Connecting Mathematics and Cybersecurity: A Structured Review
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गोषवारा
Cybersecurity has grown into a scientific field for which mathematical tools and methods are the basis for ensuring digital systems. This paper attempts to shed light on the relationship between mathematics and cybersecurity and underlines the role of the different branches of mathematics (number theory, graph theory, probability and game theory) in the development of cryptographic algorithms, defending networks, intrusion detection, and risk modeling. We show that mathematical rigor not only helps to support theoretical models but can also be used to improve the practical applications in encryption, authentication and threat mitigation through a literature review of recent studies. The paper concludes with identification of new research directions that would benefit from the use of advanced mathematics to further change the nature of cybersecurity.
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संदर्भ
1. Trenchev, I., Dimitrov, W., Dimitrov, G., Ostrovska, T., & Trencheva, M. (2023). Mathematical Approaches Transform Cybersecurity from Protoscience to Science. Applied Sciences, 13(11), 6508. https://doi.org/10.3390/app13116508
2. Stallings, W. (2017). Cryptography and Network Security: Principles and Practice (7th ed.). Pearson. ISBN: 9780134444284.
3. Menezes, A., van Oorschot, P., & Vanstone, S. (1996). Handbook of Applied Cryptography. CRC Press. ISBN: 9780849385230.
4. Schneier, B. (2015). Applied Cryptography: Protocols, Algorithms, and Source Code in C (2nd ed.). Wiley. ISBN: 9781119096726.
5. Koblitz, N. (1987). Elliptic Curve Cryptosystems. Mathematics of Computation, 48(177), 203–209. https://doi.org/10.1090/S0025-5718-1987-0866109-5 (doi.org in Bing)
6. Shor, P. W. (1994). Algorithms for Quantum Computation: Discrete Logarithms and Factoring. Proceedings of the 35th Annual Symposium on Foundations of Computer Science, 124–134. https://doi.org/10.1109/SFCS.1994.365700 (doi.org in Bing)
7. mAnderson, R. (2020). Security Engineering: A Guide to Building Dependable Distributed Systems (3rd ed.). Wiley. ISBN: 9781119642787.
8. Bishop, M. (2018). Computer Security: Art and Science. Addison-Wesley. ISBN: 9780321712332.
9. Alpcan, T., & Başar, T. (2010). Network Security: A Decision and Game-Theoretic Approach. Cambridge University Press. ISBN: 9780521119357.
10. Roy, S., & Ellis, C. (2017). A Survey of Game Theory in Cybersecurity. ACM Computing Surveys, 50(2), 30. https://doi.org/10.1145/3057269
11. Newman, M. (2010). Networks: An Introduction. Oxford University Press. ISBN: 9780199206650.
12. Barabási, A.-L. (2016). Network Science. Cambridge University Press. ISBN: 9781107076266.
13. Mitzenmacher, M., & Upfal, E. (2005). Probability and Computing: Randomized Algorithms and Probabilistic Analysis. Cambridge University Press. ISBN: 9780521835400.
14. Ross, S. M. (2014). Introduction to Probability Models (11th ed.). Academic Press. ISBN: 9780124079489.
15. Lye, K.-W., & Wing, J. M. (2005). Game Strategies in Network Security. International Journal of Information Security, 4(1–2), 71–86. https://doi.org/10.1007/s10207-004-0058-7
16. Moore, T., & Anderson, R. (2012). Economics and Security. IEEE Security & Privacy, 10(3), 68–71. https://doi.org/10.1109/MSP.2012.54 Wang, P., & Lu, W. (2018). Graph-Based Intrusion Detection. Computers & Security, 78, 263–273. https://doi.org/10.1016/j.cose.2018.07.002
17. Liu, Y., & Chen, H. (2019). Markov Models in Cybersecurity Risk Assessment. Journal of Information Security, 10(2), 123–135. https://doi.org/10.4236/jis.2019.102008 Xu, S., & Li, Z. (2020). Catastrophe Theory in Cybersecurity. Future Generation Computer Systems, 108, 418–427. https://doi.org/10.1016/j.future.2020.02.028
18. Kim, J., & Park, Y. (2021). Queuing Models for Denial-of-Service Attack Analysis. Journal of Network and Computer Applications, 174, 102889. https://doi.org/10.1016/j.jnca.2020.102889