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  5. VOL 40, NO 2 (2018)
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  7. 2014 год
  8. 36-2

Electronic Modeling

VOL 36, NO 2 (2014)

CONTENTS

Mathematical Methods and Models

  VINNICHUK S.D., ZHILIN A.V., MISKO V.N.
Algorithm of Fermat of Factorization of Numbers of the Form N = pq Due to Thinning Method
3-14
  KVETNYY R.N., BUNYAK Yu. A., SOFINA O. Yu.
Method of Conjugated Zero Space for Blind Identification of Blur Function
15-26

Informational Technologies

  PALAGIN A.V., OPANASENKO V.N., KRYVYI S.L.
Method for Synthesis of Structures for Transformations of a Cyclic Code Based on Programmed by the User of Valve Matrix
27-48

Computational Processes and Systems

  ZHUKOV I.A., PECHURIN N.K., KONDRATOVA L.P., PECHURIN S.N.
Representation of Interaction of the Levels of Computer Network DSSS and FHSS by the Model of Regular Languages and Grammars
49-56
  MINUKHIN S.V., LENKO D.S.
Method for Minimization of the Total Lag of Works on a Single Device Based on Rank Approach and Dominance Rules
57-80

Accuracy, Reliability, Diagnostics

  DOLGIN V.P., DOLGIN I.V.
Procedure of Dynamic Correction of a Linear System
81-88

Application of Modelling Methods and Facilities

  KOLIUSHKO D.G., RUDENKO S.S.
Mathematical Model of Grounding Connection of a Power Plant with Underlayer
89-96
  LYUBIMOVA N.A.
Statistical Model of Unwanted Trends of Controlled Parameters of Waste Gas of Power Stations
97-106

Short Notes

  CHEMERIS V.T., BORODIY I.A.
Modeling of Wave Processes in Thin-Layered Cores of Load-Bearing Element of Pulsed Devices
107-112
  SYTNIK A.A., PROTASOV S.Yu., TIKHOKHOD V.A.
Use of Measuring Converters of Nonselective Action in Multiply Connected Control Systems
113-120

Algorithm of Fermat of Factorization of Numbers of the Form N = pq Due to Thinning Method

VINNICHUK S.D., ZHILIN A.V., MISKO V.N.

ABSTRACT

A technique for accelerating the Fermat method of factorization of numbers of the form N = pq, where p and q are simple, by thinning the test values is proposed. The method is based on the transition from the relation x2 = N + y2, describing the Fermat method, to its analogue—the equation for residue modulo of a certain number—the modulus base. It is shown that it allows one to define the requirements for the value of x for which the equation can have a solution.

KEYWORDS

factorization, Fermat method, thinning, accelerating. 

REFERENCES

1. Zhilin, A.V., Korneyko, A.V.  and  Mokhor, V.V. (2013), “Using the RSA algorithm for the tasks of cryptographic protection of information in modern information and telecommunication systems”,  Zakhist ínformatsíí̈, Kiev, NAU,Vol. 15, no.  3, pp. 225-231.
2. Song, Y.Yan. (2008), “Cryptanalytic attacks on RSA”, Springer Science and Business Media, Inc., p. 255.
3. Gorbenko, I.D., Dolgov, V.I., Potiy, A.V. and  Fedorchenko, V.N.  (1995), “Analysis of the channels of vulnerabilities RSA system”, Bezopasnost  informatsii, no.  2, pp. 22-26.
4. Brown, D.R.L. (2005), “Breaking RSA May Be as Difficult as Factoring”, available at: http://www.pgpru.com/novosti /2005/1026vzlomrsabezfaktorizaciirealennoneeffektiven.
5. Vasilenko, O.N.  (2003), Teoretiko-chislovye algoritmy v kriptografii  [Theoretical and numerical algorithms in cryptography], MTsNMO, Moscow, Russia.
6. Zhilin, A.V. and  Mokhor, V.V. (2010), “Identification parity of elements in the factorization of numbers by Fermat method”, Bezopasnost  informatsii v informatsionno- telekommunikatsionnykh sistemakh. XIII Mezhdunarodnaya nauch.-prakt. konf. Tezisy dokladov   [Information Security in information and telecommunication systems. XIII International scientific-practical. conf.  Abstracts], Kiev, ChP “EKMO”, NITs “TEZIS” NTUU “KPI”, p. 34.

