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Parallelization of Integer Factorization from the View of RSA Breaking
Breitenbacher, Dominik ; Henzl, Martin (referee) ; Homoliak, Ivan (advisor)
This paper follows up the factorization of integers. Factorization is the most popular and used method for RSA cryptoanalysis. The SIQS was chosen as a factorization method that will be used in this paper. Although SIQS is the fastest method (up to 100 digits), it can't be effectively computed at polynomial time, so it's needed to look up for options, how to speed up the method as much as possible. One of the possible ways is paralelization. In this case OpenMP was used. Other possible way is optimalization. The goal of this paper is also to show, how easily is possible to use paralelizion and thanks to detailed analyzation the source codes one can reach relatively large speed up. Used method of iterative optimalization showed itself as a very effective tool. Using this method the implementation of SIQS achieved almost 100 multiplied speed up and at some parts of the code even more.
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Development of Inverse Tasks Solved by Using the Optimizing Procedures and Large Number of Parallel Threads
Ondroušková, Jana ; Skarolek, Antonín (referee) ; Brestovič, Tomáš (referee) ; Horský, Jaroslav (advisor)
In metallurgy it is important to know a cooling efficiency of a product as well as cooling efficiency of working rolls to maximize the quality of the product and to achieve the long life of working rolls. It is possible to examine this cooling efficiency by heat transfer coefficients and surface temperatures. The surface temperature is hardly measured during the cooling. It is better to compute it together with heat transfer coefficient by inverse heat conduction problem. The computation is not easy and it uses estimated values which are verified by direct heat conduction problem. The time-consuming of this task can be several days or weeks, depends on the complexity of the model. Thus there are tendencies to shorten the computational time. This doctoral thesis considers the possible way of the computing time shortening of inverse heat conduction problem, which is the parallelization of this task and its transfer to a graphic card. It has greater computing power than the central processing unit (CPU). One computer can have more compute devices. That is why the computing time on different types of devices is compared in this thesis. Next this thesis deals with obtaining of surface temperatures for the computation by infrared line scanner and using of inverse heat conduction problem for the computing of the surface temperature and heat transfer coefficient during passing of a test sample under cooling section and cooling by high pressure nozzles.
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Development of inverse tasks solved by using the optimizing procedures and large number of parallel threads
Ondroušková, Jana ; Horský, Jaroslav (advisor)
In metallurgy it is important to know a cooling efficiency of a product as well as cooling efficiency of working rolls to maximize the quality of the product and to achieve the long life of working rolls. It is possible to examine this cooling efficiency by heat transfer coefficients and surface temperatures. The surface temperature is hardly measured during the cooling. It is better to compute it together with heat transfer coefficient by inverse heat conduction problem. The computation is not easy and it uses estimated values which are verified by direct heat conduction problem. The time-consuming of this task can be several days or weeks, depends on the complexity of the model. Thus there are tendencies to shorten the computational time. This doctoral thesis considers the possible way of the computing time shortening of inverse heat conduction problem, which is the parallelization of this task and its transfer to a graphic card. It has greater computing power than the central processing unit (CPU). One computer can have more compute devices. That is why the computing time on different types of devices is compared in this thesis. Next this thesis deals with obtaining of surface temperatures for the computation by infrared line scanner and using of inverse heat conduction problem for the computing of the surface temperature and heat transfer coefficient during passing of a test sample under cooling section and cooling by high pressure nozzles.
