In der vorliegenden Arbeit wurden die wichstigen Methoden untersucht, die bei der Realisierung von Algorithmen der asymmetrischen Kryptographie (Verteilung der –offentlichen Schlüssel, Generierung und Prüfung der elektronischen Unterschrift) verwendelt werden. Im Mittelpunkt stand die Durführung von berechnungen in den algebraischen Endstrukturen. Folgende Grundalgorithmen der asymmetrischen Kryptographie wurden in der Programiersprache C++ realisiert: die Addition (Substraktion) der Grossen Zahlen, die Potenzierung einer Grossen Zahl mit einer anderen Grossen Zahl. Eine analzse von Algorithmen der assimetrischen Kryptographie wurde durchgeführt, Schlussfolgerungen über die Effektivität der Algorithmen bei Anwendung in der Funktionen zur Berechnung und Prüfung der elektronischen digitalen Unterschrift gezogen.

Atliekant magistrinį darbą pagrindinis tikslas buvo išnagrinėti keliaujančių pirklių uždavinį su papildomais apribojimais. Darbo metu buvo pridėtas pirklio keliamosios galios apribojimas. Išanalizuoti įmanomi sprendimo budai. Darbo metu buvo realizuotas genetinis algoritmas gebantis spręsti iškeltą uždavinį. Sugalvoti ir realizuoti uždavinio sprendimui reikalingi genetiniai operatoriai. Realizuoti lokalaus optimizavimo algoritmai. Atlikti testavimo darbai bei gauti galimi sprendiniai. / The main goal of the master's thesis was to analyze travelling salesmen problem with additional limitations. The limitation of salesman's lifting force was entered during study. Possible calculation methods were analyzed. During the study genetic algorithm was applied, possible of handling current problem. Genetic operators, needed for solving travelling salesmen problem were created and applied. Besides that, local route optimization algorithms were implemented. Tests were accomplished and possible solutions found.

Darbe tiriamas ląstelinių genetinių algoritmų efektyvumas neiškiliems daugiakriteriams uždaviniams spręsti. Sprendžiant uždavinį sujungta:1) daugiakriteris genetinis algoritmas;2)daugiamačių duomenų vizualizavimo metodas; 3) grafinis vaizdavimas. / The final paper discusses the efficiency of cellular genetic algorithms for non-convex multiobjective problems. In order to solve this problem we combine: 1) multiobjective genetic algorithm;2) multidimensional data visualization method; 3) graphic visualization.

The purpose of this work was to analize parallel algorithmization principles and to present interactive multicritarial optimization tasks decision by parallel computers, MS Visual ++6.0 programming language and data transferring package MPICH. With the help of received knowledge new strategy to solve multicritarial tasks was created using computer network, applied to several users.

R-medžių analizė, taikant juos duomenų gavybos algoritmams. / Analysis of R-trees for Data Mining Algorithms.

Šiuolaikiniame finansų pasaulyje duomenų analizė bei sugebėjimas greitai prisitaikyti prie jų pokyčio yra ypatingai svarbus, o kadangi duomenų kiekis yra itin didelis, reikalingi būdai kaip greitai ir tiksliai juos apdoroti. Negana to, informacija, naudojama prekybai finansų rinkose, labai greitai kinta, dėl to būtina pastovi ir pakartotina duomenų analizė, norint jog priimami prekybos sprendimai būtų kaip įmanoma teisingesni. Magistro darbe nagrinėjamos galimybės šiuos skaičiavimus pagreitinti naudojant NVIDIA CUDA lygiagrečiųjų skaičiavimų architektūrą bei genetinius paieškos algoritmus. Darbo metu sukurta aukšto dažnio prekybos modeliavimo sistema, kurios pagalba įvertinamas skaičiavimų trukmės sumažėjimas, naudojant GPU lygiagrečiuosius skaičiavimus, bei lyginant juos su skaičiavimų trukme naudojant įprastinius kompiuterio CPU. Atliekama keleto skirtingų GPU lustų skaičiavimų trukmės analizė, apžvelgiami esminiai skaičiavimų trukmę įtakojantys veiksniai, jų optimizavimo galimybės. Pritaikius visus skaičiavimų trukmę mažinančius veiksnius, buvo pasiektas skaičiavimų trukmės sumažinimas daugiau nei 27 kartus negu naudojantis įprastiniu kompiuterio procesoriumi. / Data analysis and the ability to quickly adapt to rapidly changing market conditions is the key if you want to have success in the current financial markets. Additionally, the amount of data you have to analyze is huge and fast, but precise, data analysis methods are required. In this Master thesis, I am analyzing the possibilities to use NVIDIA CUDA parallel computing architecture to increase the data analysis speed. Additionally, I am using genetic algorithms as a search technique to further increase the computational performance. During the course of this thesis, a high frequency trading modeling system was created. It is used to compare the time it takes to generate trading results using a GPU parallel architecture and using a standard computer CPU. Analysis of a several different GPUs is done, comparing the time needed for computations in comparison to the CUDA cores and other card specifications. A detailed research of possible optimization techniques is done, providing detailed data of the calculation performance increase for each of them. At the end, after all described optimization methods are applied, a total speed-up of the computations using GPU, while compared to the regular CPU, is more than 27 times.

