2018 № 4(41)

Gusiakov V. K. MATHEMATICAL MODELING IN THE PROBLEM OF ASSESSMENT OF TSUNAMI HAZARD FOR MARINE COASTS
Imomnazarov Kh. Kh., Yusupov R. K. ON A MODEL OF THE DYNAMIC THEORY OF POROELASTICITY WITH MEMORY
Asmus V., Buchnev A., Krovotyntsev V., Pyatkin V. COMPLEX OF THE SOFTWARE IN PROBLEMS OF SPACE MONITORING OF HAZARDOUS HYDROMETEOROLOGICAL PHENOMENA
Khairetdinov M. S., Kovalevsky V. V., Voskoboinikova G. M., Sedukhina G. F. THE GEOINFORMATION TECHNOLOGY OF ACTIVE MONITORING IN THE STUDY INTERACTION OF GEOPHYSICAL FIELDS
Braginskaya L. P., Grigoruk A. P., Kovalevsky V. V. INFORMATION AND ANALYTICAL SUPPORT OF SCIENTIFIC RESEARCH IN ACTIVE SEISMOLOGY
Kalimoldayev M., Tynymbayev S., Magzom M. SOFTWARE-HARDWARE FACILITIES FOR CRYPTOSYSTEMS BASED ON POLYNOMIAL RNS

Institute of Computational Mathematics and Mathematical Geophysics SB RAS,630090, Novosibirsk, Russia

MATHEMATICAL MODELING IN THE PROBLEM OF ASSESSMENT OF TSUNAMI HAZARD FOR MARINE COASTS

UDC 550.345

Mathematical modeling is one of the most powerful and flexible tools for studying complex natural phenomena, in which the setting up of a direct full-scale experiment is, as a rule, impossible. A typical example of a dangerous natural phenomenon characterized by low frequency and severe consequences are tsunami waves that occur in the oceans and the seas after submarine earthquakes, volcanic explosions, underwater slumping and coastal landslides. By the number of casualties and the total damage, tsunamis are in fourth place among other natural disasters and catastrophes, after earthquakes, floods and typhoons. In the world statistics of victims of natural disasters in the XX century, which took more than 4 million lives, the share of tsunami was relatively small and amounted to just over 1 %. The Indonesian disaster of 2004, which took more than 227,000 lives, immediately brought the tsunami in first place in the statistics of the victims of natural disasters in the 21st century.

The damage caused by the tsunami is aggravated by their complete suddenness, transience, heavy destruction and high probability of fatal outcomes among people caught in the zone of impact of these waves. The problem of effective protection from this natural disaster is complicated by the rarity of its manifestation in a particular section of the coast. Even in the most tsunami-prone areas of the Pacific Ocean (such as Japan, Chile, Peru), strong tsunamis with casualties occur every 30–50 years, disastrous — once in 100–150 years. These return periods far exceed the frequency of occurrence, for example, of hurricanes and floods and are comparable to the return periods of earthquakes and volcanic eruptions. Due to the nature of the mechanism of occurrence, as well as due to the presence of constant sea level disturbances due to wind waves, storms and tides, tsunamis have a certain natural threshold below which they are practically unobservable, and above it immediately become dangerous. This is partly why in the event of the occurrence of this natural disaster, the degree of the population’s readiness for it turns out to be unacceptably low.

In the Siberian Branch of the Russian Academy of Sciences, studies on tsunamis initiated by M. A. Lavrent’ev, E. I. Bichenkov, R. M. Garipov and A. I. Yanushauskas in the early 1960s, were then continued and received an especially intensive development in the Computing Center SOAN USSR (now the Institute of Computational Mathematics and Mathematical Geophysics of the SB RAS). The leading role in this was played by Anatoly A. Alekseev, at that time the Head of the Laboratory of Mathematical Problems of Seismology. The idea of A. S. Alekseev was to include consideration of gravity term into the standard Lame’s equation of motion for the liquid layer overlying the elastic half-space. In such a model among the solutions of the dispersion equation there must be a root corresponding to the surface gravitational wave in the fluid layer, i.e. tsunami. This approach turned out to be very fruitful and made it possible to study the dependence of tsunami amplitudes on the parameters of a seismic source, used in seismology and determined from observations of seismic waves (seismic moment, depth, mechanism). It was called the elastic model of tsunami generation, which was considered as an alternative to the hydrodynamic piston model, in which the fluid is considered incompressible and the bottom is rigid. The elastic model makes it possible to carry out a joint analysis of the generation conditions for the surface seismic waves (Rayleigh waves) and tsunami in order to determine the existence of physical connections or correlations between them, which could be used for tsunami prediction.

