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
DOI: https://doi.org/10.26599/BDMA.2020.9020010
Google Scholar
Barbeau, A. (2003). Pell’s equation. New York: Springer.
DOI: https://doi.org/10.1007/b97610
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
DOI: 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
DOI: 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.
DOI: https://doi.org/10.4310/CDM.1995.v1995.n1.a1
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
DOI: 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
DOI: 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
DOI: https://doi.org/10.1109/HPCC/SmartCity/DSS.2019.00112
Google Scholar
Picciotto, H. (1987). Math McPuzzle. 85(52).
DOI: https://doi.org/10.1163/22116117-90001475
Google Scholar
Pólya, G. (1956). On Picture-Writing. The American Mathematical Monthly, 63(10), 689–697. https://doi.org/10.1080/00029890.1956.11988895
DOI: https://doi.org/10.1080/00029890.1956.11988895
Google Scholar
Schell, E. D. (1945). Weighed and found wanting. 52(42).
DOI: https://doi.org/10.2307/2304840
Google Scholar
Stark, H. (1973). Effective estimates of solutions of some diophantine equations. 24(3), 251–259.
DOI: https://doi.org/10.4064/aa-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
DOI: 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.
DOI: https://doi.org/10.1007/978-3-0348-9078-6_18
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
DOI: 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
Statistics
Abstract views: 229PDF downloads: 73
License

This work is licensed under a Creative Commons Attribution 4.0 International License.
All articles published in Applied Computer Science are open-access and distributed under the terms of the Creative Commons Attribution 4.0 International License.
Most read articles by the same author(s)
- Grzegorz BOCEWICZ, Robert WÓJCIK, Paweł SITEK, Zbigniew BANASZAK, TOWARDS DIGITAL TWIN-DRIVEN PERFORMANCE EVALUATION METHODOLOGY OF FMS , Applied Computer Science: Vol. 18 No. 3 (2022)
- Grzegorz RADZKI, Amila THIBBOTUWAWA, Grzegorz BOCEWICZ, UAVS FLIGHT ROUTES OPTIMIZATION IN CHANGING WEATHER CONDITIONS – CONSTRAINT PROGRAMMING APPROACH , Applied Computer Science: Vol. 15 No. 3 (2019)
- Janani DEWMINI, W Madushan FERNANDO, Izabela Iwa NIELSEN, Grzegorz BOCEWICZ, Amila THIBBOTUWAWA, Zbigniew BANASZAK, IDENTIFYING THE POTENTIAL OF UNMANNED AERIAL VEHICLE ROUTING FOR BLOOD DISTRIBUTION IN EMERGENCY REQUESTS , Applied Computer Science: Vol. 19 No. 4 (2023)
Similar Articles
- Saheed A. ADEWUYI, Segun AINA, Adeniran I. OLUWARANTI, A DEEP LEARNING MODEL FOR ELECTRICITY DEMAND FORECASTING BASED ON A TROPICAL DATA , Applied Computer Science: Vol. 16 No. 1 (2020)
- Archana Gunakala, Afzal Hussain Shahid, A COMPARATIVE STUDY ON PERFORMANCE OF BASIC AND ENSEMBLE CLASSIFIERS WITH VARIOUS DATASETS , Applied Computer Science: Vol. 19 No. 1 (2023)
- Piotr WITTBRODT, Iwona ŁAPUŃKA, Gulzhan BAYTIKENOVA, Arkadiusz GOLA, Alfiya ZAKIMOVA, IDENTIFICATION OF THE IMPACT OF THE AVAILABILITY FACTOR ON THE EFFICIENCY OF PRODUCTION PROCESSES USING THE AHP AND FUZZY AHP METHODS , Applied Computer Science: Vol. 18 No. 4 (2022)
- Elmehdi BENMALEK, Jamal EL MHAMDI, Abdelilah JILBAB, Atman JBARI, A COUGH-BASED COVID-19 DETECTION SYSTEM USING PCA AND MACHINE LEARNING CLASSIFIERS , Applied Computer Science: Vol. 18 No. 4 (2022)
- Wiesław FRĄCZ, Grzegorz JANOWSKI, Grażyna RYZIŃSKA, THE POSSIBILITY OF USING WOOD FIBER MATS IN PRODUCTS MANUFACTURING MADE OF POLYMER COMPOSITES BASED ON NUMERICAL SIMULATIONS , Applied Computer Science: Vol. 13 No. 4 (2017)
- Konrad BIERCEWICZ, Mariusz BORAWSKI, Anna BORAWSKA, Jarosław DUDA, DETERMINING THE DEGREE OF PLAYER ENGAGEMENT IN A COMPUTER GAME WITH ELEMENTS OF A SOCIAL CAMPAIGN USING COGNITIVE NEUROSCIENCE TECHNIQUES , Applied Computer Science: Vol. 18 No. 4 (2022)
- Grzegorz SUCHANEK, Roman FILIPEK, COMPUTATIONAL FLUID DYNAMICS (CFD) AIDED DESIGN OF A MULTI-ROTOR FLYING ROBOT FOR LOCATING SOURCES OF PARTICULATE MATTER POLLUTION , Applied Computer Science: Vol. 18 No. 3 (2022)
- Ekhlas H. KARAM, Eman H. JADOO, DESIGN OF MODIFIED SECOND ORDER SLIDING MODE CONTROLLER BASED ON ST ALGORITHM FOR BLOOD GLUCOSE REGULATION SYSTEMS , Applied Computer Science: Vol. 16 No. 2 (2020)
- Konrad PIETRYKOWSKI, Paweł KARPIŃSKI, SIMULATION STUDY OF HYDRODYNAMIC CAVITATION IN THE ORIFICE FLOW , Applied Computer Science: Vol. 18 No. 3 (2022)
- Robert KARPIŃSKI, KNEE JOINT OSTEOARTHRITIS DIAGNOSIS BASED ON SELECTED ACOUSTIC SIGNAL DISCRIMINANTS USING MACHINE LEARNING , Applied Computer Science: Vol. 18 No. 2 (2022)
You may also start an advanced similarity search for this article.