Random number generator based on semiconductor nanoheterostructures with quantum dots and optical feedback

Petrenko A.А., Kovalev A.V., Bugrov, V.Е.

Full text «Opticheskii Zhurnal»

Full text on elibrary.ru

Publication in Journal of Optical Technology

For Russian citation (Opticheskii Zhurnal):

Петренко А.А., Ковалев А.В., Бугров В.Е. Моделирование генератора случайных чисел на основе полупроводниковых наногетероструктур с квантовыми точками с оптической обратной связью // Оптический журнал. 2022. Т. 89. № 9. С. 3–10. http://doi.org/10.17586/1023-5086-2022-89-09-03-10

Petrenko A.A., Kovalev A.V., Bougrov V. E. Random number generator based on semiconductor nanoheterostructures with quantum dots and optical feedback [in Russian] // Opticheskii Zhurnal. 2022. V.89. № 9. P. 3–10. http://doi.org/ 10.17586/1023-5086-2022-89-09-03-10

For citation (Journal of Optical Technology):

A. A. Petrenko, A. V. Kovalev, and V. E. Bougrov, "Random number generator based on semiconductor nanoheterostructures with quantum dots and optical feedback," Journal of Optical Technology. 89(9), 506-510 (2022). https://doi.org/10.1364/JOT.89.000506

Abstract:

Subject of study. This study models the generation process of random bit sequences using an array of coupled lasers. It is based on quantum dot (QD) micropillars with optical feedback that is realized via a mirror positioned at some distance from the array. A model of the array of coupled micropillar lasers consists of QD laser rate equations accounting for the global optical feedback. Aim of study. This study aimed to numerically model and analyze a random number generator using an array of coupled lasers based on QD micropillars. Method. The dynamic behavior was modeled through numerical integration of the delayed differential equation system using a semi-implicit Euler method implemented using the Julia programming language. To generate sequences of random bits, an algorithm was used that involved the sampling of the total field intensity of the array, normalization and discretization with 12 bit resolution, conversion of discretized values to bit representation, selection of four less significant bits, and concatenation of the bit values into the final sequence. Main results. The process of generating a sequence of random bits at the rate of 400 Gb/s, which met the criteria of NIST 800-22 statistical tests for the p-value of 0.01 at the sampling rate of total field intensity of the array equal to 100 Gsamples/s and a sequence length of 11,142,860 bits, was modeled. The model of an array of coupled lasers based on QD micropillars with optical feedback was analyzed using bifurcation analysis. The feedback time delay signature was traced in the chaotic signal of the emission intensity. However, it did not affect the quality of the random number generation. Practical significance. The optical feedback resulted in the chaotic generation of an array of lasers based on the QD micropillars, which can be used to generate random numbers.

Keywords:

random number generator, micro-columns with quantum dots, lasers with external feedback, bifurcation analysis

Acknowledgements:

the work was carried out with the support of the Ministry of Science and Higher Education of the Russian Federation, draft research topics No. 2019-1442.

OCIS codes: 140.5960

References:

1. 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).

2. N. Li, B. Kim, D. Choi, V. N. Chizhevsky, A. Locquet, M. Bloch, D. S. Citrin, and W. Pan, “Fast random bit generation with a single chaotic laser subjected to optical feedback,” Proc. SPIE 9134, 913427 (2014).

3. G. Kim, J. H. In, Y. S. Kim, H. Rhee, W. Park, H. Song, J. Park, and K. M. Kim, “Self-clocking fast and variation tolerant true random number generator based on a stochastic mott memristor,” Nat. Commun. 12(1), 2906 (2021).

4. A. Rukhin, J. Soto, J. Nechvatal, M. Smid, E. Barker, S. Leigh, M. Levenson, M. Vangel, D. Banks, A. Heckert, and J. Dray, “A statistical test suite for random and pseudorandom number generators for cryptographic applications,” NIST Special Publication 800-22 Rev 1a

(NIST, 2010).

5. T. Butler, C. Durkan, D. Goulding, S. Slepneva, B. Kelleher, S. P. Hegarty, and G. Huyet, “Optical ultrafast random number generation at 1 Tb/s using a turbulent semiconductor ring cavity laser,” Opt. Lett. 41(2), 388–391 (2016).

6. M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9(3), 151–162 (2015).

7. N. Oliver, M. C. Soriano, D. W. Sukow, and I. Fischer, “Fast random bit generation using a chaotic laser: approaching the information theoretic limit,” IEEE J. Quantum Electron. 49(11), 910–918 (2013).

8. L. Zhang, B. Pan, G. Chen, L. Guo, D. Lu, L. Zhao, and W. Wang, “640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser,” Sci. Rep. 7(1), 45900 (2017).

9. R. M. Nguimdo, G. Verschaffelt, J. Danckaert, X. Leijtens, J. Bolk, and G. Van der Sande, “Fast random bits generation based on a single chaotic semiconductor ring laser,” Opt. Express 20(27), 28603–28613 (2012).

10. M. Virte, E. Mercier, H. Thienpont, K. Panajotov, and M. Sciamanna, “Physical random bit generation from chaotic solitary laser diode,” Opt. Express 22(14), 17271–17280 (2014).

11. D. Rontani, A. Locquet, M. Sciamanna, and D. S. Citrin, “Loss of time-delay signature in the chaotic output of a semiconductor laser with optical feedback,” Opt. Lett. 32(20), 2960–2962 (2007).

12. S. Kreinberg, X. Porte, D. Schicke, B. Lingnau, C. Schneider, S. Höfling, I. Kanter, K. Lüdge, and S. Reitzenstein, “Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels,” Nat. Commun. 10(1), 1539 (2019).

13. C. Gies and S. Reitzenstein, “Quantum dot micropillar lasers,” Semicond. Sci. Technol. 34(7), 073001 (2019).

14. A. A. Petrenko, A. V. Kovalev, and V. E. Bougrov, “Random number generation with arrays of coupled micropillar quantum dot lasers,” Nauchno-Tekh. Vestn. Inf. Tekhnol. Mekh. Opt. 21(6), 962–968 (2021).

15. G. Kozyreff, A. G. Vladimirov, and P. Mandel, “Global coupling with time delay in an array of semiconductor lasers,” Phys. Rev. Lett. 85(18), 3809–3812 (2000).

16. S. Holzinger, C. Schneider, S. Höfling, X. Porte, and S. Reitzenstein, “Quantum-dot micropillar lasers subject to coherent time-delayed optical feedback from a short external cavity,” Sci. Rep. 9(1), 631 (2019).

17. S. K. Ang, “NIST randomness test suit,” https://github.com/ stevenang/randomness_testsuite.