The possibility of considering both elastic waves and tsunami waves within the framework of a unified model made it possible for the first time to obtain estimates of the fraction of seismic energy radiated by a model source that goes to the formation of tsunami waves. It was found that the upper limit of the share of seismic energy, transferring into tsunami waves (about 10 %) is reached for a point source of the vertical dip-slip type, located at a shallow (about 10 km) depth. For the parameters of model sources corresponding to the real tsunamigenic earthquakes in the Pacific, the fraction of tsunami energy does not exceed 1 % of the total seismic energy.

The two main scientific and practical tasks in the tsunami problem are the operational tsunami forecast and preliminary tsunamizoning of the coast. The main problem of operational tsunami forecast on the Far Eastern coast of the Russian Federation is to reduce the number of false alarms, which can be achieved by limiting the size of coastal zone for the alarm released after the submarine earthquake with magnitude above threshold value as well as shifting from a binary to a three-level alarm scheme. The main problem of assessing the tsunami hazard of the ocean coast, which has a subduction zone in front of it, is to obtain realistic estimates of the place and time of occurrence of M9 class mega-earthquake in the nearest segments of this zone. Obtaining such estimates is a complex scientific and practical problem and in fact corresponds to solving the problem of a long-term forecast of the strongest earthquakes.
The results presented in this paper were partially obtained during the implementation of the RFBR project 16-05-00450.

Key words: mathematical modeling, earthquake sources, seismotectonics, tsunami, operational warning, tsunami hazard, tsunami-zoning.

References

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Bibliographic reference: Gusiakov V. K. Mathematical modeling in the problem of assessment of tsunami hazard for marine coasts //journal “Problems of informatics”. 2018, № 4. P. 7-24.

article

Imomnazarov Kh. Kh., Yusupov R. K.

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
Karakalpak State University named after Berdakh, 742000, Nukus, Uzbekistan

ON A MODEL OF THE DYNAMIC THEORY OF POROELASTICITY WITH MEMORY

UDC 517.956.3

This paper deals with obtaining a closed system of first order dynamic integro-differential equations for the velocity components of the displacement vector of an elastic porous body, a saturating fluid, and a stress tensor in a dissipative hydrodynamic approximation. The generalization of the poroelasticity theory consists as a rule, of taking into account dispersion and absorption. The main effect of the dissipation in a homogeneous medium of the theory of poroelasticity is caused by the friction at the boundaries between the saturating fluid and the matrix in the pores (the viscous dissipation mechanism) and leads to the introduction of additional terms into the equations of motion of the poroelasticity theory. In the published works of some authors, it is proposed to introduce additional terms with relaxation cores into the mathematical model of the poroelasticity of dissipation, as well as to take into account the non-ideality of both phases (for example, visco-poroelastic models of the medium). In different types of acoustic waves, the effect of dissipation manifests itself in various ways. An important result of the research into the propagation of acoustic waves in a saturated porous medium was the prediction of the existence of three types of oscillations: longitudinal waves of the first and second types (sometimes called fast and slow longitudinal waves) and a transverse wave (shear wave). If fast longitudinal and shear waves are inherently close to the waves in an infinite elastic medium, then a slow longitudinal wave with its considerable dispersion and attenuation caused by the movement of fluid particles relative to the skeleton is a new characteristic of a saturated porous medium. It is a slow longitudinal wave which is generated as a result of the viscous dissipation that is the strongest frequency-dependent attenuation, thus making this wave difficult to observe in fluid-saturated rocks. In the region of seismic (low) frequencies in a saturated porous fluid, described by the equations of the poroelasticity theory in the dissipative approximation, only fast longitudinal and transverse waves with low dispersion and attenuation propagate; the second longitudinal mode is diffusional and becomes a propagating wave only at sufficiently high frequencies. In particular, the theoretical and applied tasks of scientific instrumentation often have to deal with both ordinary problems of mechanics of porous fluid-saturated media (for example, the case of zone electrophoresis, when a porous medium (gel) is fluid-saturated), and problems of acoustics of porous media. This system of equations was obtained from a system of thermodynamically consistent system of quasilinear equations under the following assumptions: the porosity coefficient is a small parameter, the shear coefficients, and the inter-phase friction is a function of strain rate and relative phases velocities, respectively. The dependence of the dispersion relation of the resulting system on the physical and kinetic parameters was investigated. This mathematical model allows a correct passage to the limit with the disappearance of porosity to a nonlinear one-dimensional model of the elasticity theory in the case when the shear coefficient is a function of the strain rate. It is shown that the propagation velocity of shear waves in the high-frequency approximation tends to the velocity of the transverse wave for a homogeneous porous medium saturated with fluid.

