002 > Article

Laser & Optoelectronics Progress
Vol. 58, Issue 9, 0927002 (2021)

Secure Transmission of Identification Code in Loran C Station Based on EPR States

Luhan Zhao, Chunyan Yang^*, Chao Chen, and Junwen Luo

Author Affiliations

Information and Navigation College, Air Force Engineering University, Xi'an , Shaanxi 710077, China

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DOI: 10.3788/LOP202158.0927002 Cite this Article Set citation alerts

Luhan Zhao, Chunyan Yang, Chao Chen, Junwen Luo. Secure Transmission of Identification Code in Loran C Station Based on EPR States[J]. Laser & Optoelectronics Progress, 2021, 58(9): 0927002 Copy Citation Text

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Abstract

The identification and secure transmission of the station phase codes in the Loran C system are the premise of judging chains and receiving signals for hyperbolic positioning. Aiming at the problem that the Loran C system cannot achieve high security transmission by classical means, we propose a phase code transmission scheme based on EPR state quantum signals and analyse the security of this scheme under the entanglement attack and spectroscopic attack. The relationship between the information transmission efficiency and the transmission coefficient of the spectroscope as well as that between the information transmission efficiency and the compression degree of the spectroscope is obtained, which verifies that the proposed scheme can effectively improve the security of phase code transmission between the main station and the secondary station in the Loran C system.

Keywords

Loran C quantum optics secure transmission station identification code two mode squeezed states

i_{0} (t) = A {(t - τ)}^{2} e x p [- 2 \frac{(t - τ)}{65}] s i n (0.2 π t + p_{0})

，（1）

\{\begin{array}{l} a_{11} = S {(r, ϕ)}^{+} a_{10} S (r, ϕ) = a_{10} c o s h (r) + a_{20}^{+} s i n h (r) \\ a_{21} = S {(r, ϕ)}^{+} a_{20}^{} S (r, ϕ) = a_{20}^{} c o s h (r) + a_{10}^{+} s i n h (r) \end{array}

，（2）

S (r, ϕ) = e x p [r e x p (- i ϕ) a_{10} a_{20}^{} - r e x p (i ϕ) a_{10}^{+} a_{20}^{+}]

，（3）

\{\begin{array}{l} X_{a_{11}} = X_{a_{10}} c o s h (r) + X_{a_{10}} s i n h (r) \\ X_{a_{21}} = X_{a_{20}} c o s h (r) + X_{a_{10}} s i n h (r) \\ P_{a_{11}} = P_{a_{10}} c o s h (r) - P_{a_{20}} s i n h (r) \\ P_{a_{21}} = P_{a_{20}} c o s h (r) - P_{a_{10}} s i n h (r) \end{array}

，（4）

\{\begin{matrix} \underset{r \to + \infty}{l i m} X_{a_{11}} = X_{a_{21}} \\ \underset{r \to + \infty}{l i m} P_{a_{11}} = - P_{a_{21}} \end{matrix}

。（5）

\{\begin{matrix} X_{u 0} = \frac{1}{\sqrt[]{2}} (X_{a_{11}} - X_{a_{21}}) \\ P_{u 0} = \frac{1}{\sqrt[]{2}} (P_{a_{11}} + P_{a_{21}}) \end{matrix}

。（6）

\{\begin{array}{l} a_{12} = D_{A}^{+} a_{11} D_{A} \\ a_{12}^{*} = D_{M}^{+} a_{12} D_{M} \end{array}

，（7）

\{\begin{array}{l} X_{a_{12}} = X_{a_{11}} + x_{A} \\ X_{a_{12}^{*}} = X_{a_{12}} + x_{M} \end{array}

，（8）

\{\begin{array}{l} X_{u 1} = \frac{1}{\sqrt[]{2}} (X_{a_{14}} - X_{a_{23}}) = \frac{1}{\sqrt[]{2}} (X_{a_{11}} + X_{x_{A}} - X_{a_{21}}) \\ P_{u 1} = \frac{1}{\sqrt[]{2}} (P_{a_{14}} + P_{a_{23}}) = \frac{1}{\sqrt[]{2}} (P_{a_{11}} + P_{y_{A}} + P_{a_{21}}) \end{array}

，（9）

\{\begin{array}{l} X_{u}^{'} = \frac{1}{\sqrt[]{2}} (X_{a_{11}} + x_{A} - X_{a_{21}}) \\ P_{u}^{'} = \frac{1}{\sqrt[]{2}} (P_{a_{11}} + y_{A} + P_{a_{21}}) \end{array}

。（10）

\{\begin{array}{l} x_{A} = \sqrt[]{2} (X_{u}^{'} - X_{u 0}) \\ y_{A} = \sqrt[]{2} (P_{u}^{'} - P_{u 0}) \end{array}

