[pt] Essa dissertação se propõe a introduzir nas aulas de matemática da escola básica um tema que traga significado e interesse ao alunado e que, a partir dele, seja possível desenvolver conteúdos novos e clássicos da disciplina, pertinentes a esse nível de escolaridade. O tema escolhido foi a criptografia que possibilitou o desenvolvimento de uma abordagem histórica da sua evolução até o código RSA, a promoção de discussões sobre a relevância atual do assunto até os nossos dias e o trabalho com conteúdos importantes da matemática. Com o intuito de aprimorar e avaliar a proposta, uma pequena aplicação numa escola pública foi feita, através de uma oficina, com resultados bastante satisfatórios. Pretende-se que este trabalho seja mais uma fonte para auxiliar diversos professores na construção de novas propostas pedagógicas adaptadas à realidade de cada sala de aula com olhar motivador, significativo e contemporâneo. / [en] This dissertation proposes to introduce in the math class of the elementary school a theme that brings meaning and interest to the students and, from it, it is possible to develop new and classic content, relevant discipline at this level of education. The theme chosen was the encryption that made possible the development of a historical approach of its development until the RSA code, the promotion of discussions on the current relevance of the subject until our days and working with important content of mathematics. In order to improve and evaluate the proposal, a small application in a public school was made, through a workshop, with results quite satisfactory. It is intended that this work is more a source to assist several teachers in the construction of new pedagogical proposals adapted to the reality of each classroom with motivating, meaningful and contemporary look.

Please read the abstract (Summary)in the section 08summary of this document / Dissertation (MSc (Botany))--University of Pretoria, 2002. / Please note that Chapter 2 is removed due to sensitive information / Plant Science / MSc / Unrestricted

The development of emotion regulation skills is an imperative task early in development. Respiratory sinus arrhythmia (RSA), a physiological proxy of regulation, is indicative of one’s regulatory capacity and can be predictive of behavior in later life (Graham, Ablow, & Measelle, 2010; Moore, 2010). Children begin regulating their emotions at a physiological level early in infancy. Infants who are able to properly suppress RSA have higher quality social interactions in childhood (Graziano, Keane, & Calkins, 2007). Previous work has suggested that parents play a role in predicting infant RSA (Conradt & Ablow, 2010). For example, parent marital satisfaction is known to impact infants’ physiological regulation, such that infants whose parents are less satisfied with their marriages have a decreased ability to regulate physiologically (Moore et al., 2009; Porter, Wouden-Miller, Silva, & Porter, 2003). Previous research has found that parent personality impacts parenting strategies (Cummings & Davies, 1994; Prinzie, Stams, Deković, Reijntjes, & Belsky, 2009), however work examining how parent personality interacts with marital satisfaction to predict infant RSA is lacking. Moreover, the majority of previous work assessing the parent predictors of infant RSA focused on mothers (e.g., Moore et al., 2009). There are known differences in the way mothers and fathers interact with their infants, as well as differences in the way fathers and mothers respond to marital dissatisfaction (Forbes, Cohn, Allen, & Lewinsohn, 2004; Karney & Bradbury, 1995). The present study focused on examining how marital satisfaction and parent personality predicts infant RSA with mothers and fathers. The current study involved 38 families (6-month old infants, mothers, and fathers). Parents completed questionnaires measuring marital satisfaction and personality. Mother-infant and fatherinfant dyads participated in a baseline and face-to-face play task (Still Face Paradigm; Tronick, Als, Adamson, Wise, & Brazelton, 1978), where infant physiological regulation was assessed. Results involving mothers did not yield significant findings predicting infant physiological regulation. For fathers, results indicated that parent personality and parent marital satisfaction predicted infant physiological regulation. The current study highlights the importance of examining the roles of both mothers and fathers predicting infant physiological regulation.