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Method of Conjugated Zero Space for Blind Identification of Blur Function

KVETNYY R.N., BUNYAK Yu. A., SOFINA O. Yu.

ABSTRACT

Method for blind identification of the blur function in the conjugated zero space of image model operator was proposed. The spectral approach to optimization of the blur function estimation, evaluation and optimization of the inverse blur function was considered. The adequacy of the method with respect to the blur nature and degree was demonstrated by test examples.

KEYWORDS

blindidentification,  point  blurfunction, deconvolution. 

REFERENCES

1.Kundur, D. and Hatzinakos, D. (1996), “Blind Image  Deconvolution”,  IEEE Signal Proc. Mag., no. 5, pp. 43-64.
2. Verlan, A.F., Goroshko, I.O., Karpenko, E.Yu.  and et al.  (2011), Metody i algoritmy vosstanovleniya signalov i izobrazheniy [The methods and algorithms for reconstruction of signals and images],  Izd. In-t problem modelirovaniya v energetike  im. Pukhov, G.Ye.  NAN Ukrainy, Kiev, Ukraine.
3. Blind Image  Deconvolution: Theory and Applications ( 2007),  Ed. Campisi, P., Egiazarian, K., CRC Press.
4. Lane, R.G. and  Bates, R.H.  (1987),   “Automatic Multidimensional   Deconvolution”, J. Opt. Soc. Am., Vol. A4, pp. 180-188.
5. Aogaki, S., Moritani, I., Sugai, T. and  et  al.  (2007),  “Simple Method to Eliminating Blurs Based on Lane and Bates Algorithm”, ICITA, Vol.1, pp. 227-229.
6. Pai,  H.T. and  Bovik, A.C.  (1997), “Exact Multichannel Blind Image Restoration”, IEEE Signal Proc. Lett., Vol. 4,  no. 8, pp. 217-220.
7. Marpl Jr, S.L. (1988), Tsifrovoy spektralnyy analiz i ego prilozheniya   [Digital spectral analysis and its applications],  Mir,  Moscow, Russia.
8. Verlan, A.F. and  Sizikov, V.S.  (1978),  Metody resheniya integralnykh uravneniy s programmami dlya EVM. Spravochnoe posobie  [Methods for solving integral equations with computer programs.  Reference  manual],  Naukova dumka, Kiev, Ukraine. 
9. Tikhonov, A.N. and  Arsenin, V.Ya.  (1979), Metody resheniya nekorrektnykh zadach [Methods  of solving ill-posed problems], Nauka, Moscow, Russia.
10. Levin, A., Weiss, Y., Durand, F. and  Freeman, W.T.  (2011), “Efficient Marginal Likelihood Optimization in Blind  Deconvolution”,  IEEE Trans. Patt. Anal. and Machine Intel., Vol. 33, pp. 2354-2367.
11. Gabarda, S.  and  Cristobal, G.  (2008), “Image Quality Assessment  Through a Logarithmic Anisotropic Measure”, Proc. of SPIE 7000, 70000J, pp. 1-11.

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Method for Synthesis of Structures for Transformations of a Cyclic Code Based on Programmed by the User of Valve Matrix

PALAGIN A.V., OPANASENKO V.N., KRYVYI S.L.

ABSTRACT

The correctness of functioning of multilevel structure (of sequential and parallel-sequential types) of converter of cyclic code words containing the cyclic group of contiguous units on the basis of Boolean functions of AND and XOR is substantiated. The offered structures are implemented in the PLIC element basis.

KEYWORDS

Hamming cyclic code, programmed by the user valve matrix, multilevel structure. 

