Direct generation of all-optical random numbers from optical pulse amplitude chaos

doi:10.1364/OE.20.004297

Direct generation of all-optical random numbers from optical pulse amplitude chaos

Pu Li, Yun-Cai Wang, An-Bang Wang, Ling-Zhen Yang, Ming-Jiang Zhang, and Jian-Zhong Zhang »View Author Affiliations

Optics Express, Vol. 20, Issue 4, pp. 4297-4308 (2012)
http://dx.doi.org/10.1364/OE.20.004297

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Abstract

We propose and theoretically demonstrate an all-optical method for directly generating all-optical random numbers from pulse amplitude chaos produced by a mode-locked fiber ring laser. Under an appropriate pump intensity, the mode-locked laser can experience a quasi-periodic route to chaos. Such a chaos consists of a stream of pulses with a fixed repetition frequency but random intensities. In this method, we do not require sampling procedure and external triggered clocks but directly quantize the chaotic pulses stream into random number sequence via an all-optical flip-flop. Moreover, our simulation results show that the pulse amplitude chaos has no periodicity and possesses a highly symmetric distribution of amplitude. Thus, in theory, the obtained random number sequence without post-processing has a high-quality randomness verified by industry-standard statistical tests.

OCIS Codes
(060.4510) Fiber optics and optical communications : Optical communications
(140.4050) Lasers and laser optics : Mode-locked lasers
(190.3100) Nonlinear optics : Instabilities and chaos
(200.4740) Optics in computing : Optical processing
(230.1150) Optical devices : All-optical devices

ToC Category:
Optics in Computing

History
Original Manuscript: November 28, 2011
Revised Manuscript: January 15, 2012
Manuscript Accepted: January 16, 2012
Published: February 7, 2012

Citation
Pu Li, Yun-Cai Wang, An-Bang Wang, Ling-Zhen Yang, Ming-Jiang Zhang, and Jian-Zhong Zhang, "Direct generation of all-optical random numbers from optical pulse amplitude chaos," Opt. Express 20, 4297-4308 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-4-4297

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References

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002). [CrossRef]
J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math. Series12, 36–38 (1951).
C. S. Petrie and J. A. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl.47(5), 615–621 (2000). [CrossRef]
C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express18(23), 23584–23597 (2010). [CrossRef] [PubMed]
J. Walker, “HotBits: Genuine Random Numbers, Generated by Radioactive Decay,” http://www.fourmilab.ch/hotbits/ .
M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput.52(4), 403–409 (2003). [CrossRef]
D. S. Ornstein, “Ergodic theory, randomness, and “chaos”,” Science243(4888), 182–187 (1989). [CrossRef] [PubMed]
G. M. Bernstein and M. A. Lieberman, “Secure random number generation using chaotic circuits,” IEEE Trans. Circ. Syst.37(9), 1157–1164 (1990). [CrossRef]
T. Stojanovski and L. Kocarev, “Chaos-based random number generators - Part I: analysis [cryptography],” IEEE Trans. Circ. Syst. I Fundam. Theory Appl.48, 281–288 (2001). [CrossRef]
T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators - Part II: practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl.48(3), 382–385 (2001). [CrossRef]
A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008). [CrossRef]
I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103(2), 024102 (2009). [CrossRef] [PubMed]
I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010). [CrossRef]
K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010). [CrossRef] [PubMed]
T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A83(3), 031803 (2011). [CrossRef]
A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express18(18), 18763–18768 (2010). [CrossRef] [PubMed]
P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express18(19), 20360–20369 (2010). [CrossRef] [PubMed]
Y. C. Wang, P. Li, and J. Z. Zhang, “Fast random bit generation in optical domain with ultrawide bandwidth chaotic laser,” IEEE Photon. Technol. Lett.22, 1680–1682 (2010).
R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm.17(4), 539–550 (1999). [CrossRef]
A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “NIST Statistical Tests Suite,” http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html .
G. Marsaglia, “DIEHARD: A battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard/ .
L. M. Zhao, D. Y. Tang, F. Lin, and B. Zhao, “Observation of period-doubling bifurcations in a femtosecond fiber soliton laser with dispersion management cavity,” Opt. Express12(19), 4573–4578 (2004). [CrossRef] [PubMed]
D. Y. Tang, L. M. Zhao, and F. Lin, “Numerical studies of routes to chaos in passively mode-locked ﬁber soliton ring lasers with dispersion-managed cavity,” Europhys. Lett.71(1), 56–62 (2005). [CrossRef]
L. Z. Yang, J. F. Zhu, Z. D. Qiao, X. Y. Yan, and Y. C. Wang, “Periodic intensity variations on the pulse-train of a passively mode-locked ﬁber ring laser,” Opt. Commun.283(19), 3798–3802 (2010). [CrossRef]
H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express17(2), 455–460 (2009). [CrossRef] [PubMed]
H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A80(4), 045803 (2009). [CrossRef]
H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express16(17), 12618–12623 (2008). [PubMed]
P. Grassberger and I. Procaccia, “Characterization of Strange Attractors,” Phys. Rev. Lett.50(5), 346–349 (1983). [CrossRef]
D. Prichard and J. Theiler, “Generating surrogate data for time series with several simultaneously measured variables,” Phys. Rev. Lett.73(7), 951–954 (1994). [CrossRef] [PubMed]
K. Huybrechts, W. D'Oosterlinck, G. Morthier, and R. Baets, “Proposal for an All-Optical Flip-Flop Using a Single Distributed Feedback Laser Diode,” IEEE Photon. Technol. Lett.20(1), 18–20 (2008). [CrossRef]
K. Huybrechts, G. Morthier, and R. Baets, “Fast all-optical flip-flop based on a single distributed feedback laser diode,” Opt. Express16(15), 11405–11410 (2008). [CrossRef] [PubMed]
K. Huybrechts, A. Ali, T. Tanemura, Y. Nakano, and G. Morthier, “Numerical and experimental study of the switching times and energies of DFB-laser based All-optical flip-flops,” presented at the International Conference on Photonics in Switching, Pisa, Italy, 15–19 Sept. 2009.