Key words: porous medium, force friction, permeability, hyperbolic system, displacement velocity, relative velocity, convolution integral.

References

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Bibliographic reference: Imomnazarov Kh. Kh., Yusupov R. K. On a model of the dynamic theory of poroelasticity with memory //journal “Problems of informatics”. 2018, № 4. P. 25-32.

article

Asmus V., Buchnev A., Krovotyntsev V., Pyatkin V.

Research Center Planeta,123242, Moscow, Russia
Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

COMPLEX OF THE SOFTWARE IN PROBLEMS OF SPACE MONITORING OF HAZARDOUS HYDROMETEOROLOGICAL PHENOMENA

UDC 528.852

The PlanetaMonitoring software complex, developed jointly by the Scientific Research Center Planeta and the Institute of Computational Mathematics and Mathematical Geophysics of the Siberian Branch of the Russian Academy of Sciences, is in constant development with regard to the launch of new Russian and foreign spacecraft. The complex is a representative set of software technologies that allow solving various problems of processing Earth remote sensing (ERS) data. Here are some of these software technologies: satellite image filtering; radiometric and geometric correction; geo-referencing; transformation into cartographic projections and images mounting; detection of lineaments and ring structures; recognition and classification of environmental objects (cluster analysis and supervised classification); determination of spatial displacements of objects using multi-temporal satellite images. These technologies are widely used in solving problems of monitoring hydro meteorological hazards (floods, ice conditions, wind over the sea surface, pollution, etc.).

When it comes to analyzing space images, the monitoring of the natural environment as part of solving applied problems of ERS comes across a problem of detection of extended objects of a given shape, such as linear and ring structures on random background. When processing space images in order to detect interesting objects on them, one usually prefers a nonparametric statistical approach for a number of reasons. The main reason is that, due to the randomness of natural processes, the data of remote measurements (images with combined spectra) contain many random variations masking differences in the brightness values of the images at the points of the object region and at the points of the background region. The main idea of this approach is to calculate statistics based on the analysis of image pixels values along the normals to the intended object position. For each possible position, the decision on the presence of an object is made based on the result of comparing the calculated statistics values with predefined threshold values obtained on the basis of the input parameters.

The large generalization of details during observations from space provides space monitoring of floods taking into account regional features of the river network and allows tracing the development of flooding processes along the entire length of the river. The selection of the boundaries of the flooded areas on multi-zone satellite images is carried out using the algorithms of uncontrolled classification. At the first stage of the uncontrolled classification, the selection of the environmental object classes on the satellite image occurs, based on the difference in their spectral properties. At the second stage, the selected classes are grouped into water and non-water objects. At the final stage of the thematic processing of satellite data, the flooded areas are combined with topographic maps.

Clustering methods for multispectral satellite images are actively used to recognize the characteristics of sea ice (mobility, age, private cohesion, ice forms). For such cases, it is advisable to first perform an uncontrolled classification of multi-zone satellite images and recognize the characteristics of ice concentrated in a small ice area, and then build an ice map using the recognition results.

