For over two decades, mathematicians and cryptologists have evaluated and presented the theoretical performance of Elliptic-curve scalar point-multiplication in projective geometry. Because computation in projective domain is composed of a wide array of formulations and computing optimizations, there is not a comprehensive performance comparison of point-multiplication using projective transformation available to verify its realistic efficiency in 64-bit x86 computing platforms. Today, research on explicit mathematical formulations in projective domain continues to excel by seeking higher computational efficiency and ease of realization. An explicit performance evaluation will help implementers choose better implementation methods and improve Elliptic-curve scalar point-multiplication. This paper was founded on the practical solution that obtaining realistic performance figures should be based on more precise computational cost metrics and specific computing platforms. As part of that solution, an empirical performance benchmark comparison between two approaches implementing projective Elliptic-curve scalar point-multiplication will be presented to provide the selection of, and subsequently ways to improve scalar point-multiplication technology executing in a 64-bit x86 runtime environment.

Today most computer have a multicore processor and are depending on parallel execution to be able to keep up with the demanding tasks that exist today, that forces developers to write software that can take advantage of multicore systems. There are multiple programming languages and frameworks that makes it possible to execute the code in parallel on different threads, this study looks at the performance and effort required to work with two of the frameworks that are available to the C programming language, POSIX Threads(Pthreads) and OpenMP. The performance is measured by paralleling three algorithms, Matrix multiplication, Quick Sort and calculation of the Mandelbrot set using both Pthreads and OpenMP, and comparing first against a sequential version and then the parallel version against each other. The effort required to modify the sequential program using OpenMP and Pthreads is measured in number of lines the final source code has. The results shows that OpenMP does perform better than Pthreads in Matrix Multiplication and Mandelbrot set calculation but not on Quick Sort because OpenMP has problem with recursion and Pthreads does not. OpenMP wins the effort required on all the tests but because there is a large performance difference between OpenMP and Pthreads on Quick Sort OpenMP cannot be recommended for paralleling Quick Sort or other recursive programs.

Thesis (PhD)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: This thesis deals with a function eld analog of the André-Oort conjecture. The (classical) André-Oort conjecture concerns the distribution of special points on Shimura varieties. In our case we consider the André-Oort conjecture for special points in the product of Drinfeld modular varieties. We in particular manage to prove the André- Oort conjecture for subvarieties in a product of two Drinfeld modular surfaces under a characteristic assumption. / AFRIKAANSE OPSOMMING: Hierdie tesis handel van 'n funksieliggaam analoog van die André-Oort Vermoeding. Die (Klassieke) André-Oort Vermoeding het betrekking tot die verspreiding van spesiale punte op Shimura varietiete. Ons geval beskou ons die André-Oort Vermoeding vir spesiale punte op die produk Drinfeldse modulvarietiete. In die besonders, bewys ons die André-Oort Vermoeding vir ondervarieteite van 'n produk van twee Drinfeldse modulvarietiete, onderhewig aan 'n karakteristiek-aanname.

The aims of this thesis are to reduce the complexity and increasethe accuracy of rotations carried out inthe fast Fourier transform (FFT) at algorithmic and arithmetic level.In FFT algorithms, rotations appear after every hardware stage, which are alsoreferred to as twiddle factor multiplications. At algorithmic level, the focus is on the development and analysisof FFT algorithms. With this goal, a new approach based on binary tree decompositionis proposed. It uses the Cooley Tukey algorithm to generate a large number ofFFT algorithms. These FFT algorithms have identical butterfly operations and data flow but differ inthe value of the rotations. Along with this, a technique for computing the indices of the twiddle factors based on the binary tree representation has been proposed. We have analyzed thealgorithms in terms of switching activity, coefficient memory size, number of non-trivial multiplicationsand round-off noise. These parameters have impact on the power consumption, area, and accuracy of the architecture.Furthermore, we have analyzed some specific cases in more detail for subsets of the generated algorithms. At arithmetic level, the focus is on the hardware implementation of the rotations.These can be implemented using a complex multiplier,the CORDIC algorithm, and constant multiplications. Architectures based on the CORDIC and constant multiplication use shift and add operations, whereas the complex multiplication generally uses four real multiplications and two adders.The sine and cosine coefficients of the rotation angles fora complex multiplier are normally stored in a memory.The implementation of the coefficient memory is analyzed and the best possible approaches are analyzed.Furthermore, a number of twiddle factor multiplication architectures based on constant multiplications is investigated and proposed. In the first approach, the number of twiddle factor coefficients is reduced by trigonometric identities. By considering the addition aware quantization method, the accuracy and adder count of the coefficients are improved. A second architecture based on scaling the rotations such that they no longer have unity gain is proposed. This results in twiddle factor multipliers with even lower complexity and/or higher accuracy compared to the first proposed architecture.

