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Electronic modeling

Vol 40, No 5 (2018)

https://doi.org/10.15407/emodel.40.05

CONTENTS

Mathematical Modeling and Computation Methods

  VYNNYCHUK S.D., MISKO V.M.
Method Multiple Quadratic k-Silve Integer Factoring
3-26
  KALINOVSKY Ya.A., BOYARINOVA Yu.E., KHITSKO Ya.V., SUKALO A.S.
Use of Methods for Generating Isomorphic Hypercomplex Number Systems to Increase the Efficiency of Multiplying Hypercomplex Numbers
27-40
  MAKARICHEV A.V., KUD A.A., SHCHUKIN A.B.
Assessment of the Probability of System Failure with Maximum Service Accumulation Elements
41-48 

Computational Processes and Systems

  ZHARIKOV E.V.
Structural Optimization of the Resource Consumption Forecasting Models in Virtualized Environment
49-66
  ZUBOK V.Yu.
Determining the Ways of Counteraction to Cyberattacks on the Internet Global Routing
67-76

Application of Modeling Methods and Facilities

 
77-90
  DUNAYEVSKA N.I., ZASIADKO YA.I., SHCHUDLO T.S.
The Study of Thermal Destruction Kinetics of Coal and Solid Biomass Mixtures
91-110
  KUTSAN U.G., GODUN O.V., KYRIANCHUK V.N.
Application of Nest Code for Comparative Economic Evaluation of Energy Systems
111-118

 

THE METHOD OF MULTIPLE QUADRATIC K-SILVE INTEGER FACTORIZATION

S.D. Vynnychuk, V.M. Misko
THE GEORGY PUKHOV INSTITUTE FOR ENERGY MODELLING THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE

Èlektron. model. 2018, 40(5):03-26
https://doi.org/10.15407/emodel.40.05.003

ABSTRACT

A modification of the quadratic sieve method (QS) was proposed, in which the search for B-smooth numbers uses the polynomials X2- kN. In contrast to the QS and multiple polynomial quadratic sieve (MPQS) methods, the method ùà multiple quadratic k-sieve (MQkS) uses a common factor base (FB), which was detailed for each k value. The algorithm takes into account the fact that, the number of B-smooth is relatively larger with smaller values of the numbers of the sifting interval. It was confirmed by the data of numerical experiments. The steps for the proposed algorithm and their implementation were described. On the basis of numerical experiments, it was demonstrated that, using of the MQkS method, it is possible to achieve a decrease in the average time of the formation of the B-smooth set over against of the QS method with a smaller size of FB.

KEYWORDS

integer factoring, quadratic k-sieve, multiple sieve.

REFERENCES

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  2. Daniel L. Brown. Breaking RSA May Be As Difficult As Factoring. Retrieved from: http://www.pgpru.com/novosti/2005/1026vzlomrsabezfaktorizaciirealennoneeffektiven.
  3. Kannan Balasubramanian; M Algorithmic strategies for solving complex problems in cryptography. // Advances in information security, privacy, and ethics (AISPE) book series. Hershey, Pennsylvania (701 E. Chocolate Avenue, Hershey, Pennsylvania, 17033, USA) : IGI Global, [2018].
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  12. Sahadeo Padhye; Rajeev Anand Sahu; Vishal Introduction to Cryptography. Boca Raton, FL : CRC Press, 2018. https://doi.org/10.1201/9781315114590
  13. Misko, (2018). Pryskorennia metodu kvadratychnoho resheta na osnovi vykorystanni umovno B-hladkykh  hysel. Zbirnyk « System research and information technologies», 1.
  14. Vinnichuk, & Misko, V. (2017). Pryskorennia metodu kvadratychnoho resheta na osnovi vykorystanni rozshyrenoi faktornoi bazy ta formuvannia dostatnoi kilkosti B-hladkykh chysel. Zbirnyk «Information technology and security», 5, 2nd ser.
  15. Vynnychuck , Misko V. Acceleration analysis of the quadratic sieve method based on the online matrix solving. // Mathematics and cybernetics – applied aspects., 2018. DOI: 10.15587/1729-061.2018.133603
  16. Silverman D. The multiple polynomial quadratic sieve // Math. Comp. 1987. V. 48 (177). P. 329-339. https://doi.org/10.1090/S0025-5718-1987-0866119-8
  17. D. Breitenbacher, I. Homoliak, J. Jaros, P. Hanacek. Impact of Optimization and Parallelism on Factorization Speed of SIQS. Journal of Systemics 2016; 4 (3), 51-58.

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USE OF METHODS FOR GENERATING ISOMORPHIC HYPERCOMPLEX NUMBER SYSTEMS TO INCREASE THE EFFICIENCY OF MULTIPLYING HYPERCOMPLEX NUMBERS

Ya.A. Kalinovsky, Institute for information recording NAS of Ukraine
Yu.E. Boyarinova, Institute for information recording NAS of Ukraine, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute»
Ya.V. Khitsko, National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute»
A.S. Sukalo, National University of Water Management and Environmental Management

Èlektron. model. 2018, 40(5):27-40
https://doi.org/10.15407/emodel.40.05.027

ABSTRACT

The method of multiplication of hypercomplex numbers is proposed, which provides a significant reduction in the volume of real operations. The method consists in the transition to weakly filled isomorphic hypercomplex number systems (HNS) in which a smaller number of real multiplications is required for hypercomplex multiplication. Such pairs of isomorphic HNS, as well as expressions for isomorphism operators, have been synthesized. The developed method should be used to construct fast linear convolutional algorithms.