Another type of regularly produced satellite information products using the PlanetaMonitoring software package is the automatic preparation of maps of fields (speeds and directions) of the wind over the sea surface of the seas of Russia according to the data of ASCAT microwave scatter meters, placed on European polar-orbital satellites METOP-A and METOP-B. Maps of fields of the wind over the sea surface in the internal seas of Russia are built 1–2 times a day, however, due to the thickening of longitudes in northern latitudes, each Arctic sea can be covered by a scatterometric survey at several adjacent turns in running.

One of the important directions of using satellite data is monitoring of marine environment pollution. The task of construction of pollution displacements fields of the marine environment using multi-temporal satellite data is closely related to the problem of determining the vectors (velocity and direction) of spatial displacements of water masses. The technology uses the method of restoring fields of spatial displacements of water masses on the identified changes in the position of some water bodies (tracers) on multi-temporal satellite images, which are combined in a single cartographic projection. Determination of the coordinates of water bodies is achieved using piecewise affine transformations based on Delaunay triangulation. Simultaneously with the construction of the map, histograms of velocities and directions of spatial displacements of water masses are calculated.

Key words: remote sensing, PlanetaMonitoring software package, pre-processing, supervised classification, clustering, statistical detection of linear and ring structures, spatial displacements of natural objects, floods, ice conditions, wind over the sea surface, pollution.

References

1. Asmus V. V., Buchnev A. A., Krovotyntsev V. A., Pyatkin V. P., Salov G. I. Kompleks programmnogo obespecheniya PLANETAMONITORING v prikladnykh zadachakh distantsionnogo zondirovaniya //Avtometriya. 2018. T. 54. N 3. S. 14–23.
2. Distantsionnoe zondirovanie: kolichestvennyi podkhod // Per. s angl. Pyatkina V. P. i Yudinoi O. A. pod red. A. S. Alekseeva. M.: Nedra, 1983.
3. Shovengerdt R. A. Distantsionnoe zondirovanie. Modeli i metody obrabotki izobrazhenii. M., Tekhnosfera, 2010.
4. Asmus V. V. Programmno-apparatnyi kompleks obrabotki sputnikovykh dannykh i ego primenenie dlya zadach gidrometeorologii i monitoringa prirodnoi sredy. Dissertatsiya v vide nauchnogo doklada na soiskanie uchenoi stepeni doktora fiziko-matematicheskikh nauk. Na pravakh rukopisi. Moskva, 2002.
5. Krovotyntsev V. A., Trenina I. S., Volgutov R. V., Maksimov A. A., Maslova N. A. Informatsionnaya produktsiya sputnikovogo monitoringa polyarnykh akvatorii Zemli i zamerzayushchikh morei Rossii //Meteospektr. 2014. N 2. S. 89–98.
6. Bedritskii A. I., Asmus V. V., Krovotyntsev V. A., Lavrova O. Yu., Ostrovskii A. G. Sputnikovyi monitoring zagryazneniya rossiiskogo sektora Chernogo i Azovskogo morei v 2003–2007 gg. // Meteorologiya i gidrologiya. 2007. N 11. S. 5–13.
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8. Asmus V. V., Buchnev A. A., Pyatkin V. P. Klasternyi analiz dannykh distantsionnogo zondirovaniya Zemli // Avtometriya. 2010. N 2. S. 58–66.
9. Salov G. I. O moshchnosti neparametricheskikh kriteriev dlya obnaruzheniya protyazhennykh ob’ektov na sluchainom fone // Avtometriya. 1997. N 3. S. 60–75.
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11. Asmus V. V., Buchnev A. A., Pyatkin V. P., Salov G. I. Software System for Satellite Data Processing of Applied Tasks in Remote Sensing of the Earth // Pattern Recognition and Image Analysis. 2009. Vol. 19. N 3. P. 69–74.
12. Buchnev A. A., Pyatkin V. P. Monitoring oblachnykh obrazovanii po dannym geostatsionarnykh sputnikov Zemli // Avtometriya. 2009. N 4. S. 40–47.

Bibliographic reference: Asmus V., Buchnev A., Krovotyntsev V., Pyatkin V. Complex of the software in problems of space monitoring of hazardous hydrometeorological phenomena //journal “Problems of informatics”. 2018, № 4. P. 33-48.

article

Khairetdinov M. S., Kovalevsky V. V., Voskoboinikova G. M., Sedukhina G. F.