The problem of the study is the delineation and subsequent application of a system of theoretical concepts associated with teaching addition, subtraction, multiplication, and division of whole numbers--referred to as the "operations of arithmetic."

Esta pesquisa objetiva descrever as implicações da vivência institucionalizada na construção cultural do Self em um sistema prisional no qual a pessoa assume uma dupla posição: cumpre sua pena, mas também participa da administração da instituição penal, como responsável pela segurança. A pesquisa foi realizada em duas fases: 1) uma discussão teórico-metodológica a partir da noção de multiplicação dialógica (Guimarães, 2013); e 2) um estudo de caso na Associação de Proteção e Assistência os Condenados - APAC, método alternativo de cumprimento de pena privativa de liberdade que prescinde de presença policial e compartilha a administração com a comunidade local. A participação observante (Bastien, 2007; Malfitano & Marques, 2011), enquanto recurso metodológico para o estudo de caso foi utilizada para descrever e analisar as relações concretas no âmbito da Instituição penal APAC. Realizei 12 visitas à Instituição para observar como se davam as relações interpessoais, bem como uma visita a duas unidades de referência do método APAC e à Fraternidade Brasileira de Assistência aos Condenados, órgão fiscalizador das APAC´s. Efetuei o registro das informações em um diário de campo. Dezoito pessoas participaram da pesquisa, perante consentimento prévio. As entrevistas semiestruturadas foram gravadas em áudio e transcritas em sua íntegra para o posterior processo de análise dialógica interpretativa dos enunciados. A partir das informações levantadas na pesquisa, elaborei um protocolo de análise pelo qual identifiquei antinomias e aspectos expressivos (Wertsch, 1993) que emergiram das experiências vividas com os participantes em três campos-tema (cf. Spink, 2003) selecionados para análise, relações interpessoais, relações intrapessoais, e relação APAC-sistema prisional convencional. Cada contexto de convívio interpessoal apresenta um sistema de valores distinto que baliza múltiplas trajetórias de ação (cf. Boesch, 1991) para a pessoa. Então, qual o papel que a Instituição APAC ocupa na construção cultural do Self da pessoa que cumpre pena privativa de liberdade? Observamos a construção de sistemas de valores, que passam a orientar as ações no presente e em relação ao futuro iminente, que canalizam a construção pelo Self de posicionamentos e reposicionamentos enquanto tentativas de elaborar tensões dialógicas experimentadas pelos participantes. E o Self se desenvolve como uma possibilidade de organização das múltiplas trajetórias de ação disponíveis por meio das ações simbólicas. A análise dialógica dos dados aqui proposta nos guia para uma compreensão que a pessoa que cumpre pena no método APAC reconstrói suas vivências na sociedade e no presídio em memórias transformadas, em uma síntese criativa das antinomias emergentes da experiência e em uma hierarquia de sentidos afetivo-cognitivamente organizados. Como desdobramento da pesquisa, proponho um constructo teórico próprio na dinâmica de compreensão do Self que contemple as dimensões institucionais, uma noção preliminar, a ser aprofundada em estudos posteriores- o Self Institucional, enquanto um modo de subjetivação e de estabelecimento de relações intra e interpessoais que se guia por uma articulação entre aspectos históricos, culturais e afetivo-relacionais no contexto institucional / This research aims to describe the implications of the institutionalized experience in the cultural construction of the Self in a prison system in which the person assumes a double position: he fulfills his sentence, but also engages in the administration of the penal institution, as one responsible for the security. The research was developed in two phases: 1) a theoretical-methodological discussion based on the notion of the dialogic multiplication (Guimarães, 2013); and 2) a case study in the Protection and Assistance to Convicts Association - APAC, an alternative method of serving a custodial sentence that dispenses the police presence and shares administration with the local community. The observational participation (Bastien, 2007; Malfitano & Marques, 2011), as a methodological resource for the case study was used to describe and analyze the concrete relations within the scope of the APAC Criminal Institution. Ive visited the Institution 12 times to observe how the interpersonal relations were given, and I visited another two reference units of the APAC method and the Brazilian Fraternity to Convicts Assistance, APAC\'s inspection body. I recorded the information in a field diary. Eighteen people formed the corpus of the research, with prior consent. The semistructured interviews were recorded in audio and fully transcribed for the subsequent process of interpretative dialogical analysis of the statements. From the information collected, I developed a protocol of analysis in which I identified antinomies and expressive aspects (Wertsch, 1993) that emerged from the experiences with participants in three subject fields (Spink, 2003) selected for analysis: intrapersonal relations, interpersonal relations and APAC relationship-conventional prison system. Each context of interpersonal living presents a distinct value system that targets multiple action paths (cf. Boesch, 1991) for the individual. So, what role does the APAC Institution play in the cultural construction of the Self of the person who is serving custodial sentence? We observe the construction of value systems, which guide the actions in the present and regarding the imminent future and lead the construction by the Self of positioning and repositioning as attempts to elaborate the dialogical tensions experienced by the participants. And the Self works as an organizational possibility of the multiple paths of action available through symbolic actions. The dialogical analysis of the data proposed here guides us to an understanding that the condemned person in the APAC method reconstructs his experiences in society and prison by transforming memories, in a creative synthesis of the emerging antinomies of experience and in a hierarchy of affective-cognitively organized. As a result of the research, I propose a theoretical construct in the dynamics of Self, understanding that it contemplates the institutional dimensions, a preliminary notion, to be deepened in later studies - Institutional Self, as a way of subjectivation and establishment of intra and interpersonal relations which is guided by an articulation between historical, cultural and affective-relational aspects in the institutional context

