SCIENTIA SINICA Informationis, Volume 49, Issue 4: 486-502(2019) https://doi.org/10.1360/N112018-00119

Nonagreement secret key generation based on spatial symmetric scrambling and secure polar coding

More info
  • ReceivedMay 16, 2018
  • AcceptedDec 25, 2018
  • PublishedApr 3, 2019


Most existing secret key generation (SKG) methods are complicated and depend on the security capacity. This study aims to propose a non-agreement SKG method based on spatial symmetric scrambling (SSS) and secure polar coding (SPC), which only consists of secure transmission and privacy amplification. First, SSS provides a channel advantage and high security by replacing traditional Gaussian artificial noise with signal-like noise to ensure the existence of secure capacity. Second, the SPC is designed through Gaussian approximation and generic algorithm based on the acquired channel advantage and desired SKG performance to guarantee the security of transmitted information. Finally, the secret information is safely transmitted through SPC and SSS, and secret keys can be further generated by privacy amplification. The simulated results verify the feasibility of SSS and SPC and further illustrate that the proposed SKG method can meet the designed performance requirement. The National Institute of Standards and Technology test is also conducted and the results show the strong randomness of the generated keys.

Funded by








[1] Zou Y, Zhu J, Wang X. A Survey on Wireless Security: Technical Challenges, Recent Advances, and Future Trends. Proc IEEE, 2016, 104: 1727-1765 CrossRef Google Scholar

[2] Rezki Z, Zorgui M, Alomair B. Secret Key Agreement: Fundamental Limits and Practical Challenges. IEEE Wireless Commun, 2017, 24: 72-79 CrossRef Google Scholar

[3] Maurer U M. Secret key agreement by public discussion from common information. IEEE Trans Inform Theor, 1993, 39: 733-742 CrossRef Google Scholar

[4] Ahlswede R, Csiszar I. Common randomness in information theory and cryptography. I. Secret sharing. IEEE Trans Inform Theor, 1993, 39: 1121-1132 CrossRef Google Scholar

[5] Zhang J, Duong T Q, Marshall A. Key Generation From Wireless Channels: A Review. IEEE Access, 2016, 4: 614-626 CrossRef Google Scholar

[6] Goel S, Negi R. Guaranteeing Secrecy using Artificial Noise. IEEE Trans Wireless Commun, 2008, 7: 2180-2189 CrossRef Google Scholar

[7] Koyluoglu O O, El Gamal H. Polar Coding for Secure Transmission and Key Agreement. IEEE TransInformForensic Secur, 2012, 7: 1472-1483 CrossRef Google Scholar

[8] Chou R A, Bloch M R, Abbe E. Polar Coding for Secret-Key Generation. IEEE Trans Inform Theor, 2015, 61: 6213-6237 CrossRef Google Scholar

[9] Liu L. Research on MISO spatial scrambling techniques: interference suppression and secrecy enhancement. Dissertation for Master Degree. Zhengzhou: Information Engineering University, 2013. Google Scholar

[10] Mahdavifar H, Vardy A. Achieving the Secrecy Capacity of Wiretap Channels Using Polar Codes. IEEE Trans Inform Theor, 2011, 57: 6428-6443 CrossRef Google Scholar

[11] Gulcu T C, Barg A. Achieving Secrecy Capacity of the Wiretap Channel and Broadcast Channel With a Confidential Component. IEEE Trans Inform Theor, 2017, 63: 1311-1324 CrossRef Google Scholar

[12] Maurer U M, Wolf S. Secret-key agreement over unauthenticated public channels-part III: privacy amplification. IEEE Trans Inform Theor, 2003, 49: 839-851 CrossRef Google Scholar

[13] Zhou X, McKay M R. Secure Transmission With Artificial Noise Over Fading Channels: Achievable Rate and Optimal Power Allocation. IEEE Trans Veh Technol, 2010, 59: 3831-3842 CrossRef Google Scholar

[14] Li N. Performance analysis of physical layer security in multiuser communications. Dissertation for Ph.D. Degree. Beijing: Beijing University of Posts and Telecommunications, 2015. Google Scholar