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia
*Novosibirsk State Technical University, 630092, Novosibirsk, Russia

THE GEOINFORMATION TECHNOLOGY OF ACTIVE MONITORING IN THE STUDY INTERACTION OF GEOPHYSICAL FIELDS

UDC 534:621.382

The problem of predicting the geoecological effect of various technogenic explosions, namely, short-delay quarry blasts, test site ones, falling rocket stages etc., on the natural environment and social infrastructure is of primary importance. Mass explosions that have been made recently for the purpose of eliminating the utilizable ammunition stock are a serious hazard. Powerful natural explosions include, first of all, eruptions of magmatic and mud volcanoes and falls of celestial bodies. It is well-known that the major geoecological effects of explosions are due to the formation of air-shock and underground seismic waves, formation and propagation of dust clouds and electric pulses. Investigation of the seismic and acoustic effects of mass explosions damaging industrial and residential objects and the shock action on bio-objects is of greatest interest. Such effects were considered earlier. Nevertheless, it should be noted that the dependence of these effects on external factors, such as the wind direction and velocity, temperature inversion, atmospheric turbulence, and the surrounding area relief and landscape, has been poorly studied. This is all the more important since the influence of such factors can greatly enhance the destructive ecological action of explosions on the environment. It is proved that meteo-dependent processes of propagation of infrasound from explosions in the atmosphere can enhance many times the ecological loading on the social and natural environments.

Taking into account the above factors,it is necessary to predict the geoecological risk of powerful explosions, which calls for additional investigations of the physical effects of propagation of seismic and acoustic waves from mass explosions. The objective of this paper is to present a methodological approach to carrying out such investigations and obtaining experimental and numerical results. The approach being proposed is based on seismic vibrators as sources imitating explosions, but having, in contrast to them, a much smaller power. In this case, as compared to explosions, ecological cleanness and repeatability of experiments are achieved. This is due to a high-precision power and frequency-temporal characteristics of vibrational sources. The approach proposed to prediction with seismic vibrators was used because of the ability of vibrators to simultaneously generate both seismic and acoustic oscillations. This was proved earlier both theoretically and in numerous experiments for this class of sources.The use of the approach of active monitoring of the natural environment makes it possible to achieve ecological purity, high repeatability and precision accuracy of the measurement parameters being estimated.

As an integral characteristic in studying the destructive properties of infrasound from explosions for the environment, we take the specific acoustic energy density. Admissible acoustic effects on objects of social infrastructure are determined by the specific energy density values.

The determining factor for acoustic energy density values is the wave pressure. The acoustic pressure is a function of many parameters determined by the radiation conditions and the propagation of acoustic oscillations.The multi-factor model of integral pressure can be described by the energy balance equation, which includes: the pressure at the recording point at distance r from the source; the frequency-dependent acoustic pressure of the vibrator;the absorption of infrasound depending on the distance determined by the inhomogeneity of the atmosphere and the state of the Earth’s daily surface; the pressure at the recording point as a function of meteorological parameters: the pressure resulting from the spherical divergence of the wavefront. In general case obtaining of estimates of integral pressure in analytical form is difficult, since there are no full a priori data about the meteorological conditions along the long propagation path of acoustic oscillations. There are also factors due to the peculiarities of absorption of the energy of acoustic oscillations caused by the presence of forested areas, snow cover, and geological irregularities of the Earth’s daily surface (hills, mountains, etc.) along the long propagation path of acoustic oscillations.

One way to avoid prior uncertainty is obtaining the estimates of integral pressurein experiments with seismic vibrators as emitters of infralow-frequency acoustic oscillations. The both (analytical and experimental) variants are considered in the present paper. The results of the works are illustrated by data of numerous experiments and numerical calculations.

Key words: geoinformation technology, acousto-seismo-meteo fields, interaction, seismic vibrators, technogenic and natural explosions, geoecological risk, prediction.

References

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Bibliographic reference: Khairetdinov M. S., Kovalevsky V. V., Voskoboinikova G. M., Sedukhina G. F. The geoinformation technology of active monitoring in the study interaction of geophysical fields //journal “Problems of informatics”. 2018, № 4. P. 49-61.

article

Braginskaya L. P., Grigoruk A. P., Kovalevsky V. V.