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[1] N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys.74(1), 145–195 (2002). [CrossRef]

[2] J. Von Neumann, “Various techniques used in connection with random digits,” Appl. Math. Series12, 36–38 (1951).

[3] C. S. Petrie and J. A. Connelly, “A noise-based IC random number generator for applications in cryptography,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl.47(5), 615–621 (2000). [CrossRef]

[4] C. R. S. Williams, J. C. Salevan, X. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express18(23), 23584–23597 (2010). [CrossRef] [PubMed]

[5] J. Walker, “HotBits: Genuine Random Numbers, Generated by Radioactive Decay,” http://www.fourmilab.ch/hotbits/ .

[6] M. Bucci, L. Germani, R. Luzzi, A. Trifiletti, and M. Varanonuovo, “A high-speed oscillator-based truly random number source for cryptographic applications on a Smart Card IC,” IEEE Trans. Comput.52(4), 403–409 (2003). [CrossRef]

[7] D. S. Ornstein, “Ergodic theory, randomness, and “chaos”,” Science243(4888), 182–187 (1989). [CrossRef] [PubMed]

[8] G. M. Bernstein and M. A. Lieberman, “Secure random number generation using chaotic circuits,” IEEE Trans. Circ. Syst.37(9), 1157–1164 (1990). [CrossRef]

[9] T. Stojanovski and L. Kocarev, “Chaos-based random number generators - Part I: analysis [cryptography],” IEEE Trans. Circ. Syst. I Fundam. Theory Appl.48, 281–288 (2001). [CrossRef]

[10] T. Stojanovski, J. Pihl, and L. Kocarev, “Chaos-based random number generators - Part II: practical realization,” IEEE Trans. Circ. Syst. I Fundam. Theory Appl.48(3), 382–385 (2001). [CrossRef]

[11] A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics2(12), 728–732 (2008). [CrossRef]

[12] I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett.103(2), 024102 (2009). [CrossRef] [PubMed]

[13] I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics4(1), 58–61 (2010). [CrossRef]

[14] K. Hirano, T. Yamazaki, S. Morikatsu, H. Okumura, H. Aida, A. Uchida, S. Yoshimori, K. Yoshimura, T. Harayama, and P. Davis, “Fast random bit generation with bandwidth-enhanced chaos in semiconductor lasers,” Opt. Express18(6), 5512–5524 (2010). [CrossRef] [PubMed]

