## Implementation of 140 Gb/s true random bit generator based on a chaotic photonic integrated circuit |

Optics Express, Vol. 18, Issue 18, pp. 18763-18768 (2010)

http://dx.doi.org/10.1364/OE.18.018763

Acrobat PDF (1121 KB)

### Abstract

In the present work a photonic integrated circuit (PIC) that emits broadband chaotic signals is employed for ultra-fast generation of true random bit sequences. Chaotic dynamics emerge from a DFB laser, accompanied by a monolithic integrated 1-cm long external cavity (EC) that provides controllable optical feedback. The short length minimizes the existence of external cavity modes, so flattened broadband spectra with minimized intrinsic periodicities can emerge. After sampling and quantization - without including optical de-correlation techniques and using most significant bits (MSB) elimination post-processing - truly random bit streams with bit-rates as high as 140 Gb/s can be generated. Finally, the extreme robustness of the random bit generator for adaptive bit-rate operation and for various operating conditions of the PIC is demonstrated.

© 2010 OSA

## 1. Introduction

3. W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. **44**(6), 521–528 (1997). [CrossRef]

8. J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. **93**(3), 031109 (2008). [CrossRef]

9. B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. **35**(3), 312–314 (2010). [CrossRef] [PubMed]

10. M. A. Wayne and P. G. Kwiat, “Low-bias high-speed quantum random number generator via shaped optical pulses,” Opt. Express **18**(9), 9351–9357 (2010). [CrossRef] [PubMed]

11. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. **16**(3), 347–355 (1980). [CrossRef]

12. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. **28**(1), 93–108 (1992). [CrossRef]

13. 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**(12), 728–732 (2008). [CrossRef]

15. 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]

16. I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics **4**(1), 58–61 (2010). [CrossRef]

17. 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**(6), 5512–5524 (2010). [CrossRef] [PubMed]

## 2. Experimental setup

18. A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. **100**(19), 194101 (2008). [CrossRef] [PubMed]

11. R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. **16**(3), 347–355 (1980). [CrossRef]

12. J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. **28**(1), 93–108 (1992). [CrossRef]

*k*) of the LSBs retained in each sample of the output sequence determines the final bit rate generation.

## 3. Analog signal generation

19. A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express **18**(5), 5188–5198 (2010). [CrossRef] [PubMed]

*I*= 25mA – provides chaotic signals that include low frequency fluctuations (LFFs) [20] when biased up to 28mA. Beyond that values and for EC feedback ratio (i.e. the ratio of the DFB laser’s optical output that is re-injected after running a roundtrip path in the integrated external cavity) above

_{th}*P*0.5%, chaotic signals with powerful broadband spectra emerge. Two cases of

_{f}=*P*have been examined in this work, by appropriately biasing the G/As. In the G/As unbiased case,

_{f}*P*= 1.6%, while when G/As is biased with 0.1mA (0.733mV),

_{f}*P*= 3.3%. The microwave spectra that correspond to these two feedback conditions, for different DFB laser current values, are presented in Fig. 3 . ECMs with spacing 3.3GHz – that correspond to the EC length – appear only in the

_{f}*P*= 3.3% case, while suppressed significantly when increasing the biasing DFB laser current (Fig. 3b). The prerequisite for a potential analog signal to seed successfully an ultra-fast TRBG is a broad and flat spectrum, without periodicities. Under these specifications, the most prominent operating condition of the PIC is expected from signals with a spectral distribution of Fig. 3a, at high current values (e.g. 50mA case).

_{f}## 4. Random bit generation and verification

*k*LSBs adopted in each case – are evaluated. Pass criteria are determined by the sequence length and the significance level. A significance level

*α*= 0.01 is set for the p-values of each sequence test, with a desirable uniformity

*P-*value larger than 0.0001. For the 1000 samples, the proportion of sequences that satisfy

*p-*value >

*α*, is estimated to be 0.99 ± 0.0094.

*k*= 1 to

*k*= 16 – for the two optical feedback conditions presented in Fig. 3a and 3b. The complete absence of ECMs and the powerful broadband spectral distribution of the chaotic signal, for the case of

*P*= 1.6% (Fig. 3a) and for laser biasing current above 47mA, allows the most favorable performance. All NIST tests are passed, even when including 14 LSBs, which is translated into bit-rate generation of 140Gb/s. A representative analysis of the NIST statistical tests results, for the worst value of the obtained p-values for each test, is presented in Table 1 . Lower current values alter the chaotic spectral profile, either by reducing its bandwidth or by revealing ECM periodicities. The adoption of gradually decreased number of LSBs in each sample allows even now a random bit stream with verified randomness. However, in all cases – even at the PIC’s LFF operating region just above threshold – a minimum 90Gb/s TRBG is guaranteed. As shown in Fig. 3b, the increase of the optical feedback strength to 3.3% results in evident ECMs. The corresponding randomness mapping for this case is shown in Fig. 4b. For large laser current values ECMs are partially suppressed, permitting the TRNG to operate successfully at bit-rates between 80Gb/s and 120Gb/s. Even at lower laser biasing current values and albeit the apparent ECM existence TRNG can be claimed at bit-rates as high as 70Gb/s.