The purpose of this study is to examine how respiratory sinus arrhythmia (RSA) is affected across paced breathing, attention, inhibition, and emotion-eliciting tasks and how those relationships may be mediated by emotion regulation strategies in children with different levels of externalizing and internalizing behaviors between the ages of 8 and 12 years. The first aim was to determine whether externalizing and internalizing symptoms during a paced breathing or natural breathing task better predicted RSA levels. The hypothesis was that internalizing and externalizing behaviors would be more predictive of RSA baseline levels when utilizing a paced-breathing method of measuring RSA. The second aim was to determine how RSA levels across an attention, inhibition, sad, and anger task are predicted by internalizing and externalizing symptoms after controlling for baseline RSA levels. There were four hypotheses: (1) as levels of externalizing behaviors increase, levels of baseline RSA would decrease, (2) as levels of internalizing behaviors increase, levels of baseline RSA will decrease, (3) there will be significantly smaller changes in RSA reactivity) as the level of externalizing behaviors increases, and (4) as levels of internalizing symptoms increase, there will be significantly larger changes in RSA levels relative to RSA baseline levels (RSA reactivity).The results showed that externalizing and internalizing behaviors did not predict RSA levels during a paced or natural breathing task. Additionally, there was very little difference in the outcomes when used either a natural or paced breathing method of RSA as a control variable except when predicting RSA levels during a sad emotion-eliciting task. Although RSA levels during three experimental tasks (attention, inhibition, and sad) were not significant, there were moderate effect sizes for externalizing and/or internalizing symptoms predicting various RSA reactivity (i.e., RSA levels after controlling for baseline) across these conditions. One model was significant in predicting the level of variance of RSA reactivity during an anger emotion-eliciting task, with internalizing and hyperactivity/inattention symptoms contributing the most variation in the model. Findings point towards understanding how internalizing and externalizing symptoms may impact an individual's physiological response during a task.

This thesis, Parallels in portraits of leadership in mega churches of Gauteng (RSA) and Florida (USA), the researcher, studied literature on church leadership with special reference to the leadership of mega churches. He researched issues relating to the nature of church leadership by exploring relevant Bible passages, the lives of certain Bible characters that the Bible presents as good but not perfect leaders, as well as relevant key theological conceptions of leadership. The study accordingly also reviewed different models of church leadership on the hand of a study of some Bible passages and current theological thinking about the matter. The thesis demonstrated that the leadership of mega churches requires certain leadership qualities, values, and competencies. The contribution of the study lies therein that it confirmed and identified through a comparative empirical analysis of details collected through basic research in mega churches of Florida (USA) and Gauteng (RSA) the qualities, values and competencies that are essential for successful leadership of mega churches in very different contexts and church families. The study therefore recommends a desirable leadership style and essential qualities for effective church leadership of mega churches. The study also makes a contribution to the theological understanding of a new but growing church type in urban settings, the mega church; and is of great value to those that lead and study such churches. / PhD, Biblical Studies, North-West University, Vaal Triangle Campus, 2012

The RSA cryptosystem, named after its inventors, Rivest, Shamir and Adleman, is the most widely known and widely used public-key cryptosystem in the world today. Compared to other public-key cryptosystems, such as elliptic curve cryptography, RSA requires longer keylengths and is computationally more expensive. In order to address these shortcomings, many variants of RSA have been proposed over the years. While the security of RSA has been well studied since it was proposed in 1977, many of these variants have not. In this thesis, we investigate the security of five of these variants of RSA. In particular, we provide detailed analyses of the best known algebraic attacks (including some new attacks) on instances of RSA with certain special private exponents, multiple instances of RSA sharing a common small private exponent, Multi-prime RSA, Common Prime RSA and Dual RSA.

The communication technology is changing rapidly every day, and the internet has played a very important role in our lives. Through specific protocols, people transform the data into 0¡¦s and 1¡¦s as digital signals and transfer them from sender to receiver via the network. Unfortunately, data transfer through the internet is open to the public, and too much exposure of private data may be a serious risk. To avoid this situation, we can encrypt the data before transmission to guarantee data confidentiality and privacy. The RSA encryption system is a simple and highly secure public key cryptosystem, but the encryption and decryption process requires a lot of exponentiation operations and division operations. In order to improve the reliability of the encrypted data, the operands are usually larger than 512 bits. If software is used to perform encryption and decryption, real time application will not be sufficed, since software lacks performance. For this reason, the RSA must be implemented in hardware. Since then, many methods of refining the effectiveness of the RSA encryption and decryption hardware have began to be developed. This research proposes a new Modular Multiplier architecture similar to the original Montgomery Modular Multiplier and the RSA encryption system, which is composed by simple adders, shifting registers and multiplexers. What¡¦s more, we¡¦ve also proposed new concepts including the Quotient Lookahead and the Superfluous Operation Elimination to further enhance the performance. The test results show that our design can reduce the total cycle count by 19%, and also save the overall energy consumption. Due to the features of high performance and energy saving, the proposed design is suitable for portable devices which have low power requirements.

