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Random source is important for the security of key distribution. In this paper, a novel secure key distribution scheme based on unidirectional injection of vertical cavity surface emitting laser (VCSEL) system is proposed. In the proposed scheme, a chaotic signal without time delay signature is generated by a VCSEL subject to unidirectional optical injection, which is regarded as a master laser. The chaotic signal generated by the master VCSEL is further injected into two slave VCSELs to obtain synchronized bandwidth-enhanced chaotic signals. After that, by sampling, quantizing and XOR operation on the two synchronized chaotic signals, two key streams can be obtained. Based on the well-known spin-flip model, the time delay signature of chaotic signals generated by master VCSEL and the synchronization performance between the master VCSELs and two slave VCSELs are numerically investigated in detail. It is shown that by the unidirectional injection, the chaotic outputs can be achieved in the master VCSEL in a wide range of frequency detuning and coupling strength. More importantly, no time delay signature can be observed in the auto correlation function of the chaotic intensity time series generated by the master VCSEL. Besides, we find that high quality synchronization is achieved between the bandwidth-enhanced chaotic signals generated by two slave VCSELs under the common driving of master VCSEL. The synchronization coefficient between two slave VCSELs increases up to 0.99, and the synchronization coefficient between master VCSEL and salve VCSEL is only 0.74. Note that such a high quality synchronization between two slave VCSELs while relatively low quality synchronization between the master and slave VCSEL is conducible to ensuring the security of key distribution. In addition, the effects of tunable parameters on key bit error rate are considered, and two quantization methods are employed for comparison. Numerical simulation results show that the key bit error rate between two legitimate users is as low as 1%, and the key bit error rate between legitimate user and eavesdropper is higher than 10% in the single-threshold case; the bit error rate can even be as low as 10-6 in the double-threshold case. The influence of parameter mismatch on key bit error rate is also discussed, and it is suggested that two salve VCSELs should be finely matched to ensure low bit error rate. Finally, NIST randomness test is performed for the generated key streams. Hence, the proposed scheme enhances the security of key distribution, which is valuable for further developing the chaos communication systems.
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Keywords:
- vertical cavity surface emitting laser /
- key distribution /
- secure communication /
- chaotic synchronization
[1] Diffie W, Hellman M 1976 IEEE Trans. Inf. Theory 22 644
[2] Huang D, Huang P, Lin D, Wang C, Zeng G 2015 Opt. Lett. 40 3695
[3] Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360
[4] Guo X X, Xiang S Y, Zhang Y H, Wen A J, Hao Y 2018 IEEE J. Quantum Electron. 54 2000308
[5] Zhang J B, Zhang J Z, Yang Y B, Liang J S, Wang Y C 2010 Acta Phys. Sin. 59 7679 (in Chinese)[张继兵, 张建忠, 杨毅彪, 梁君生, 王云才 2010 物理学报 59 7679]
[6] Yoshimura K, Muramatsu J, Davis P, Harayama T, Okumura H, Morikatsu S, Aida H, Uchida A 2012 Phys. Rev. Lett. 108 070602
[7] Koizumi H, Morikatsu S, Aida H, Nozawa T, Kakesu I, Uchida A, Yoshimura K, Muramatsu J, Davis P 2013 Opt. Express 211 7869
