On modeling random data to evaluate the performance of statistical tests in cryptography
https://doi.org/10.37661//1816-0301-2024-21-4-37-45
Abstract
Objectives. Financial networks with a rule of constrained equal awards for the distribution of the agent’s estate between its creditors are considered. The aim of the study is to develop an algorithm for constructing greatest clearing matrices for such networks under zero cash reserves of all agents.
Methods. Graph theory and mathematical programming methods are used.
Results. A polynomial-time algorithm for constructing the greatest clearing matrices for financial networks with a rule of constrained equal awards for the distribution of the agent's estate between its creditors is proposed. It is assumed that the cash reserves of each agent are equal to zero (funds received from other agents are distributed among creditors). The algorithm is based on the use of the identified properties of weighted strongly connected graphs. Necessary and sufficient conditions are obtained under which the greatest clearing matrix is different from zero at zero cash reserves of agents'.
Conclusion. The developed approach can be used in constructing clearing algorithms for financial networks with other rules for distributing the agent’s estate between its creditors.
Keywords
cryptographic generator,
statistical testing,
discrete probability distribution,
distribution on a hypersphere,
triangular matrix,
mathematical modeling
Supporting agencies: The work was performed with the financial support within the framework of the separate project No. 20231671 of the Ministry of Education of the Republic of Belarus.
About the Authors
U. Y. Palukha
https://apmi.bsu.by/personal/palukha.html
Research Institute for Applied Mathematics and Informatics Belarusian State University
Belarus
Research Institute for Applied Mathematics and Informatics Belarusian State University
Belarus
Uladzimir Y. Palukha, Ph. D. (Phys.-Math.), Assoc. Prof., Head of the Research Laboratory of Mathematical Methods of Information Security
av. Nezavisimosti, 4, Minsk, 220030
M. A. Prokharchyk
Research Institute for Applied Mathematics and Informatics Belarusian State University
Belarus
Belarus
Mikalay A. Prokharchyk, Junior Researcher, Research Laboratory of Mathematical Methods of Information Security
av. Nezavisimosti, 4, Minsk, 220030
Yu. S. Kharin
https://apmi.bsu.by/personal/yu.s.-xarin.html
Research Institute for Applied Mathematics and Informatics Belarusian State University
Belarus
Research Institute for Applied Mathematics and Informatics Belarusian State University
Belarus
Yuriy S. Kharin, D. Sc. (Phys.-Math.), Prof., Acad. of the National Academy of Sciences of Belarus, Dir., Research Institute for Applied Mathematics and Informatics
av. Nezavisimosti, 4, Minsk, 220030
References
1. Eisenberg L., Noe T. H. Systemic risk in financial systems. Management Science, 2001, vol. 47(2), pp. 236–249.
2. Schaarsberg G. M., Reijnierse H., Borm P. On solving mutual liability problems. Mathematical Methods of Operations Research, 2018, vol. 87(3), pp. 383–409.
3. Jackson M. O., Pernoud A. Systemic risk in financial networks: A survey. Annual Review of Economics, 2021, vol. 13(1), рр. 171–202.
4. Csóka P., Herings P. J.-J. Centralized clearing mechanisms in financial networks: A programming approach. Journal of Mechanism and Institution Design, 2022, vol. 7(1), pp. 45–69.
5. Csóka P., Herings P. J.-J. Uniqueness of clearing payment matrices in financial networks. Mathematics of Operations Research, 2024, vol. 49(1), pp. 232–250.
6. Elliott M., Golub B. Networks and economic fragility. Annual Review of Economics, 2022, vol. 14(1), pp. 665–696.
7. Thomson W. How to Divide When There Isn’t Enough. Cambridge, Cambridge University Press, 2019, 508 p.
8. Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I. Lekcii po teorii grafov. Lectures on Graph Theory. Moscow, Nauka, 1990, 384 p. (In Russ.).
9. Tarjan R. E. Depth-first search and linear graph algorithms. SIAM Journal on Computing, 1972, vol. 1(2), pp. 146–160.
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For citations:
Palukha U.Y., Prokharchyk M.A., Kharin Yu.S. On modeling random data to evaluate the performance of statistical tests in cryptography. Informatics. 2024;21(4):37-45. (In Russ.) https://doi.org/10.37661//1816-0301-2024-21-4-37-45
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