AN AUTHENTICATION METHOD BASED ON A DIOPHANTINE MODEL OF THE COIN BAG PROBLEM
Krzysztof NIEMIEC
(Poland)
https://orcid.org/0009-0008-8101-2789
Grzegorz BOCEWICZ
grzegorz.bocewicz@tu.koszalin.plKoszalin Univeristy of Technology (Poland)
https://orcid.org/0000-0002-5181-2872
Abstract
The article presents the so-called coin bag problem, which is modeled by linear Diophantine equations. The problem in question involves assessing the contents of a set of coins based on its weight. Since this type of problem is undecidable, a special variant of the problem was proposed for which effective problem-solving algorithms can be developed. In this paper, an original heuristic is presented (an algorithm based on problem decomposition) which allows to solve the coin bag problem in fewer steps compared to a brute force algorithm. The proposed approach was verified in a series of computational experiments. Additionally, an authentication scheme making use of the approach was proposed as an example of potential practical use.
Keywords:
Diophantine equations coin bag problem, decomposition algorithm, branch-and-bound method, authenticationReferences
Azrour, M., Mabrouki, J., Guezzaz, A., & Farhaoui, Y. (2021). New enhanced authentication protocol for Internet of Things. Big Data Mining and Analytics, 4(1), 1–9. https://doi.org/10.26599/BDMA.2020.9020010
Google Scholar
Barbeau, A. (2003). Pell’s equation. New York: Springer.
Google Scholar
Brody, J., & Verbin, E. (2010). The Coin Problem and Pseudorandomness for Branching Programs. 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, 30–39. https://doi.org/10.1109/FOCS.2010.10
Google Scholar
Clausen, M., & Fortenbacher, A. (1989). Efficient solution of linear diophantine equations. Journal of Symbolic Computation, 8(1–2), 201–216. https://doi.org/10.1016/S0747-7171(89)80025-2
Google Scholar
Darmon, H., Diamond, F., & Taylor, R. (1995). Fermat’s last theorem. Current developments in mathematics.
Google Scholar
Gilbert, W. J., & Pathria, A. (1990). Linear Diophantine Equation. Manuscript.
Google Scholar
Haakegaard, R., & Lang, J. (2015). The Elliptic Curve Diffie-Hellman (ECDH).
Google Scholar
Jonsson, F., & Tornkvist, M. (2017). RSA authentication in Internet of Things: Technical limitations and industry expectations. Dissertation.
Google Scholar
Kane, D. M. (2006). An elementary derivation of the asymptotics of partition functions. The Ramanujan Journal, 11(1), 49–66. https://doi.org/10.1007/s11139-006-5307-x
Google Scholar
Karimi, E., Kazemi, F., Heidarzadeh, A., & Sprintson, A. (2018). A Simple and Efficient Strategy for the Coin Weighing Problem with a Spring Scale. 2018 IEEE International Symposium on Information Theory (ISIT), 1730–1734. https://doi.org/10.1109/ISIT.2018.8437774
Google Scholar
Matiyasevich, Y. (1993). Hilbert’s 10th Problem. MIT press.
Google Scholar
Mordell, L. J. (1969). Diophantine Equations. Academic Press.
Google Scholar
Mumtaz, M., Akram, J., & Ping, L. (2019). An RSA Based Authentication System for Smart IoT Environment. 2019 IEEE 21st International Conference on High Performance Computing and Communications; IEEE 17th International Conference on Smart City; IEEE 5th International Conference on Data Science and Systems (HPCC/SmartCity/DSS), 758–765. https://doi.org/10.1109/HPCC/SmartCity/DSS.2019.00112
Google Scholar
Picciotto, H. (1987). Math McPuzzle. 85(52).
Google Scholar
Pólya, G. (1956). On Picture-Writing. The American Mathematical Monthly, 63(10), 689–697. https://doi.org/10.1080/00029890.1956.11988895
Google Scholar
Schell, E. D. (1945). Weighed and found wanting. 52(42).
Google Scholar
Stark, H. (1973). Effective estimates of solutions of some diophantine equations. 24(3), 251–259.
Google Scholar
Tripathi, A. (1978). On a linear Diophantine problem of Frobenius. Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal), 1978(301), 171–178. https://doi.org/10.1515/crll.1978.301.171
Google Scholar
Wiles, A. (1995). Modular elliptic curves and Fermat’s last theorem. Annals of mathematics.
Google Scholar
Wright, J. W. (1975). The Change-Making Problem. Journal of the ACM, 22(1), 125–128. https://doi.org/10.1145/321864.321874
Google Scholar
Authors
Grzegorz BOCEWICZgrzegorz.bocewicz@tu.koszalin.pl
Koszalin Univeristy of Technology Poland
https://orcid.org/0000-0002-5181-2872
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