[8] Wang L, Guo Y, Sun Y, Zhao Q, Lan D, Wang Y, Wang A 2015 IEEE J. Quantum Electron. 51 8000208
[9] Jiang N, Xue C, Liu D, Lv Y, Qiu K 2017 Opt. Lett. 42 1055
[10] Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 141 (in Chinese)[唐曦, 吴加贵, 夏光琼, 吴正茂 2011 物理学报 60 141]
[11] Yang F, Tang X, Zhong Z Q, Xia G Q, Wu Z M 2016 Acta Phys. Sin. 65 118 (in Chinese)[杨峰, 唐曦, 钟祝强, 夏光琼, 吴正茂 2016 物理学报 65 118]
[12] Jiang N, Pan W, Yan L, Luo B, Xiang S, Yang L, Zheng D, Li N 2011 IEEE J. Sel. Top. Quantum Electron. 17 1220
[13] Argyris A, Pikasis E, Syvridis D 2016 J. Lightwave Technol. 34 5325
[14] Martin-Regalado J, Prati F, Miguel M San, Abraham N B 1997 IEEE J. Quantum Electron. 33 765
[15] Zhang H, Xiang S Y, Zhang Y H, Guo X X 2017 Appl. Opt. 56 6728
[16] Xiang S Y, Zhang H, Guo X X, Li J F, Wen A J, Pan W, Hao Y 2017 IEEE J. Sel. Top. Quantum Electron. 23 1700207
[17] Hong Y, Paul J, Spencer P S, Shore K A 2006 JOSA B 23 2285
[18] Lin F Y, Liu J M 2003 Opt. Commun. 221 173
[19] Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimiri S, Davis P 2008 Nat. Photonics 2 728
[20] Buskila O, Eyal A, Shtaif M 2008 Opt. Express 16 3383
[21] Xue C, Jiang N, Qiu K, Lv Y 2015 Opt. Express 23 14510
[22] Liu J, Wu Z M, Xia G Q 2009 Opt. Express 17 12619
[23] Yang H B, Wu Z M, Tang X, Wu J G, Xia G Q 2015 Acta Phys. Sin. 64 084204 (in Chinese)[杨海波, 吴正茂, 唐曦, 吴加贵, 夏光琼 2015 物理学报 64 084204]
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[1] Diffie W, Hellman M 1976 IEEE Trans. Inf. Theory 22 644
[2] Huang D, Huang P, Lin D, Wang C, Zeng G 2015 Opt. Lett. 40 3695
[3] Li P, Wang Y C, Zhang J Z 2010 Opt. Express 18 20360
[4] Guo X X, Xiang S Y, Zhang Y H, Wen A J, Hao Y 2018 IEEE J. Quantum Electron. 54 2000308
[5] Zhang J B, Zhang J Z, Yang Y B, Liang J S, Wang Y C 2010 Acta Phys. Sin. 59 7679 (in Chinese)[张继兵, 张建忠, 杨毅彪, 梁君生, 王云才 2010 物理学报 59 7679]
[6] Yoshimura K, Muramatsu J, Davis P, Harayama T, Okumura H, Morikatsu S, Aida H, Uchida A 2012 Phys. Rev. Lett. 108 070602
[7] Koizumi H, Morikatsu S, Aida H, Nozawa T, Kakesu I, Uchida A, Yoshimura K, Muramatsu J, Davis P 2013 Opt. Express 211 7869
[8] Wang L, Guo Y, Sun Y, Zhao Q, Lan D, Wang Y, Wang A 2015 IEEE J. Quantum Electron. 51 8000208
[9] Jiang N, Xue C, Liu D, Lv Y, Qiu K 2017 Opt. Lett. 42 1055
[10] Tang X, Wu J G, Xia G Q, Wu Z M 2011 Acta Phys. Sin. 60 141 (in Chinese)[唐曦, 吴加贵, 夏光琼, 吴正茂 2011 物理学报 60 141]
[11] Yang F, Tang X, Zhong Z Q, Xia G Q, Wu Z M 2016 Acta Phys. Sin. 65 118 (in Chinese)[杨峰, 唐曦, 钟祝强, 夏光琼, 吴正茂 2016 物理学报 65 118]
[12] Jiang N, Pan W, Yan L, Luo B, Xiang S, Yang L, Zheng D, Li N 2011 IEEE J. Sel. Top. Quantum Electron. 17 1220
[13] Argyris A, Pikasis E, Syvridis D 2016 J. Lightwave Technol. 34 5325
[14] Martin-Regalado J, Prati F, Miguel M San, Abraham N B 1997 IEEE J. Quantum Electron. 33 765
[15] Zhang H, Xiang S Y, Zhang Y H, Guo X X 2017 Appl. Opt. 56 6728
[16] Xiang S Y, Zhang H, Guo X X, Li J F, Wen A J, Pan W, Hao Y 2017 IEEE J. Sel. Top. Quantum Electron. 23 1700207
[17] Hong Y, Paul J, Spencer P S, Shore K A 2006 JOSA B 23 2285
[18] Lin F Y, Liu J M 2003 Opt. Commun. 221 173
[19] Uchida A, Amano K, Inoue M, Hirano K, Naito S, Someya H, Oowada I, Kurashige T, Shiki M, Yoshimiri S, Davis P 2008 Nat. Photonics 2 728
[20] Buskila O, Eyal A, Shtaif M 2008 Opt. Express 16 3383
[21] Xue C, Jiang N, Qiu K, Lv Y 2015 Opt. Express 23 14510
[22] Liu J, Wu Z M, Xia G Q 2009 Opt. Express 17 12619
[23] Yang H B, Wu Z M, Tang X, Wu J G, Xia G Q 2015 Acta Phys. Sin. 64 084204 (in Chinese)[杨海波, 吴正茂, 唐曦, 吴加贵, 夏光琼 2015 物理学报 64 084204]
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