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Optimization of Secondary Cooling Parameters of Continuous Steel Casting
Klimeš, Lubomír ; Raudenský, Miroslav (referee) ; Pyszko, René (referee) ; Buček, Pavol (referee) ; Štětina, Josef (advisor)
Continuous casting is a dominant production technology of steelmaking which is currently used for more that 95% of the world steel production. Mathematical modelling and optimal control of casting machine are crucial tasks in continuous steel casting which directly influence productivity and quality of produced steel, competitiveness of steelworks, safety of casting machine operation and its impact on the environment. This thesis concerns with the development and implementation of the numerical model of temperature field for continuously cast steel billets and its use for optimal control of the casting machine. The numerical model was developed and implemented in MATLAB. Due to computational demands the model was parallelized by means of the computation on graphics processing units NVIDIA with the computational architecture CUDA. Validation and verification of the model were performed with the use of operational data from Trinecke zelezarny steelworks. The model was then utilized as a part of the developed model-based predictive control system for the optimal control of dynamic situations in the casting machine operation. The behaviour of the developed control system was examined by means of dynamic model situations that have confirmed the ability of the implemented system to optimally control dynamic operations of the continuous casting machine. Both the numerical model of the temperature field and the model-based predictive control system have been implemented so that they can be modified for any casting machine and this allows for their prospective commercial applications.
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Segmentwise Discrete Wavelet Transform
Průša, Zdeněk ; Vargic,, Radoslav (referee) ; Dr. Peter L. Sndergaard (referee) ; Rajmic, Pavel (advisor)
Dizertační práce se zabývá algoritmy SegDWT pro segmentový výpočet Diskrétní Waveletové Transformace – DWT jedno i vícedimenzionálních dat. Segmentovým výpočtem se rozumí způsob výpočtu waveletové analýzy a syntézy po nezávislých segmentech (blocích) s určitým překryvem tak, že nevznikají blokové artefakty. Analyzující část algoritmu pracuje na principu odstranění přesahu a produkuje vždy část waveletových koeficientů z waveletové transformace celého signálu, které mohou být následně libovolně zpracovány a podrobeny zpětné transformaci. Rekonstruované segmenty jsou pak skládány podle principu přičtení přesahu. Algoritmus SegDWT, ze kterého tato práce vychází, není v současné podobně přímo použitelný pro vícerozměrné signály. Tato práce obsahuje několik jeho modifikací a následné zobecnění pro vícerozměrné signály pomocí principu separability. Kromě toho je v práci představen algoritmus SegLWT, který myšlenku SegDWT přenáší na výpočet waveletové transformace pomocí nekauzálních struktur filtrů typu lifting.
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Stochastic Programming Algorithms
Klimeš, Lubomír ; Mrázková, Eva (referee) ; Popela, Pavel (advisor)
Stochastické programování a optimalizace jsou mocnými nástroji pro řešení široké škály inženýrských problémů zahrnujících neurčitost. Algoritmus progressive hedging je efektivní dekompoziční metoda určená pro řešení scénářových stochastických úloh. Z důvodu vertikální dekompozice je možno tento algoritmus implementovat paralelně, čímž lze významně ušetřit výpočetní čas a ostatní prostředky. Teoretická část této diplomové práce se zabývá matematickým a zejména pak stochastickým programováním a detailně popisuje algoritmus progressive hedging. V praktické části je navržena a diskutována původní paralelní implementace algoritmu progressive hedging, která je pak otestována na jednoduchých úlohách. Dále je uvedená paralelní implementace použita pro řešení inženýrského problému plynulého odlévání ocelové bramy a na závěr jsou získané výsledky zhodnoceny.
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Graphic filter library implemented in CUDA language
Peroutková, Hedvika ; Šedivá, Zuzana (advisor) ; Sedláček, David (referee)
This thesis deals with the problem of reducing computation time of raster image processing by parallel computing on graphics processing unit. Raster image processing thereby refers to the application of graphic filters, which can be applied in sequence with different settings. This thesis evaluates the suitability of using parallelization on graphic card for raster image adjustments based on multicriterial choice. Filters are implemented for graphics processing unit in CUDA language. Opacity and image merging mode can be set for filters. Various types of filters were implemented like histogram, color, convolution filters and others. Within the frame of this thesis a graphic user interface was developed, which enables filter applying and setting for chosen image, measuring time needed for filter changes and saving final image.
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