Institute of Computational Mathematics and Mathematical Geophysics SB RAS, 630090, Novosibirsk, Russia

INFORMATION AND ANALYTICAL SUPPORT OF SCIENTIFIC RESEARCH IN ACTIVE SEISMOLOGY

UDC 550.34

The paper discusses the principles of organizing an Internet resource for informational and analytical support for theoretical and applied research in the field of active seismology and related fields of science. Active seismology is one of the modern directions of studying the structure of the Earth’s crust and geodynamic processes in seismically active zones. The development of active seismology with powerful vibration sources of seismic waves was started in the 70s of the last century by the RAS scientific program Vibrational Sounding of the Earth, which was carried out by the Institutes of the SB RAS under the guidance of academician A. S. Alekseev.

As with many other scientific fields, research in the field of active seismology is characterized by a growth of data arrays obtained as a result of computational and field experiments, therefore services that provide effective access to both the data obtained from field and computational experiments and to the means of their analysis are important and in demand . With many heterogeneous data sources, there is the task of organizing an infrastructure that allows not only to accumulate information for its reuse in various studies, but also to systematize the knowledge and data of the subject area, to provide meaningful access and preliminary analysis of data.

The paper proposes a method for solving the problem of information support for research in active seismology by building an intellectual thematic Internet resource. The architecture of an Internet resource can be represented as two interacting subsystems.

The first subsystem — Scientific Information System (SIS) Active Seismology — provides users with access to the data obtained during field and computational experiments on the vibrational sounding of the Earth’s and to the tools for the analysis, and also includes a thematic electronic library replenished by users, containing reports, full texts of articles and other documents.

The main components of the SIS Active Seismology are: the Informatics-computational system (ICS) Vibrational Sounding of the Earth, Database of results of computational experiments (Synthetic seismograms), Archive of wave field images (Wave fields), Database of scientific works — electronic library and bibliographic catalog.
(ICS) Vibrational Sounding of the Earth provides the following main functions: obtaining from the database detailed information on any of the experiments performed; index and parametric search of seismic trace simultaneously by 18 parameters of vibrosounding; automatic construction of interactive maps with search results with seismic sources and recorders marked on them; interactive analysis of seismic signals in the time, frequency, time-frequency and spatial domains. The analysis is carried out online with the results displayed in the user’s web browser.

The second subsystem — the Knowledge Portal — is intended both for systematization of the given subject area as a whole, and heterogeneous data and means of their processing, presented in the SIS Active Seismology . The basis of the portal’s knowledge system is ontology and the associated description of the corresponding network resources.
Ontology is a description of active seismology, as a scientific section of geophysics, and a description of scientific activities related to this discipline. The ontology of active seismology was created according to the method developed in the Laboratory of artificial intelligence of the Institute of Informatics Systems SB RAS. The portal ontology introduces formal descriptions of domain concepts in the form of classes of objects and relations between them, thereby defining structures for representing real objects and their connections. Accordingly, the data on the portal is presented in the form of a semantic network, i.e. as many different types of interconnected information objects. Substantial access to systematized knowledge and information resources is provided with the help of the advanced navigation and search tools provided by the portal, the operation of which is also based on ontology.
Information objects are presented on the Portal pages by hyperlinks. The Knowledge Portal on hyperlinks allows you to refer to the sections of the SIS Active Seismology, including the ICS Vibrational Sounding of the Earth.

The use of ontology as a conceptual basis of a scientific Internet resource allowed to create an effective information-analytical environment convenient for researchers in the field of active seismology and related branches of scientific knowledge, since the knowledge and data presented in it as objects and relations between them is the most natural to man. The Internet resource is available at http://opg.sscc.ru/.

Key words: active seismology, ontology, knowledge portal, information-computing system.