Pociene, Jurgita. Informatics Master’s Final Thesis. Elliptic Curve Points Calculation Algorithms and their Application. Work leader dr. R. Steuding. Siauliai University. Siauliai, 2006. 35 pages In the work I analyse calculation algorithms of the points on elliptic curves above a body Fp (the body is above primary numbers’ field) and their application opportunities. Basic aims, set for the master’s thesis (to analyse elliptic curve points calculation algorithms and to compare them, to review application of elliptic curve points calculation algorithms, to realize Schoof elliptic curve points calculation algorithm and to analyse their effectivization possibilities) were attained. Elliptic curve points calculation algorithms were analysed and compared. System, realizing Schoof algorithm – one of the most important of elliptic curve points calculation algorithms – was created. Main problems encountered include: standard programming system data types are insufficient to operate with large (~2150) numbers, therefore MIRACL library was employed, enabling use of large numbers in a program to find out whether the number is primary and to perform calculations with polynomials. For result output HTML was used as the form more acceptable for user (to derive polynomial equations). Also it was concluded that finding order of elliptic curves is important for cryptosystem to select a safe curve. A number of methods were created to calculate order of a curve, including one or the most... [to full text]

This paper investigates four methods of one variable function minimising that are used in the optimisation process („Golden cut”, „DSK”, „Pauel”, „Half distribution”), executes the comparison of their efficiency and generalises the results of this research.

Genetic algorithms (GA) are among the widely used in various areas of computer science, including optimization problems. Genetic algorithms (GA) are based on the biological process of natural selection. Many simulations have demonstrated the efficiency of GAs on different optimization problems, among them, bin-packing, qaudratic assignment problem, graph partitioning, job-shop scheduling problem, set covering problem, traveling salesman problem, vehicle routing. The quadratic assignment problem (QAP) belong to the class of NP-hard combinatorial optimization problems. One of the main operators in GA is a crossover (i.e. solution recombination). This operator plays a very important role by constructing competitive genetic algorithms (GAs). In this work, we investigate several crossover operators for the QAP, among them, ULX (uniform like crossover), SPX (swap path crossover), OPX (one point crossover), COHX (cohesive crossover), MPX (multiple parent crossover) and others. Comparison of these crossover operators was performed. The results show high efficiency of the cohesive crossover.

Genetinių algoritmų panaudojimo galimybės ir paplitimas nuolat didėja. Daugelyje nagrinėtų mokslinių darbų, genetiniai algoritmai yra naudojami uždavinių optimizavimui. Optimizavimui naudojama daug skirtingų metodų. Sprendžiant konkretų uždavinį mokslinėje literatūroje paprastai pritaikoma keletas metodų tam, kad būtų pagerinti gauti rezultatai, t.y., išbandoma keletas strategijų. Deja, nepavyko rasti tyrimų, kaip tos pačios genetinės paieškos strategijos gali būti pritaikytos kitoms analogiškoms problemoms spręsti. Šiame darbe pateikiama probleminės srities apžvalga, tyrimo aprašymas bandymų rezultatai ir išvados. / The use of genetic algorithms considerably increases. In some research works GA‘s are investigated to optimize graph problems. There are many different strategies for GA optimization. Unfortunately, there are no investigations if a strategy, suitable for a particular graph problem, will be useful solving other graph problems. In this work I originated, described and developed some GA learning strategy elements. Also I developed some that are available in other research works. These elements are: generation of initial population, selection of individuals, mutation, crossover and some other parameters. All possible strategies (about 300) are tested in this work for three graph problems: shortest path, longest path and traveling salesman problem. Results are summarized and described.