REFERENCES

1. Piterson, U.  and  Ueldon, E.  (1976), Kody, ispravlyayushchie oshibki: Perevod s angliyskogo [Error-correcting codes],  Translation from English, Mir, Moscow, Russia.
2. Breyton, R.K., Khetchel, G.D.  and  Sandzhovanni, A.L.  (1990), “Synthesis of multi-level combinational logic circuits”, Vinchentelli, TIIER, Vol. 78, no.  2, pp. 38-83.
3. Opanasenko, V.N.  and  Kryvyi, S.L.  (2012), “Partitioning the Full Range of Boolean Functions Based on the Threshold and Threshold Relation”,  Cybernetics and Systems Analysis, Vol. 48, no.  3, pp. 459-468
4. Palagin, A.V. and Opanasenko, V.N. (2011), “Design and Application of the PLD-based Reconfigurable Devices”, Design of Digital Systems and Devices, Springer, Berlin, Vol. 79, pp. 59-91. 

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Representation of Interaction of the Levels of Computer Network DSSS and FHSS by the Model of Regular Languages and Grammars

ZHUKOV I.A., PECHURIN N.K., KONDRATOVA L.P., PECHURIN S.N.

ABSTRACT

It is proposed to use the models of regular languages and grammars to describe the protocol data units transformations at the physical and data link levels of the open systems interconnection reference model. The proposed way to describe the modules’ translation is based on the regular grammars tools and ensures the adequate representation of the inter-layer transformation in the transition between the lower hierarchical levels of the reference model.

KEYWORDS

model, regularlanguagesandgrammars, protocoldataunit,  wireless computer network. 

REFERENCES

1. Lisetskiy, Yu.M.   and  Bobrov, S.I.   (2008), “WiMAX  networks. Implementation and prospects”, USiM, no.  4, pp.  88-92.
2. Fomina, G.A., Kozhanov,  E.A. and Stepina, A.N.  (2008), “Information security in wireless networks”,  Telematika-2008. Trudy XV Vserossiyskoy nauch.-metod. konf. Sankt-Peterburg [Telematics-2008. Proceedings of the XV All-Russian scientific-method. conf.], St. Petersburg, June 23-26, 2008, pp. 187-188.
3. Pechurin, N.K., Kondratova, L.P. and  Pechurin, S.N.  (2012), “The approach to cluster analysis of functions of reference model open systems interconnection using of tools directly aimed artificial neural networks”,   Problemy informatyzatsiyi ta upravlinnya. Zbirnyk naukovykh prats, Vol. 3 (39), pp. 36-43.
4. Pechurin, N.K., Kondratova, L.P. and  Pechurin, S.N. (2012), “Use of  tools  of formal grammars for reclassification functions of reference model open systems interconnection in a wireless computer network”,  Problemy informatyzatsiyi ta upravlinnya. Zbirnyk naukovykh prats, Vol. 2 (38), pp. 19-26.
5. Kamer,  D.E. (2002), Kompyuternye seti i Internet. Razrabotka prilozheniy dlya Internet  [Computer networks and the Internet. Developing of applications for Internet], Izd. dom Vilyams, Moscow, Russia.
6. Roshan, P. and   Lieri, Dzh.   (2004), Osnovy postroeniya besprovodnykh lokalnykh setey standarta 802.11.  [Fundamentals of Wireless LANs 802.11.], Izd. dom  Vilyams, Moscow, Russia.
7. Kapitonova, Yu.V., Kryvyy, S.L., Letychevskyy, A.A. and et al.  (2002), Osnovy dyskretnoyi matematyky [Fundamentals of discrete mathematics], Naukova dumka, Kiev, Ukraine.
8. Zhabin, V.I., Zhukov, I.A., Klimenko, I.A. and  Tkachenko, V.V.  (2007),  Prikladnaya teoriya tsifrovykh avtomatov  [Applied theory of digital machines],  Izd. NAU, Kiev, Ukraine.
9. Romanets, Yu.V., Timofeev, P.A. and  Shangin, V.F.  (1999),  Zashchita informatsii v kompyuternykh sistemakh i setyakh. Pod red. Shangina, V.F.  [Protecting information in computer systems and networks. Ed. Shangin, V.F.], Radio i svyaz, Moscow, Russia. 

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