References

1. Alekseev A. S., Glinskii B. M., Kovalevskii V. V. et al. Aktivnaya seismologiya c moshnimi vibratsionnimi istochnikami. Editor in Chief G.M. Tsibulchik. Novosibirsk: Inst. of Comp. Math. and Math. Geoph. Publ., GEO SB RAS Publ., 2004.
2. Gruber T. R. A translation approach to portable ontologies // Knowledge Acquisition. 1993. N 5 (2). P. 199–220.
3. Zagorulko Y., Zagorulko G. Ontology-Based Technology for Development of Intelligent Scientific Internet Resources // Intelligent Software Methodologies, Tools and Techniques. Proceedings of the 14th International Conference, SoMet 2015, Naples, Italy, September 15–17, 2015. Communications in Computer and Information Science. 2015. Vol. 532, Springer Intern. Publishing Switzerland 2015. P. 227–241/
4. Braginskaya L., Kovalevsky V., Grigoryuk A. Structure and services of the information support system for vibroseismic researches // All-Russian Conference SDM-2017 CEUR Workshop Proceedings, Vol. 2033, Published: 2016.
5. Zagorulko Y. A., Borovikova O., Zagorulko G. Primenenie patternov ontologicheskogo proektirovaniya pri pazrabotke ontologiy nauchnih predmetnih oblastey // DAMDID/RCDL. 2017. P. 258–265.
6. Braginskaya L., Kovalevsky V., Grigoryuk A. Zagorulko G. Ontological approach to information support of investigations in active seismology // Computer Technology and Applications (RPC), 2017. Second Russia and Pacific Conference.
7. Braginskaya L., Grigoryuk A., Kovalevsky V. Struktura i servisi informatsionnoy podderzhki vibroseismicheskih issledovaniy // Obrabotka prostransvennih dannih v zadachah monitoring prirodnih i antropogennih protsessov (SDM-2017) Sbornik trudov vserossiyskoy konferentsii. 29–31 avgusta 2017, Berdsk. Novosibirsk: ICT SB RAS, 2017. P. 241–245 [El. res.]: http://conf.nsc.ru/files/conferences/SDM-2017/416796/(S3)BraginskayaLP.pdf
8. Grigoryuk A. P., Kratov S. V. Data Experiments Management on Web- Technologies Basis // In Proceedings of the 12th International Conference on Actual Problems of Electronic Instrument Engineering, APEIE 2014, Novosibirsk, October 2014. Vol. 3. P. 259–261.

Bibliographic reference: Braginskaya L. P., Grigoruk A. P., Kovalevsky V. V. Information and analytical support of scientific research in active seismology //journal “Problems of informatics”. 2018, № 4. P. 62-70.

article

Kalimoldayev M., Tynymbayev S., Magzom M.

The Institute of Information and Computational Technologies, 050010, Almaty, Republic of Kazakhstan

SOFTWARE-HARDWARE FACILITIES FOR CRYPTOSYSTEMS BASED ON POLYNOMIAL RNS

UDC 004.056.5

This paperis dedicated to the development of software-hardware facilities for cryptosystems based on polynomial residue number system.

Today, there is a significant increase in the transfer and processing of personal data from different sources, and this huge amount of data is stored in various information systems and environments. There are many security threats to sensitive data that are processed and stored on such systems.

One of the most reliable ways to solve data protection problems in computer systems and networks is data encryption. With the development of communication networks and embed systems, there is a growing need to create efficient hardware solutions for performing encryption.

The most of the known conventional software-hardware cryptosystems are implemented using positional number system. The main difficulty with performance occurs during work with large data blocks (for instance, with long encryption keys) in cryptographic transformations.

As a result of searching for ways to increase the productivity of electronic computers, methods of detecting and correcting errors, and building highly reliable computer systems, in the middle of the 20th century research has begun in the field of non-positional notation systems.

In this article we discuss some aspect of software and hardware implementation of the encryption scheme based on polynomial residue number system (RNS), which is a system of data representation in computational arithmetic. In RNS, a multi-digit integer in the positional number system is represented as a sequence of several small-digit positional numbers. These numbers are the residues (deductions) from dividing the original number by the bases of the RNS, which are mutually prime numbers.

RNS is the one of the known methods for optimizing computations in existing cryptographic algorithms. It is a nonpositional number system, which is also known as modular arithmetic. In particular, the usage of systems of residual classes allows to increase the speed of operations due to lack of carry bit transfer during addition and splitting a large block of input data into smaller sub-blocks and their parallel processing.