[15] T. Harayama, S. Sunada, K. Yoshimura, P. Davis, K. Tsuzuki, and A. Uchida, “Fast nondeterministic random-bit generation using on-chip chaos lasers,” Phys. Rev. A83(3), 031803 (2011). [CrossRef]

[16] A. Argyris, S. Deligiannidis, E. Pikasis, A. Bogris, and D. Syvridis, “Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit,” Opt. Express18(18), 18763–18768 (2010). [CrossRef] [PubMed]

[17] P. Li, Y. C. Wang, and J. Z. Zhang, “All-optical fast random number generator,” Opt. Express18(19), 20360–20369 (2010). [CrossRef] [PubMed]

[18] Y. C. Wang, P. Li, and J. Z. Zhang, “Fast random bit generation in optical domain with ultrawide bandwidth chaotic laser,” IEEE Photon. Technol. Lett.22, 1680–1682 (2010).

[19] R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Comm.17(4), 539–550 (1999). [CrossRef]

[20] A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, J. Dray, and S. Vo, “NIST Statistical Tests Suite,” http://csrc.nist.gov/groups/ST/toolkit/rng/documentation_software.html .

[21] G. Marsaglia, “DIEHARD: A battery of tests of randomness,” http://www.stat.fsu.edu/pub/diehard/ .

[22] L. M. Zhao, D. Y. Tang, F. Lin, and B. Zhao, “Observation of period-doubling bifurcations in a femtosecond fiber soliton laser with dispersion management cavity,” Opt. Express12(19), 4573–4578 (2004). [CrossRef] [PubMed]

[23] D. Y. Tang, L. M. Zhao, and F. Lin, “Numerical studies of routes to chaos in passively mode-locked ﬁber soliton ring lasers with dispersion-managed cavity,” Europhys. Lett.71(1), 56–62 (2005). [CrossRef]

[24] L. Z. Yang, J. F. Zhu, Z. D. Qiao, X. Y. Yan, and Y. C. Wang, “Periodic intensity variations on the pulse-train of a passively mode-locked ﬁber ring laser,” Opt. Commun.283(19), 3798–3802 (2010). [CrossRef]

[25] H. Zhang, D. Y. Tang, L. M. Zhao, X. Wu, and H. Y. Tam, “Dissipative vector solitons in a dispersionmanaged cavity fiber laser with net positive cavity dispersion,” Opt. Express17(2), 455–460 (2009). [CrossRef] [PubMed]

[26] H. Zhang, D. Y. Tang, L. M. Zhao, and X. Wu, “Dark pulse emission of a fiber laser,” Phys. Rev. A80(4), 045803 (2009). [CrossRef]

[27] H. Zhang, D. Y. Tang, L. M. Zhao, and N. Xiang, “Coherent energy exchange between components of a vector soliton in fiber lasers,” Opt. Express16(17), 12618–12623 (2008). [PubMed]

[28] P. Grassberger and I. Procaccia, “Characterization of Strange Attractors,” Phys. Rev. Lett.50(5), 346–349 (1983). [CrossRef]

[29] D. Prichard and J. Theiler, “Generating surrogate data for time series with several simultaneously measured variables,” Phys. Rev. Lett.73(7), 951–954 (1994). [CrossRef] [PubMed]

[30] K. Huybrechts, W. D'Oosterlinck, G. Morthier, and R. Baets, “Proposal for an All-Optical Flip-Flop Using a Single Distributed Feedback Laser Diode,” IEEE Photon. Technol. Lett.20(1), 18–20 (2008). [CrossRef]

[31] K. Huybrechts, G. Morthier, and R. Baets, “Fast all-optical flip-flop based on a single distributed feedback laser diode,” Opt. Express16(15), 11405–11410 (2008). [CrossRef] [PubMed]

[32] K. Huybrechts, A. Ali, T. Tanemura, Y. Nakano, and G. Morthier, “Numerical and experimental study of the switching times and energies of DFB-laser based All-optical flip-flops,” presented at the International Conference on Photonics in Switching, Pisa, Italy, 15–19 Sept. 2009.

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Direct generation of all-optical random numbers from optical pulse amplitude chaos