_{f}*m*MSBs of each sample. By optimizing the operating conditions – and thus the analog signal distribution within the 16-bit quantized window – an attempt to minimize the

*m*value is performed. This has been achieved, for example, for the conditions of Table 1, where

*m*= 2. Less symmetrical histogram representations of the chaotic signal just require the exclusion of a further increased number of

*m*values in order to obtain a verified TRBG. Such a performance establishes the proposed configuration as a robust, compact device for TRBG with an ultra-fast adaptive bit-rate performance.

## 5. Conclusions

## Acknowledgement

## References and links

1. | N. Ferguson, and B. Schneier, |

2. | http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf (2001). |

3. | W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. |

4. | J. T. Gleeson, “Truly random number generator based on turbulent electroconvection,” Appl. Phys. Lett. |

5. | 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. |

6. | C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-state Circuits |

7. | J.-L. Danger, S. Guilley, and P. Hoogvorst, “High speed true random number generator based on open loop structures in FPGAs,” Microelectron. J. |

8. | J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. |

9. | B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. |

10. | M. A. Wayne and P. G. Kwiat, “Low-bias high-speed quantum random number generator via shaped optical pulses,” Opt. Express |

11. | R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. |

12. | J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. |

13. | 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 |

14. | K. Petermann, |

15. | I. Reidler, Y. Aviad, M. Rosenbluh, and I. Kanter, “Ultrahigh-speed random number generation based on a chaotic semiconductor laser,” Phys. Rev. Lett. |

16. | I. Kanter, Y. Aviad, I. Reidler, E. Cohen, and M. Rosenbluh, “An optical ultrafast random bit generator,” Nat. Photonics |

17. | 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. | A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. |

19. | A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express |

20. | J. Ohtsubo, |

21. | 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, “A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,” NIST Special Publication 800–22 Revision 1a (2010). |

**OCIS Codes**

(130.3120) Integrated optics : Integrated optics devices

(140.1540) Lasers and laser optics : Chaos

(320.7080) Ultrafast optics : Ultrafast devices

**ToC Category:**

Integrated Optics

**History**

Original Manuscript: June 17, 2010

Revised Manuscript: July 20, 2010

Manuscript Accepted: July 20, 2010

Published: August 18, 2010

**Citation**

Apostolos Argyris, Stavros Deligiannidis, Evangelos Pikasis, Adonis Bogris, and Dimitris Syvridis, "Implementation of 140 Gb/s true random bit generator based on a chaotic
photonic integrated circuit," Opt. Express **18**, 18763-18768 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-18-18763

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### References

- N. Ferguson, and B. Schneier, Practical Cryptography (John Wiley & Sons, 2003).
- http://csrc.nist.gov/publications/fips/fips140-2/fips1402.pdf (2001).
- W. T. Holman, J. A. Connelly, and A. B. Dowlatabadi, “An integrated analog/digital random noise source,” IEEE Trans. Circuits Syst., I: Fundam. Theory Appl. 44(6), 521–528 (1997). [CrossRef]
- J. T. Gleeson, “Truly random number generator based on turbulent electroconvection,” Appl. Phys. Lett. 81(11), 1949 (2002). [CrossRef]
- 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]
- C. Tokunaga, D. Blaauw, and T. Mudge, “True random number generator with a metastability-based quality control,” IEEE J. Solid-state Circuits 43(1), 78–85 (2008). [CrossRef]
- J.-L. Danger, S. Guilley, and P. Hoogvorst, “High speed true random number generator based on open loop structures in FPGAs,” Microelectron. J. 40(11), 1650–1656 (2009). [CrossRef]
- J. F. Dynes, Z. L. Yuan, A. W. Sharpe, and A. J. Shields, “A high speed, post-processing free, quantum random number generator,” Appl. Phys. Lett. 93(3), 031109 (2008). [CrossRef]
- B. Qi, Y.-M. Chi, H.-K. Lo, and L. Qian, “High-speed quantum random number generation by measuring phase noise of a single-mode laser,” Opt. Lett. 35(3), 312–314 (2010). [CrossRef] [PubMed]
- M. A. Wayne and P. G. Kwiat, “Low-bias high-speed quantum random number generator via shaped optical pulses,” Opt. Express 18(9), 9351–9357 (2010). [CrossRef] [PubMed]
- R. Lang and K. Kobayashi, “External optical feedback effects on semiconductor injection laser properties,” IEEE J. Quantum Electron. 16(3), 347–355 (1980). [CrossRef]
- J. Mork, B. Tromborg, and J. Mark, “Chaos in semiconductor lasers with optical feedback: theory and experiment,” IEEE J. Quantum Electron. 28(1), 93–108 (1992). [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. Photonics 2(12), 728–732 (2008). [CrossRef]
- K. Petermann, Laser diode modulation and noise, (Kluwer Academic Publ., 1991).
- 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. Photonics 4(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. Express 18(6), 5512–5524 (2010). [CrossRef] [PubMed]
- A. Argyris, M. Hamacher, K. E. Chlouverakis, A. Bogris, and D. Syvridis, “Photonic integrated device for chaos applications in communications,” Phys. Rev. Lett. 100(19), 194101 (2008). [CrossRef] [PubMed]
- A. Argyris, E. Grivas, M. Hamacher, A. Bogris, and D. Syvridis, “Chaos-on-a-chip secures data transmission in optical fiber links,” Opt. Express 18(5), 5188–5198 (2010). [CrossRef] [PubMed]
- J. Ohtsubo, Semiconductor Lasers: Stability, Instability and Chaos (Springer-Verlag, 2006).
- 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, “A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications,” NIST Special Publication 800–22 Revision 1a (2010).

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