O presente trabalho consiste numa pesquisa qualitativa sobre o ensino e a aprendizagem de matemática, cujo objetivo foi o de propor uma metodologia, fundamentada no construtivismo piagetiano, para ensinar multiplicação nos anos iniciais do Ensino Fundamental. A observação de que o ensino desse conteúdo, em muitas escolas, privilegia a memorização da tabuada e a aplicação de algoritmos, em detrimento da compreensão, mobilizou uma investigação sobre como organizar o ensino dessa noção privilegiando o desenvolvimento da racionalidade e a aquisição de competências que transcendem o âmbito da matemática. Para isso foi realizada uma intervenção de ensino, planejada e desenvolvida pela própria pesquisadora, ao longo de um semestre (21 aulas) em uma turma de terceira série de uma escola da rede municipal de Curitiba. A multiplicação foi explorada em problemas de proporcionalidade simples (situações de correspondência um-para-muitos e de arranjo retangular). A divisão, por ser sua operação inversa, foi explorada em algumas atividades e dados relativos a essa operação foram incorporados ao estudo. As aulas foram gravadas em vídeo e transcritas em diários enriquecidos com observações e comentários da pesquisadora os quais, junto com as produções dos alunos e relatórios feitos pela professora da turma, compuseram nossa base de dados. Na análise buscamos indicativos da ocorrência de uma interação construtiva, caracterizada por progressos nos seguintes âmbitos: relações intelectuais (compreensão das operações aritméticas em questão pelas crianças); relações sociais/morais (conquistas que transcendem o conteúdo matemático); relações didáticas (efeitos sobre o próprio processo interventivo). Os resultados apontam para uma interação de qualidade construtiva uma vez que a intervenção teve efeito de aperfeiçoamento sobre os sujeitos envolvidos. Verificamos a substituição progressiva de estratégias de contagem por estratégias de cálculo, aquisição de competências aritméticas e interações entre as crianças (indícios de uma relação de cooperação). Apontamos ainda para mudanças de atitudes dos alunos no que se refere às seguintes questões: envolvimento nas atividades propostas, relação com a matemática, forma de tratar os problemas apresentados, comunicação e expressão em sala de aula. No âmbito didático destacamos o tratamento dispensado ao erro, usado como estratégia didática, o papel interventivo que a avaliação exerceu no processo de ensino e a importância da escrita para a reflexão do professor sobre a sua própria prática. / The present work consists of a qualitative research in education and the mathematics learning that objective was to propose a methodology based on Piaget´s constructivism, to teach multiplication in the early years of Eleentary School. The observation that shows how this content has been treated, in many schools, as a memorization and application matter, rather than a comprehension issue, directed to an investigation how about organize the teaching of this matter prioritizing the development of racionality and the acquisition of competences that go beyond matheatics. For that, a planned learning intervention was developed and made by the researcher herself over a period of one semester (21 classes) in a third grade public school from Curitiba. The multiplication was explored in simple proportionality problems (in one-tomany correspondence and rectangular array problems). The division, as it´s the inverse, was also explored in some activities and the data collected was also included in this study. The classes were recorded in video and a transcript enriched by observations and comments from the the researcher was produced. The transcript, the student´s works and daily reports done by the teacher form our database. In the analysis, we look for indications of a constructive interaction, characterized by progresses in the following areas: intellectual relationships (comprehension of the arithmetical operations used); social/moral relationships (acquisition of non mathematical aptitudes); didactic relationships (effects on the intervention process itself). The results show a constructive quality interaction as the intervention had a development effect on the subjects involved. We verified the progressive substitution of the counting strategies for calculation strategies, the acquisition of arithmetical aptitudes and interaction between the students (signs of a cooperative relationship). Also some attitudes changes were observed in the students regarding the following matters: the engagement in the activities, the relationship with mathematics, the approach on the problems, communication and expressionat the classroom. In the didactic field, we highlight the treatment regarding the errors, used as a didatic strategy, the interfered paper the avaliation exerced to the teaching process and the importance of writing for the teacher´s reflection about its practice.

