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Model of the diffusion process in a nanostructured system as a generator of pseudorandom sequences

A.V. Shishulin, A.V. Shishulina

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

DOI: 10.26456/pcascnn/2026.18.NNN2

Original article

Abstract: Complex random number generators that combine rapid pseudorandom sequence generation with hardware entropy sources have numerous practical applications in stochastic process modeling, machine learning, and information security. This paper presents a method for generating pseudorandom sequences based on a physical model of particle diffusion within a nanoscale periodic structure featuring a nonlinear potential and thermal noise, which serve as sources of dynamic chaos. The sequence of thermally activated transitions between potential minima exhibits irregular and chaotic behavior. The sequence generation is achieved through the digitalization of the particle’s stochastic motion along the energy landscape of the nanostructure. Particle diffusion in a nanostructured medium is described by the Langevin equation and is integrating by using the Verlet method. Additionally, a software implementation of the suggested algorithm is provided in the Ruby programming language. The obtained results demonstrate the potential for using a «pseudophysical» approach, which is based on nonlinear potentials of various physical natures, as a viable alternative to a «purely mathematical» methodology in the tasks involving the generation of random number sets.

Keywords: nanostructures, diffusion, nonlinear potential, dynamic chaos, pseudorandom numbers

  • Alexander V. Shishulin – Ph. D., Associate Professor, Nizhny Novgorod State Technical University n.a. R.E. Alekseev
  • Anna V. Shishulina – Ph. D., Associate Professor, Nizhny Novgorod State Technical University n.a. R.E. Alekseev

For citation:

Shishulin A.V., Shishulina A.V. Model diffuzii v nanostrukturirovannoj sisteme kak generator psevdosluchajnykh posledovatelnostej [Model of the diffusion process in a nanostructured system as a generator of pseudorandom sequences], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2026, issue 18, pp. __-__. DOI: 10.26456/pcascnn/2026.18.NNN2. ⎘

Full article (in Russian): download PDF file

References:

1. van Tilborg Henk C.A., Jajodia S. Encyclopedia of cryptography and security, 2nd ed. New-York: Springer, 2014, 1416 p. DOI: 10.1007/978-1-4419-5906-5.
2. Peterson I. The jungles of randomness: a mathematical safari. New-York: John Wiley & Sons, 1998, 272 p.
3. Stipčević M., Koç Ç.K. True random number generators, Open Problems in Mathematical and Computational Sciences, ed. by Ç.K. Koç. Cham: Springer, 2014, pp. 275-315. DOI: 10.1007/978-3-319-10683-0_12.
4. Herrero-Collantes M., Garcia-Escartin J.C. Quantum random number generators, Reviews of Modern Physics, 2017, vol. 89, issue 1, pp. 015004-1-015004-48. DOI: 10.1103/revmodphys.89.015004.
5. Bardis N.G., Markovskyi A.P., Doukas N., Karadimas N.V. True random number generation based on environmental noise measurements for military applications, ISPRA'09: Proceedings of the 8th WSEAS International Conference on Signal Processing, Robotics and Automation, 21-23 February 2009, Cambridge UK. Stevens Point, Wisconsin: World Scientific and Engineering Academy and Society, 2009, pp. 68-73.
6. Zhun H., Hongui C. A truly random number generator based on thermal noise, ASICON 2001: 4th International Conference on ASIC Proceedings, 23-25 October 2001, Shanghai, China. New York: IEEE Publ., 2001, pp. 862-864. DOI: 10.1109/ICASIC.2001.982700.
7. Zhou Q., Liao X., Wong K., Hu Y., Xiao D. True random number generator based on mouse movement and chaotic hash function, Information Sciences, 2009, vol. 179, issue 19, pp. 3442-3450. DOI: 10.1016/j.ins.2009.06.005.
8. Laskaris N. A., Zafeiriou S. P., Garefa L. Use of random time intervals (RTIs) generation for biometric verification, Pattern Recognition, 2009, vol. 42, issue 11, pp. 2787-2796. DOI: 10.1016/j.patcog.2008.12.028.
9. Knuth D. The art of computer programming. Vol. 2: Seminumerical algorithms, 3rd ed. Massachusetts: Addison-Wesley Publ., 1997, XIV, 762 p.
10. Matsumoto M., Nashimura T. Mersenne twister: A-623-dimensionally equidistributed uniform pseudorandom generator, ACM Transactions on Modeling and Computer Simulation (TOMACS), 1998, vol. 8, issue 1, pp. 3-30. DOI: 10.1145/272991.272995.
11. Stavroulakis P. Chaos applications in telecommunications, Boca-Raton, CRC Press, 2006, 440 p.
12. Cui B., Zaccone A. Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields, Physical Review E, 2018, vol. 97, issue 6, pp. 060102-1-060102-5. DOI: 10.1103/PhysRevE.97.060102.
13. Salomatina A.Yu., Fedotov A.Yu., Severyukhina O.Yu., Vinogradov F.A. Issledovaniye marnitnykh svoistv nanokompozita Co-Fe [Study of Co-Fe nanocomposite magnetic properties], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2024, issue 16, pp. 267-276. DOI: 10.26456/pcascnn/2024.16.267. (In Russian).
14. Loskutov A.Yu. Fascination of chaos, Physics-Uspekhi, 2010, vol. 53, issue 12, pp. 1257-1280. DOI: 10.3367/UFNe.0180.201012d.1305.
15. Lu J., Wu X. Chaos of charged particles near a renormalized group improved Kerr black hole in an external magnetic field, The European Physical Journal C, 2025, vol. 85, issue 9, art. no 1122, 13 p. DOI: 10.1140/epjc/s10052-025-14853-z.
16. Fedoseev V.B. Ostsilliruyushchie fazovye perekhody «rastvor – gaz» i «rastvor – kristall» v kaplyakh rastvorov s odnim kristallizuyushchimsya komponentom [Solution-gas and solution-crystal oscillatory phase transitions in the drops of aqueous solutions with one crystallizable component], Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics], 2017, vol. 13, issue 2, pp. 195-206. DOI: 10.20537/nd1702004. (In Russian).
17. Hairer E., Lubich C., Wanner G. Geometric numerical integration. Berlin, Heidelberg: Springer-Verlag, 2006, XVI, 644 p. DOI: 10.1007/3-540-30666-8.
18. Box G.E.P., Muller M.E. A note on the generation of random normal deviates, The Annals of Mathematical Statistics, 1958, vol. 29, issue 2, pp. 610-611. DOI: 10.1214/aoms/1177706645.
19. Ruby official portal. Available at: https://www.ruby-lang.org/en/ (accessed 25.11.2025).
20. Malinetsky G.G. Khaos. Struktury. Vychislitel'nyj eksperiment. Vvedenie v nelinejnuyu dinamiku [Chaos. Structures. A computational experiment. Introduction to nonlinear dynamics]. Moscow, URSS, 2001, 312 p. (In Russian).
21 Zaslavsky G.M., Sagdeev R.Z. Vvedeniye v nelinejnuyu fiziku: ot maiatnika do turbulentnosti i khaosa [Introduction to nonlinear physics: from the pendulum to turbulence and chaos]. Moscow, Nauka, 1988, 368 p. (In Russian).
22. Anofriev V.A., Antonov A.S., Vasilyev S.A., Kuzmin N.B., Sdobnyakov N.Yu. Sravnitel’nyi analiz protsessa formirovamiya fraktal’nykh metallichenskikh plenok: atomisticheskoye modelirovaniye [Comparative analysis of the process of formation of fractal metal films: atomistic simulation], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 339-35. DOI: 10.26456/pcascnn/2025.17.339. (In Russian)
23. Shishulin A.V., Shishulina A.V. O shirine zapreshchennoj zony v mezoporistykh poluprovodnikakh [On the energy bandgap in mesoporous semiconductors], Fiziko-khimicheskie aspekty izucheniya klasterov, nanostruktur i nanomaterialov [Physical and chemical aspects of the study of clusters, nanostructures and nanomaterials], 2025, issue 17, pp. 317-327. DOI: 10.26456/pcascnn/2025.17.317. (In Russian).
24. Shishulin A.V., Potapov A.A., Shishulina A.V. Fractal nanoparticles of phase-separating solid solutions: nanoscale effects on phase equilibria, thermal conductivity, thermoelectric performance, Springer Proceedings in Complexity, ed. by C.H. Skiadas, Y. Dimotikalis. Cham, Springer, 2022, pp. 421-432. DOI: 10.1007/978-3-030-96964-6_30.

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