REVIEW article
Front. Comput. Sci.
Sec. Computer Security
Volume 7 - 2025 | doi: 10.3389/fcomp.2025.1649256
BROWNIAN MOTION MODELS: CRYPTOGRAPHIC APPLICATIONS, CAPABILITIES, AND LIMITATIONS
Provisionally accepted
- 1Arab Open University, Riyadh, Saudi Arabia
- 2Mansoura University, Mansoura, Egypt
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Abstract: Brownian motion (BM) is a stochastic model that has been extensively studied in physics, finance, and engineering. However, its potential use in cryptographic applications remains underexplored. This paper presents a comprehensive review of the capabilities, limitations, and cryptographic properties of various BM models, including the Wiener process, geometric BM, fractional BM, Ornstein–Uhlenbeck process, multidimensional BM, and reflected BM. We reviewed the mathematics of these models, simulate their random evolutions, and compare their cryptanalytic properties. A comparison of these sources highlights unique characteristics that can provide cryptographic resilience, including long-range dependence, multidimensional modeling of noise, and constraints on randomness. We also describe the main limitations and potential weaknesses of each model. This paper addresses gaps in the application of stochastic process to cryptographic design and provides a foundational guideline for the continued development of secure systems based on Brownian dynamics.
Keywords: Brownian Motion, stochastic, cryptography, information security, Pseudorandom number generator
Received: 18 Jun 2025; Accepted: 28 Aug 2025.
Copyright: © 2025 Zainalabideen, Suwais, El-Bakry and Abdelmaksoud. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Khaled Suwais, Arab Open University, Riyadh, Saudi Arabia
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