Esta pesquisa empirica discute pontos de tensoes emergidos no dialogo interetnico em torno das questoes de saude indigena, dando enfase ao tema da saude mental. As tensoes foram analisadas segundo diferentes pontos de vista sobre a promocao da saude indigena, identificadas a partir da producao de um mapeamento que expressa os conteudos discursivos marcados por um grande divisor: de um lado a perspectiva ocidental, composta pelo Estado, compreendido atraves das Politicas Publicas de Saude Indigena; do Sistema Unico de Saude e sua assistencia a saude; pelos Conselhos Federal e Regional de Psicologia e pela Organizacao Mundial da Saude. Do outro lado esta a perspectiva dos indigenas, especialmente do povo Mbya Guarani, analisados com apoio da literatura antropologica, a partir da nocao de Teko Pora (Bem Viver); dos noticiarios produzidos e veiculados por coletivos indigenas; do conteudo narrativo contido no documentario Teko Rexa - Saude Guarani Mbya e dos discursos presentes nos noticiarios produzidos por entidades indigenistas. As nocoes de saude e saude mental discutidas por Gadamer (2006), bem como as nocoes de saude e de ethos refletidas por de Figueiredo (2008), referencial teorico-metodologico assumido nesta dissertacao fundamentam sobre a importancia do territorio nos processos de saude/doenca para os povos indigenas, bem como auxiliam a refletir sobre as tensoes presentes em ambas as perspectivas. Os dados foram analisados a partir da nocao de multiplicacao dialogica (Guimaraes, 2013) no ambito do construtivismo semiotico-cultural em psicologia. A partir da identificacao de tensoes presentes, foram levantadas questoes a respeito de como estruturar o cuidado em psicologia, refletindo sobre as possibilidades de seu transito entre diferentes perspectivas em saude / This empirical research discusses points of tension emerging in the interethnic dialogue around indigenous health issues, emphasizing the theme of Mental Health. The tensions were analyzed according to different points of view on the promotion of indigenous health, identified from the production of a mapping that expresses the discursive contents marked by a great divide: on the one hand the western perspective, composed by the State, understood through Policies Public Health Indigenous; of the Unified Health System and its health care; by the Federal and Regional Councils of Psychology; and the World Health Organization. On the other side is the perspective of the indigenous people, especially the Mbya Guarani people, analyzed with the support of anthropological literature, based on the notion of Teko Pora (Bem Viver); of the news produced and transmitted by indigenous collectives; of the narrative content contained in the documentary \"Teko Rexa - Saude Guarani Mbya\" and the speeches present in the news produced by indigenist entities. The notions of \"health\" and \"mental health\" discussed by Gadamer (2006), as well as the notions of \"health\" and \"ethos\" reflected by de Figueiredo (2008), theoretical and methodological reference assumed in this dissertation, importance of the territory in health / disease processes for indigenous peoples, as well as helping to reflect on the tensions present in both perspectives. The data were analyzed from the notion of dialogical multiplication (Guimaraes, 2013), within the scope of semiotic-cultural constructivism in psychology. From the identification of present tensions, questions were raised about how to structure care in psychology, reflecting on the possibilities of its transit between different perspectives in health