。（11）

\{\begin{array}{l} X_{a_{13}} = \sqrt[]{η_{1}} X_{a_{12}^{*}} + \sqrt[]{1 - η_{1}} X_{a_{N 1}} \\ X_{a_{E 1}} = \sqrt[]{1 - η_{1}} X_{a_{12}^{*}} - \sqrt[]{η_{1}} X_{a_{N 1}} \end{array}

，（12）

\{\begin{array}{l} X_{a_{22}} = \sqrt[]{η_{2}} X_{a_{21}} + \sqrt[]{1 - η_{2}} X_{a_{N 2}} \\ X_{a_{E 2}} = \sqrt[]{1 - η_{2}} X_{a_{21}} - \sqrt[]{η_{2}} X_{a_{N 2}} \end{array}

，（13）

\{\begin{array}{l} P_{a_{13}} = \sqrt[]{η_{1}} P_{a_{12}^{*}} + \sqrt[]{1 - η_{1}} P_{a_{N 1}} \\ P_{a_{E 1}} = \sqrt[]{1 - η_{1}} P_{a_{12}^{*}} - \sqrt[]{η_{1}} P_{a_{N 1}} \end{array}

，（14）

\{\begin{array}{l} P_{a_{22}} = \sqrt[]{η_{2}} P_{a_{21}} + \sqrt[]{1 - η_{2}} P_{a_{N 2}} \\ P_{a_{E 2}} = \sqrt[]{1 - η_{2}} P_{a_{21}} - \sqrt[]{η_{2}} P_{a_{N 2}} \end{array}

，（15）

X_{u 2} = \frac{1}{\sqrt[]{2}} (X_{a_{13}} - X_{a_{22}}) = \frac{1}{\sqrt[]{2}} (\sqrt[]{η_{1}} X_{a_{12}^{*}} + \sqrt[]{1 - η_{1}} X_{a_{N 1}} - \sqrt[]{η_{2}} X_{a_{21}} - \sqrt[]{1 - η_{2}} X_{a_{N 2}}) =

\frac{1}{\sqrt[]{2}} [(\sqrt[]{η_{1}} X_{a_{10}} - \sqrt[]{η_{2}} X_{a_{20}}) c o s h (r) + (\sqrt[]{η_{1}} X_{a_{20}} - \sqrt[]{η_{2}} X_{a_{10}}) s i n h (r) + \sqrt[]{1 - η_{1}} X_{a_{N 1}} - \sqrt[]{1 - η_{2}} X_{a_{N 2}} + \sqrt[]{η_{1}} X_{x_{A}}]

，（16）

I (M a i n, S e c) = l b (1 + \frac{S_{1}}{N_{1}}) = l b \{1 + \frac{8 η_{1} V_{x_{A}}}{(η_{1} + η_{2}) [c o s h (2 r) - 1] - \sqrt[]{η_{1} η_{2}} s i n h (2 r) + 2}\},

（17）

\begin{array}{l} X_{u E} = \frac{1}{\sqrt[]{2}} (X_{a_{E 1}} - X_{a_{E 2}}) = \frac{1}{\sqrt[]{2}} (\sqrt[]{1 - η_{1}} X_{a_{12}^{*}}^{} - \sqrt[]{η_{1}} X_{a_{N 1}} - \sqrt[]{1 - η_{2}} X_{a_{21}^{}}^{} + \sqrt[]{η_{2}} X_{a_{N 2}}) = \\ \frac{1}{\sqrt[]{2}} [(\sqrt[]{1 - η_{1}} X_{a_{10}^{}}^{} - \sqrt[]{1 - η_{2}} X_{a_{20}^{}}^{}) c o s h (r) + (\sqrt[]{1 - η_{1}} X_{a_{20}^{}}^{} - \sqrt[]{1 - η_{2}} X_{a_{10}^{}}^{}) s i n h (r) - \\ \sqrt[]{η_{1}} X_{a_{N 1}} + \sqrt[]{η_{2}} X_{a_{N 2}} - \sqrt[]{(1 - η_{1})} X_{A}^{}] 。 \end{array}

（18）

I (M a i n, E v e) = l b (1 + \frac{S_{E}}{N_{E}})

。（19）

S_{E} = \frac{1}{2} (1 - η_{1}) V_{x_{A}}

，（20）

I (M a i n, E v e) = l b \{1 + \frac{8 (1 - η_{1}) V_{x_{A}}}{[2 - (η_{1} + η_{2})] c o s h (2 r) - \sqrt[]{(1 - η_{1}) (1 - η_{2})} s i n h (2 r) + η_{1} + η_{2}}\}

，（21）

Luhan Zhao, Chunyan Yang, Chao Chen, Junwen Luo. Secure Transmission of Identification Code in Loran C Station Based on EPR States[J]. Laser & Optoelectronics Progress, 2021, 58(9): 0927002

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