Absence of digits transfer in operations of addition and multiplication and no error propagation is the main advantage that allows to effectively using residue number system in some areas of computer technology. All elements of the vector in nonpositional notations are equivalent unlike the positional notations and error in one of them leads only to a reduction in the dynamic range. This fact allows designing devices with increased fault tolerance and error correction.

A work is being done to develop and implement a software-hardware system for preliminary calculation of the parameters of the non-position number system. In this implementation, the main time-consuming operation — division of a polynomial modulo an irreducible polynomial — is performed hardware-wise on a multiplication device, the scheme of which was presented in authors’ previous works.

The polynomial data for multiplication is prepared on the MicroBlaze software microprocessor, and then this data is transferred to the multiplier device to be multiplied by a modulo of an irreducible polynomial.

Currently a research project on the hardware implementation of the considered cryptosystem is in progress. As was shown above, the main advantages of using the nonpositional number system are the absence of transfer of bits in the operations of addition and multiplication, and, consequently, the possibility of parallel execution of operations on each of the bases of the system, which significantly speeds up the calculation process.

The developed design is to be implemented in HDL Verilog language and synthesized using the Xilinx Artix-7 FPGA.

The ongoing research is aimed for the development of algorithms for multiplying polynomials modulo irreducible polynomials, the synthesis and implementation of various digital multiplier circuits on their basis for the purpose of the software-hardware implementation of symmetric cryptosystems based on the nonpositional number system. The developed modular multiplier is planned to be used as a main calculation unit during hardware implementation of the proposed encryption systems built on NPNS so that calculation in the residue number system can be performed more efficiently in hardware.

In the developed multiplier, the product of polynomials is calculated by summing the rows of matrices of the partial product using multilevel tree of adders. After that a modular reduction by irreducible polynomial is performed.

The application of the non-positional number system allows accelerating slow calculations in asymmetric encryption algorithms and increasing their reliability as well.

Key words: residue number system, block cipher, nonpositional polynomial notation, FPGA programming.

References

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2. Kumar S. Elliptic Curve Cryptography for Constrained Devices, doctoral dissertation, Electrical Engineering and Information Sciences. Bochum: Germany; Ruhr University, 2006.
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6. Biyashev R., Kalimoldayev M., Nyssanbayeva S., Magzom M. Development of an encryption algorithm based on nonpositional polynomial notations // Proceedings of the International Conference on Advanced Materials Science and Environmental Engineering (AMSEE 2016). Chiang Mai, Thailand, June 26–27, 2016. P. 243–245.
7. Biyashev R., Nyssanbayeva S., Begimbayeva Ye., Magzom M. Building modified modular cryptographic systems // International Journal of Applied Mathematics and Informatics. 2015. V. 9. P. 103–109.
8. Tynymbayev S., Kapalova N., Magzom M. Development and implementation of a hardware multiplier in the non-position numeral system (in Russian) // Proceedings of IICT conference Modern problems of computer science and computer technologies. Almaty, 2017. P. 263–270.
9. Arty A7: Artix-7 FPGA Development Board for Makers and Hobbyists. [El. Res.]: https://store.digilentinc.com/arty-a7-artix-7-fpga-development-board-for... (may 2018).
10. Acosta A., Addabbo T., Tena-Sánchez E. Embedded electronic circuits for cryptography, hardware security and true random number generation: an overview // Int. J. Circ. Theor. Appl. 2017. 45. P. 145–169.
11. Rooju Chokshi, Krzysztof S. Berezowski, Aviral Shrivastava, Stanis³aw J. Piestrak. Exploiting Residue Number System for Power-Efficient Digital Signal Processing in Embedded Processors // Proceedings of the CASES ’09, Grenoble, France, P. 19–28.
12. Schinianakis D., Stouraitis T. Residue Number Systems in Cryptography: Design, Challenges, Robustness // Secure System Design and Trustable Computing. Springer, 2016.
13. Sousa L., Antão S., Martins P. Combining residue arithmetic to design efficient cryptographic circuits and systems // IEEE Circuits and Systems Magazine, 2016.

Bibliographic reference: Kalimoldayev M., Tynymbayev S., Magzom M. Software-hardware facilities for cryptosystems based on polynomial RNS //journal “Problems of informatics”. 2018, № 4. P. 71-84.

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