"It is widely recognized that security issues will play a crucial role in the majority of future computer and communication systems. A central tool for achieving system security are cryptographic algorithms. For performance as well as for physical security reasons, it is often advantageous to realize cryptographic algorithms in hardware. In order to overcome the well-known drawback of reduced flexibility that is associated with traditional ASIC solutions, this contribution proposes arithmetic architectures which are optimized for modern field programmable gate arrays (FPGAs). The proposed architectures perform modular exponentiation with very long integers. This operation is at the heart of many practical public-key algorithms such as RSA and discrete logarithm schemes. We combine two versions of Montgomery modular multiplication algorithm with new systolic array designs which are well suited for FPGA realizations. The first one is based on a radix of two and is capable of processing a variable number of bits per array cell leading to a low cost design. The second design uses a radix of sixteen, resulting in a speed-up of a factor three at the cost of more used resources. The designs are flexible, allowing any choice of operand and modulus. Unlike previous approaches, we systematically implement and compare several versions of our new architecture for different bit lengths. We provide absolute area and timing measures for each architecture on Xilinx XC4000 series FPGAs. As a first practical result we show that it is possible to implement modular exponentiation at secure bit lengths on a single commercially available FPGA. Secondly we present faster processing times than previously reported. The Diffie-Hellman key exchange scheme with a modulus of 1024 bits and an exponent of 160 bits is computed in 1.9 ms. Our fastest design computes a 1024 bit RSA decryption in 3.1 ms when the Chinese remainder theorem is applied. These times are more than ten times faster than any reported software implementation. They also outperform most of the hardware-implementations presented in technical literature."

Several algorithms for Public Key Cryptography (PKC), such as RSA, Diffie-Hellman, and Elliptic Curve Cryptography, require modular multiplication of very large operands (sizes from 160 to 4096 bits) as their core arithmetic operation. To perform this operation reasonably fast, general purpose processors are not always the best choice. This is why specialized hardware, in the form of cryptographic co-processors, become more attractive. Based upon the analysis of recent publications on hardware design for modular multiplication, this M.S. thesis presents a new architecture that is scalable with respect to word size and pipelining depth. To our knowledge, this is the first time a word based algorithm for Montgomery's method is realized using high-radix bit-parallel multipliers working with two different types of finite fields (unified architecture for GF(p) and GF(2n)). Previous approaches have relied mostly on bit serial multiplication in combination with massive pipelining, or Radix-8 multiplication with the limitation to a single type of finite field. Our approach is centered around the notion that the optimal delay in bit-parallel multipliers grows with logarithmic complexity with respect to the operand size n, O(log3/2 n), while the delay of bit serial implementations grows with linear complexity O(n). Our design has been implemented in VHDL, simulated and synthesized in 0.5μ CMOS technology. The synthesized net list has been verified in back-annotated timing simulations and analyzed in terms of performance and area consumption.