Method of Doubling the Sequence of the Items Weight in the Merkle-Hellman Knapsack Encryption Problem
VINNICHUK S.D.
ABSTRACT
The algorithm for forming the normal sequence of eccessively ascending one, based on the introduced concepts of indirect modular transformations and partial inversions with the «loophole» formation on the basis of duplicate sequences of the items weights has been developed as part of the Merkle-Hellman cryptoscheme of knapsack encryption. It is shown that under such an approach 2k options of the element of normal sequence may correspond to each element above the ascending sequence for the k-fold iterated backpack system, and the number of options of normal sequence, with all the same parameters of the modular transformations, may achieve 2kL, where L is the number of bits in the data block. In this case, the inverse problem of determining the excessively ascending sequence of the normal one can be reduced to the problem of integer linear programming only as a variant with the great number of options.
KEYWORDS
public key cryptography, crypto scheme Merkle-Hellman, encryption pack.
REFERENCES
- Shnayyer, B. (2002), Prikladnaya kriptografiya. Protokoly, algoritmy, iskhodnyye teksty na yazyke Si. Per. s angl. [Applied Cryptography. Protocols, algorithms, source code in C], Trans. from English, Izd-vo Triumf, Moscow, Russia.
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Phase-Frequency Criterion of Stability
DOLGIN V.P.
ABSTRACT
The method of stability estimation of the dynamic systems according to analysis results of characteristic polynomial of its transfer function has been considered. The phase-frequency criterion of stability estimation of the continuous linear and nonlinear systems containing linear, irrational, transcendent, nonminimum phase links and links of delay is proposed. The method of stability analysis of the systems is expounded.
KEYWORDS
criterion, stability, the transfer function, characteristic polynomial, phase vector.
REFERENCES
1. Topcheyev, Yu.I. (1989), Atlas dlya proektirovaniya sistem avtomaticheskogo regulirovaniya [Atlas for the design of automatic control systems], Mashinostroenie, Moscow, Russia.
2. Dolgin, V.P. (2003), Avtomaticheskoe upravlenie tekhnicheskimi i tekhnologicheskimi sistemami i obyektami. Metody analiza sistem i obyektov [Automatic control of technical and technological systems and objects. Methods of analysis of systems and facilities], Izd-vo SevNTU, Sevastopol, Ukraine.
3. Dolgin, V.P. and Dolgin, I.V. (2009), “The method of approximating the frequency response”, Optimizatsiya proizvodstvennykh protsessov. Vyp. 11. Sbornik nauchnykh trudov [Optimization of production processes. Vol. 11. Collection of scientific papers], Sevastopol, Izd-vo SevNTU, pp. 190-193.
4. Available at: http://www.exponenta.ru/educat/systemat/danilov/4.asp
Reduction of Calculations for the Fourier Base Discrete and Hartly Discrete Transformations under Sparse Arrays of Signals
GODLEVSKY V.S., DENISENKO A.M.
ABSTRACT
The authors perform algorithms based on the account of zero elements in the arrays of input and output signals. The use of these signals ensures the reduction of calculations of the Fourier direct and inverse base discrete transformation and Hartley direct base transformation.
KEYWORDS
reduction in computing the discrete Fourier transform, a discrete Hartley transform, accounting zero elements in algorithms.
REFERENCES
1. Rabiner, L. and Gould, B. (1978), Teoriya i primenenie tsifrovoy obrabotki signalov [Theory and application of digital signal processing], Mir, Moscow, Russia.
2. Bleykhut, R. (1989), Bystrye algoritmy tsifrovoy obrabotki signalov [Fast algorithms for digital signal processing], Mir, Moscow, Russia.
3. Breysuell, R. (1990), Preobrazovanie Khartli [Hartley Transform], Mir, Moscow, Russia.
4. Prado, Zh. (1985), “Note on the paper "Fast Hartley transform"”, TIIER, Vol. 73, no. 12, pp. 182-183.
5. Sergeev, V.V and Usachev, A.V. (1990), “A new algorithm for fast Hartley transform”, Kompyuternaya optika, Vol. 7, pp. 66-67.
6. Adaptivnye filtry. Pod red. Kouena, K.F. and Granta, P.M. (1988), ]Adaptive filters], Ed. Cowan, K.F. and Grant, P.M., Mir, Moscow, Russia.
7. Godlevskiy, V.S. and Denisenko, A.M. (2006), “Methodical errors discrete Fourier transform and methods of its compensation”, Elektronnoe modelirovanie, Vol. 28, no. 3, pp. 83-98.
8. Godlevskiy, V.S. and Denisenko, A.M. (2006), “Numerical synthesis window functions for the discrete Fourier transform”, Elektronnoe modelirovanie, Vol. 28, no. 4, pp. 75-87.
9. Markel, J.D. (1971), “FFT pruning”, IEEE Trans. Audio Electroacoust, Vol. AU-19, pp. 305-311.
10. Gentleman, W.M. and Sandle, G. (1966), “Fast Fourier transforms for fun and profit”, AFIPS Conf. Proc., Washington, D.C., Spartan, 1966, Vol. 29, pp. 563-578.
11. Skinner, D.P. (1976), “Prunning the decimation-in-time FFT algorithm”, IEEE Trans. Acoust., Speech, Signal Processing, Vol. ASSP-24, pp. 193-194.
12. Sreenivas, T.V. and Rao, P.V.S. (1979), “FFT algorithm for both input and output pruning”, Ibid., Vol. ASSP-27, pp. 291-292.
Investigation of the Impact of Errors of Certain Factors on the Error in Modelling of Contaminants Spread in the Surface Layer of the Atmosphere
KRIVAKOVSKAYA R.V., ARTEMCHUK V.A.
ABSTRACT
The article deals with assessing the impact of error of the individual factors in input data while modelling the spread of contaminants in surface layer of the atmosphere. In particular, analytical expressions for the calculation of relative error of the results of modelling the spread of contaminants in surface layer of atmosphere are determined, depending on relative error of the input parameters using statistical models modifications IAEA and Roberts’ k-model. The results of numerical experiments of assessing the impact of the relative error in the input data by changing one of the factors are given.
KEYWORDS
Mathematical modeling, the relative error.
REFERENCES
1. Popov, O.O. (2010), “Mathematical and computer modeling of man-made pressures on the city atmosphere from stationary point sources of pollution”, Abstract of Cand. Sci. (Tech.) dissertation, 01.05.02, Kiev, Ukraine.
2. Yatsyshyn, A.V., Popov, O.O. and Artemchuk, V.O. (2009), “Computer facilities predicting anthropogenic load on the atmosphere”, Skhidnoevropeyskyy zhurnal peredovykh tekhnolohiy, Vol. 5/2 (41), pp. 33-36.
3. Talerko, N.N. (2009), “Physical features and limitations of models of atmospheric transport of radionuclides for different spatial and temporal scales”, Problemy bezpeky atomnykh elektrostantsiy i Chornobylya. Vyp. 11, Vol. 11, pp. 57-62.
4. Monin, A.S. (1959), “Atmospheric diffusion”, Uspekhi fizicheskikh nauk, Vol. 37, no. 1, pp. 119-130.
5. Pampuro, V.I. (1967), Analiz radiotsepey i ikh skhemnoy nadezhnosti [Analysis radio circuits and their circuit reliability], Tekhnika, Kiev, Ukraine.
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