Fast random bits generation based on a single chaotic semiconductor ring laser

The use of the postprocessing method consisting of bitwise Exclusive-OR and least significant bits extraction to generate random bit sequences typically requires two distinct chaotic outputs. While the two signals are, in general, generated using two separated devices, e.g. two Fabry-Perot lasers, a single semiconductor ring laser can be used as an alternative due to its circular symmetry which facilitates lasing in two counterpropagating mode directions. We consider a chaotic semiconductor ring laser and investigate both numerically and experimentally its characteristics for fast random bit generation. In particular, we show that by sampling each directional mode’s output signal using a 8-bit analog-digital converter and through Exclusive-OR operation applied to the two resulting signals (after throwing away 4 most significant bits), we can achieve fast random bit-streams with a bit rate 4× 10 = 40 Gbit/s, passing the statistical randomness tests. To optimize the system performance, we also study the dependence of randomness on the main system parameters and on noise. © 2012 Optical Society of America OCIS codes: (140.3560) Laser, ring; (030.6600) Statistical optics, (060.0060) Fiber optics and optical communications; (140.1540) Chaos. References and links 1. N. Ferguson, B. Schneier, and T. Kohno, Cryptography Engineering: Design Principles and Practical Applications (Wiley, 2010). 2. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst. I, 44, 521-528 (1997). 3. T. Stojanovski and L. Kocarev, “Chaos-based random number generators part I: Analysis [cryptography],” IEEE Trans. Circuits Syst. I: Fundam. Theory Applicat. 48, 281-288 (2001). 4. R. M. Nguimdo, P. Colet, L. Larger and L. Pesquera, “Digital key for chaos communication performing time delay concealment,” Phys. Rev. Lett. 107, 034103/1-4 (2011). 5. R. M. Nguimdo and P. Colet, “Electro-optic phase chaos systems with an internal variable and a digital key,” Opt. Express 20, 25333-25344 (2012). 6. 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. Photonics 2, 728-732 (2008). 7. T. E. Murphy, and R. Roy, “The worlds fastest dice, Nat. Photonics 2, 714-715 (2008). 8. K. Hirano, K. Amano, A. Uchida, S. Naito, M. Inoue, S. Yoshimori, K. Yoshimura, and P. Davis, “Characteristics of fast physical random bit generation using chaotic semiconductor lasers,” IEEE J. Quantum Electron. 45, 13671379 (2009). 9. I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultra high-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. 103, 024102 (2009). #177551 $15.00 USD Received 5 Oct 2012; revised 16 Nov 2012; accepted 16 Nov 2012; published 10 Dec 2012 (C) 2012 OSA 17 December 2012 / Vol. 20, No. 27 / OPTICS EXPRESS 28603 10. 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. Express 18, 18763-18768 (2010). 11. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics 4, 58-61 (2010). 12. 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. Express 18, 5512-5524 (2010). 13. N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Dynamics of a semiconductor laser with polarizationrotated feedback and its utilization for random bit generation,” Opt. Lett. 36, 4632 (2011). 14. C. R. S. Williams, J. C. Salevan, X.-W. Li, R. Roy, and T. E. Murphy, “Fast physical random number generator using amplified spontaneous emission,” Opt. Express 18, 23584-23597 (2010). 15. R. H. Walden, “Analog-to-digital converter survey and analysis,” IEEE J. Sel. Areas Commun. 17, 539-550 (1999) 16. M. Sorel, G. Giuliani, A. Sciré, R. Miglierina, J. P. R. Laybourn, and S. Donati, “Operating regimes of GaAsAlGaAs semiconductor ring lasers: Experiment and model,” IEEE J. Quantum Electron. 39, 1187-1195 (2003). 17. J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: A traveling-wave description,” IEEE J. Quantum Elect. 45, 431-438 (2009). 18. S. Sunada, T. Harayama, K. Arai, K. Yoshimura, K. Tsuzuki, A. Uchida, and P. Davis, “Random optical pulse generation with bistable semiconductor ring lasers,” Opt. Express 19, 7439-7450 (2011) 19. I. V. Ermakov, G. Van der Sande and J. Danckaert, “Semiconductor ring laser subject to delayed optical feedback: bifurcations and stability”, Commun. Nonlinear Sci. Numer. Simul. 17, 4767-4779 (2012). 20. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, and G. Van der Sande, “Loss of time-delay signature in chaotic semiconductor ring lasers,” Opt. Lett. 37, 2541-2544 (2012). 21. L. Gelens, S. Beri, G. Van der Sande, G. Mezosi, M. Sorel, J. Danckaert, and G. Verschaffelt, “Exploring multistability in semiconductor ring lasers: theory and experiment,” Phys. Rev. Lett. 102, 193904 (2009). 22. N. Jiang, W. Pan, B. Luo, L. Yan, S. Xiang, L. Yang, D. Zheng, N. Li, “Influence of injection current on the synchronization and communication performance of closed-loop chaotic semiconductor lasers,” Opt. Lett. 36, 3197-3199 (2011). 23. D. Rontani, A. Locquet, M. Sciamanna, D. S. Citrin, and S. Ortin, “Time-delay identification in a chaotic semiconductor laser with optical feedback: A dynamical point of view,” IEEE J. Quantum Electron. 45, 879-891 (2009). 24. R. M. Nguimdo, M. C. Soriano, and P. Colet, “Role of the phase in the identification of delay time in semiconductor lasers with optical feedback,” Opt. Lett. 36, 4332-4334 (2011). 25. R. Vicente, J. Dauden, P. Colet, R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. Quantum Electron. 41, 541-548 (2005). 26. M. F. Booth, A. Schremer, and J. M. Ballantyne, “Spatial beam switching and bistability in a diode ring laser,” Appl. Phys. Lett. 76, 1095-1097 (2000). 27. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “Towards the generation of random bits at terahertz rates based on a chaotic semiconductor laser,” Int. Workshop on Statistical-Mechanical Informatics 1-8 (2010), 5861 (2010). 28. A. Argyris, E. Pikasis, S. Deligiannidis, and Dimitris Syvridis, “Sub-Tb/s physical random bit generators based on direct detection of amplified spontaneous emission signals,” J. Lightwave Technol. 30, 1329-1334 (2010). 29. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, and M. Levenson, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” Nat. Inst. Standards and Technology, Special Publication 800-22, 2001, Revision 1, 2008 [Online]. Available: http://csrc.nist.gov/publications/nistpubs/800-22-rev1/SP800-22rev1.pdf. 30. S. J. Kim, K. Umeno, and A. Hasegawa, “Corrections of the NIST statistical test suite for randomness,” 2004, arXiv:nlin.CD/0401040v1. 31. X. Leijtens, “JePPIX: the platform for InP-based photonics,” IET Optoelectronics 5, 202-206 (2011). 32. I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with On-Chip Filtered Optical Feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129-136 (2012).