[15] Tang X, Liu R, Spasojevic P. On the Throughput of Secure Hybrid-ARQ Protocols for Gaussian Block-Fading Channels. IEEE Trans Inform Theor, 2009, 55: 1575-1591 CrossRef Google Scholar

[16] Xu X M. Physical layer secure transmission design and optimization in random cognitive radio networks. Dissertation for Ph.D. Degree. Nanjing: PLA University of Scince and Technoledge, 2016. Google Scholar

[17] Arikan E. Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels. IEEE Trans Inform Theor, 2009, 55: 3051-3073 CrossRef Google Scholar

[18] Schürch C. A partial order for the synthesized channels of a polar code. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Barcelona, 2016. 220--224. Google Scholar

[19] Trifonov P. Efficient Design and Decoding of Polar Codes. IEEE Trans Commun, 2012, 60: 3221-3227 CrossRef Google Scholar

[20] Dai J, Niu K, Si Z. Does Gaussian Approximation Work Well for the Long-Length Polar Code Construction?. IEEE Access, 2017, 5: 7950-7963 CrossRef Google Scholar

[21] Gao H, Smith P J, Clark M V. Theoretical reliability of MMSE linear diversity combining in Rayleigh-fading additive interference channels. IEEE Trans Commun, 1998, 46: 666-672 CrossRef Google Scholar

[22] Final Report of 3GPP TSG RAN WG1 #88bis v1.0.0. document R1-1708890. 2017. Google Scholar

  • 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 4

    (Color online) Contours of $\log_{10}(P_{\rm~cop})$ ($\rho~_{\rm~B}^\tau~=$ 10 dB)

  • Figure 5

    (Color online) Contours of $\log_{10}(P_{\rm~sop})$ ($P_{\rm~cop}^{\tau}={10^{-6}}$)

  • Figure 6

    SPC model

  • Figure 7

    (Color online) $\alpha$ with different $N_{\rm~A}$

  • Figure 8

    (Color online) The average fitness of population

  • Figure 9

    (Color online) KOP with different KOP thresholds

  • Figure 10

    (Color online) KGE with different KOP thresholds

  • Figure 11

    (Color online) Bob's DBER and its upper bound

  • Figure 12

    (Color online) Eve's DBER and its lower bound

  • Table 1   Simulated parameters
    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
    ${G_{\rm~max}}~=~100$ ${P_{\rm~crossover}}~=~0.6$ ${P_{\rm~mutation}}~=~0.02$

    Algorithm 1 GA$^2$SPCC algorithm

    Require:$N,\;~{\rho~_{\rm~B}},\;~{\rho~_{\rm~E}},\;~{L_{\rm~K}},\;~{P_{\rm~kop}^\tau}$; ${N_{\rm~P}},\;~{G_{\rm~max}},\;~{P_{\rm~crossover}},\;~{P_{\rm~mutation}}$;

    Output: $({K_{\rm~M}},{{I}_{\rm~M}},{K_{\rm~R}},{{I}_{\rm~R}},{K_{\rm~F}},{{I}_{\rm~F}})$; $\eta~,{L_{\rm~I}}$;

    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 (33);

    Solve (32) by generic algorithm with the given parameters;

    Return the SPC $({K_{\rm~M}},{{I}_{\rm~M}},{K_{\rm~R}},{{I}_{\rm~R}},{K_{\rm~F}},{{I}_{\rm~F}})$ and $\eta$, $L_{\rm~I}$;


    Algorithm 2 SKG procedures at Alice


    Output: $({K_{\rm~M}},{{I}_{\rm~M}},{K_{\rm~R}},{{I}_{\rm~R}},{K_{\rm~F}},{{I}_{\rm~F}})$; $\eta~,{L_{\rm~I}},~K$;

    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 (19);

    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 ${L_{\rm~I}}$.

  • Table 2   NIST test results
    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

    Algorithm 3 SKG procedures at Bob


    Output: $K$;

    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 $L_{\rm~I}$.

Copyright 2019 Science China Press Co., Ltd. 《中国科学》杂志社有限责任公司 版权所有