KEYWORDS

hypercomplex numerical system, linear convolution, isomorphism, multiplication, complex numbers, double numbers.

REFERENCES

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  6. Kalinovsky, A. (2017), “Effective algorithms for solving the isomorphism equations for hypercomplex number systems using exponential representations”, Elektronnoe modelirovanie, Vol. 39, no. 1, pp. 75-90.
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  10. Kalinovsky, A., Boyarinova, Yu.E. and Khitsko, Ya.V. (2015), “Optimization of the total parametric sensitivity of reversible digital filters with coefficients in non-canonical hypercomplex number systems”, Elektronnoe modelirovanie, Vol. 37, no. 5, pp. 117-126.
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  12. Kalinovsky, Ya.A. (2013), “Structure of the hypercomplex method for fast calculation of linear convolution of discrete sign”, Reestratsiya, zberigannya i obrobka dannykh, Vol. 15, no. 1, pp. 31-44.

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STRUCTURAL OPTIMIZATION OF THE RESOURCE CONSUMPTION FORECASTING MODELS IN VIRTUALIZED ENVIRONMENT

E.V. Zharikov
National Technical University of Ukraine «Igor Sikorsky Kyiv Polytechnic Institute»

Èlektron. model. 2018, 40(5):49-66
https://doi.org/10.15407/emodel.40.05.049

ABSTRACT

Providing a given quality of cloud services under non-stationary workload is one of the main tasks in managing a cloud data center. To ensure a given service quality, it is necessary to apply a proactive approach to managing computing resources. It is possible to prevent problems of inadequate allocation of resources or excessive allocation of resources by forecasting the consumption of resources by virtual machines or containers. In this paper, the author proposes an adaptive method for forecasting the consumption of computational resources, which provides a smaller forecasting error than using a single forecasting method with a model obtained with fixed-size training data. The evaluation of the proposed method show that the accuracy of the forecast increases on average from 2.4% to 23.6%, depending on the statistical characteristics of the time series presented by monitoring data. Increasing the accuracy of the computing resources consumption forecast allows to reduce power consumption and to reduce the number of service-level agreement violation by more accurately allocating the necessary resources to the virtualized ap- plications of the cloud data center.

KEYWORDS

cloud computing, data center, forecasting, time series, virtualization, energy efficiency.

REFERENCES

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    https://doi.org/10.1109/CNSM.2015.7367348
  7. Farahnakian, , Liljeberg, P., and Plosila, J. (2013), «LiRCUP: Linear regression based CPU usage prediction algorithm for live migration of virtual machines in data centers», 39th EUROMICRO Conference on Software Engineering and Advanced Applications (SEAA), pp. 357—364.
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DETERMINING THE WAYS OF COUNTERACTION TO CYBERATTACKS ON THE INTERNET GLOBAL ROUTING

V.Yu. Zubok
THE GEORGY PUKHOV INSTITUTE FOR ENERGY MODELLING THE NATIONAL ACADEMY OF SCIENCES OF UKRAINE

Èlektron. model. 2018, 40(5):67-77
https://doi.org/10.15407/emodel.40.05.067

ABSTRACT

Attacking global routing is capable of harming millions of network devices (and also users) with much less effort than the well-known DoS or Ransomware attacks. The global routing protocol BGP-4, despite its fundamental significance, is not secure, because it is based on trust between the participants of global routing. In the absence of fast prospects for implementing a more secure global routing protocol, it is necessary to suggest approaches that could be applied at the scope of a large operator, industry, region, to mitigate the possible losses from attacks on global routing. For this purpose, two general directions of counteraction are proposed: a) prevention of own prefixes hijacking; b) identification of hijacked routes and blocking outbound traffic to the compromised prefixes. The first direction is proposed to be described as the task of searching for the most effective topological organization of inter-node links, which can reduce losses from route hijacking within a certain target group of nodes.

KEYWORDS

global routing, route hijacking, link optimization, cyber security.

REFERENCES

  1. Rekhter, , Li, T. and Hares, S. (2006), A border gateway protocol 4 (BGP-4), avalable at: https://tools.ietf.org/html/rfc4271 (accessed June 09, 2018).
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  3. Global ransomware damages predicted to exceed $5 billion in 2017, Cybercrime Magazine, avalable at: https://cybersecurityventures.com/ransomware-damage-report-2017-5-billion/ (accessed May 10, 2018).
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  5. Goodin, (2017), Russian-controlled telecom hijacks financial services’ Internet traffic, avalable at: https://arstechnica.com/information-technology/2017/04/russian-controlled- telecom-hijacks-financial-services-internet-traffic/ (accessed Dec. 1, 2017).
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