Unpredictable and uniform random number generation based on time of arrival using InGaAs detectors
https://doi.org/10.17586/2220-8054-2025-16-5-597-605
Abstract
Quantum random number generators are becoming mandatory in a demanding technological world of high-performing learning algorithms and security guidelines. Our implementation, based on the principles of quantum mechanics, enables us to achieve the required randomness. We have generated high-quality quantum random numbers from a weak coherent source at the telecommunication wavelength. The entropy is based on the time of arrival of quantum states within a predefined time interval. The detection of photons by the InGaAs single-photon detectors and high-precision time measurement of 5 ps enables us to generate 16 random bits per arrival time, which is the highest reported to date. We have presented the theoretical analysis and experimental verification of the random number generation methodology. The method eliminates the requirement of any randomness extractor, thereby leveraging the principles of quantum physics to generate random numbers. The output data rate averages 2.4 Mbps. The generated raw quantum random numbers are compared with the NIST-prescribed Blum-Blum-Shub pseudo-random number generator and an in-house-built hardware random number generator from FPGA, on the ENT and NIST platform.
About the Authors
D. AggarwalIndia
Deepika Aggarwal
M.G. Road, Bangalore, Karnataka
A. Banerjee
India
Anindita Banerjee
M.G. Road, Bangalore, Karnataka
A. Sharma
India
Ankush Sharma
M.G. Road, Bangalore, Karnataka
G. Yadav
India
Ganesh Yadav
M.G. Road, Bangalore, Karnataka
References
1. Knuth D.E. Art of Computer Programming, Volume 2: Seminumerical Algorithms, Addison-Wesley Professional (2014).
2. chmidt H. Quantum-mechanical random-number generator, J. Appl. Phys., 1970, 41, P. 462–468.
3. Aggarwal D., Ghatikar R., Chennuri S. and Banerjee A. Generation of 1 GB full entropy random numbers with the enhanced-NRBG method. Physica Scripta, 2023, 98(12), P. 125112.
4. Jennewein T., Achleitner U., Weihs G., Weinfurter H. and Zeilinger A. A fast and compact quantum random number generator. Rev. Sci. Instruments, 2000, 71(4), P. 1675–1680.
5. Stipcevic M. and Rogina B.M. Quantum random number generator based on photonic emission in semiconductors. Rev. Sci. Instrum, 2007, 78, P. 045104.
6. Wayne M.A., Jeffrey E.R., Akselrod G.M. and Kwiat P.G. Photon arrival time quantum random number generation. J. Mod. Opt., 2009, 56(4), P. 516–522.
7. Wahl M., Leifgen M., Berlin M., Rohlicke T., Rahn H.-J. and Benson O. An ultrafast quantum random number generator with provably bounded ¨ output bias based on photon arrival time measurements. Appl. Phys. Lett., 2011, 98, P. 171105.
8. Nie Y., Zhang H., Zhang Z., Wang J., Ma X., Zhang J. and Pan J. Practical and fast quantum random number generation based on photon arrival time relative to external reference. Appl. Phys. Lett., 2014, 104, P. 051110.
9. Yan Q., Zhao B., Hua Z., Liao Q. and Yang H. High-speed quantum-random number generation by continuous measurement of arrival time of photons. Rev. Sci. Instrum., 2015, 86, P. 073113.
10. Gabriel C., Wittmann C., Sych D., Dong R., Mauerer W., Andersen U.L., Marquardt C. and Leuchs G. A generator for unique quantum random numbers based on vacuum states. Nat. Photonics, 2010, 4, P. 711–715.
11. Shen Y., Tian L. and Zou H. Practical quantum random number generator based on measuring the shot noise of vacuum states. Phys. Rev. A, 2010, 81, P. 063814.
12. Symul T., Assad S.M. and Lam P.K. Real time demonstration of high bitrate quantum random number generation with coherent laser light. Appl. Phys. Lett., 2011, 98(23), P. 145.
13. Bruynsteen C., Gehring T., Lupo C., Bauwelinck J. and Yin X. 100-Gbit/s integrated quantum random number generator based on vacuum fluctuations. PRX Quantum, 2023, 4, P. 010330.
14. Raffaelli F., Ferranti G., Mahler D.H., Sibson P., Kennard J.E., Santamato A., Sinclair G., Bonneau D., Thompson M.G. and Matthews J.C.F. A homodyne detector integrated onto a photonic chip for measuring quantum states and generating random numbers. Quantum Sci. Technol., 2018, 3, P. 025003.
15. Guo H., Tang W., Liu Y. and Wei W. Truly random number generation based on measurement of phase noise of a laser. Phys. Rev. E, 2010, 81, P. 051137.
16. Qi B., Chi Y.-M., Lo H.-K. and Qian L. High-speed quantum random number generation by measuring phase noise of a single-mode laser. Opt. letters, 2010, 35(3), P. 312–314.
17. Marandi A., Leindecker N.C., Vodopyanov K.L. and Byer R.L. All-optical quantum random bit generation from intrinsically binary phase of parametric oscillators. Opt. Express, 2012, 20, P. 19322–19330.
18. Williams C.R.S., Salevan J.C., Li X., Roy R. and Murphy T.E. Fast physical random number generator using amplified spontaneous emission. Opt. Express, 2010, 18, P. 23584–23597.
19. Herrero-Collantes M. and Garcia-Escartin J.C. Quantum random number generators. Rev. Mod. Phys., 2017, 89, P. 015004.
20. Li S., Wang L., Wu L.-An, Ma H.-Q. and Zhai G.-J.True random number generator based on discretized encoding of the time interval between photons. J. Opt. Soc. Am. A, 2013, 30, P. 124.
21. Wayne M.A. and Kwait P.G. Low-bias high-speed quantum random number generator via shaped optical pulses. Opt. Express, 2010, 18, P. 9351.
22. Series X: Data Networks Open System Communications and security, Quantum communication Quantum noise random number generator architecture, Recommendation X.1702 (11/19).
23. Fox M. Quantum optics: an introduction. Oxford Univ. Press, Oxford, Oxford master series in atomic, optical, and laser physics, 2006.
24. Bassham III L.E., et al. A statistical test suite for random and pseudorandom number generators for cryptographic applications. Nat. Inst. Standards Technol., Gaithersburg, MD, USA, Tech. Rep. SP 800-22 Rev. 1a, 2010.
25. Walker J. ENT: A pseudo-random number sequence test program. http://www.fourmilab.ch/random/ (2008).
26. Yuan X., Zhao Q., Girolami D. and Ma X. Quantum coherence and intrinsic randomness. Advanced Quantum Technologies, 2019, 2(11), P. 1900053.
27. A. Renyi. On Measures of Entropy and Information. Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, ´ Volume 1: Contributions to the Theory of Statistics, P. 547–561, University of California Press, Berkeley, Calif., 1961.
Supplementary files
Review
For citations:
Aggarwal D., Banerjee A., Sharma A., Yadav G. Unpredictable and uniform random number generation based on time of arrival using InGaAs detectors. Nanosystems: Physics, Chemistry, Mathematics. 2025;16(5):597-605. https://doi.org/10.17586/2220-8054-2025-16-5-597-605