The explosive growth in the data communications industry has positioned the internet to hold very important roles in our lives. Sending or receiving data on an open network is an invitation for unauthorized users to obtain your personal information. In order to avoid compromising sensitive information while transferring data, the data needs to be encrypted before transmission to ensure that the information remains safe and confidential. RSA is the most widely used public-key cryptosystem. An RSA operation is a modular exponentiation, which is usually achieved by repeated modular multiplications. For security reasons, RSA operand sizes need to be 512 bits or greater. It would be difficult to achieve real time transmission on the internet by running software programs on typical processors. For this reason, we believe it is necessary to implement RSA by hardware circuit in order to speed up RSA operations. Modular exponentiation is the only operation in RSA cryptosystem and it can be done through repeated modular multiplications. The Montgomery multiplication algorithm is widely recognized as the most efficient modular multiplication algorithm. In order to improve the speed of RSA operation, many papers have proposed ways to refine the Montgomery Algorithm and its architecture. In this thesis, we focus on further improving the performance and power consumption of RSA cryptosystems. This research presents an improved Montgomery multiplier and RSA cryptosystem architecture using only one carry saver adder to significantly reduce the delays of conventional multipliers. We also proposed a low power shift register to reduce power consumption of shift register in Montgomery multiplier. Experimental results show that the proposed RSA cryptosystem not only runs with higher performance but also consumes less power, leading to this system more competitive and suitable for implementations in portable electronic products.

Thanks to the development of the Internet in recent years, we can see more and more applications on E-commerce in the world. At the same time, we have to prevent our personal information to be leaked out during the transaction. Therefore, topic on researching network security becomes increasingly popular. It is well-known that an encryption system can be applied to consolidate the network security. RSA encryption algorithm is a special kind of asymmetric cryptography, commonly used in public key encryption system on the network, by using two prime numbers as the two keys to encrypt and decrypt. These two keys are called public key and private key, and the key length is at least 512 bits. As a public key encryption, the only way to decrypt is using the private key. As long as the private key is not revealed, it is very difficult to get the private key from the public key even using the reverse engineering. Therefore, RSA encryption algorithm can be regarded as a very safe encryption and decryption algorithm. As the minimum key length has to be greater than 512 bits to ensure information security, using software to execute RSA encryption and decryption will be very slow so that the real time requirement may not be satisfied. Hence we will have to implement RSA encryption system with a hardware circuit to meet the real time requirement on the network. Modular exponentiation (i.e., ME mod N) in RSA cryptosystem is usually achieved by repeated modular multiplications on large integers. A famous approach to implement the modular multiplication into hardware circuits is based on the Montgomery modular multiplication algorithm, which replaces the trial division by modulus with a series of addition and shift operations. However, a large amount of clock cycle is still required to complete a modular multiplication. For example, Montgomery multiplication algorithm will take 512 clock cycles to complete an A․B mod N. As a result, performing one modular exponentiation ME mod N in RSA cryptosystm will need 512․512 clock cycles. To counter the above disadvantage, we employ radix-4 algorithm to reduce 50% of clock cycle number for each A•B mod N. In addition, we also modify the architecture of conventional in order to achieve the radix-4 algorithm to reduce its critical path delay so that the performance can be improved further. Experimental results show that the proposed 1024-bit radix-4 modular multiplier (Our-Booth-Radix-4) before performing as pipeline is 70% faster than the radix-2 multiplier with 24% area overhead. Furthermore, it is 20% faster than traditional radix-4 modular multiplier with 12% area reduction. Therefore, its AT is smaller than the previous architectures.

<p>The company Roxen Internet Software have an implementation of the secure network protocol SSL (Secure Sockets Layer) which is used in their web server product. This report describes the upgrading of that implementation to the TLS1.0 (Transport Layer Security) standard. It also describes a performance investigation of the SSL/TLS support in the Roxen WebServer and compares it with other common web servers. The initial setup time for the secure SSL/TLS connection was found to be very long in the Roxen Webserver compared to its competitors. The main bottleneck, in the Roxen implementation, was found to be the modular exponentiation that is the core of the RSA decryption algorithm. One suggested improvement is to upgrade the bignumber numerical package used in Roxen WebServer, GMP (The GNU Multiple Precision arithmetic library) from version 2.0 to version 4.0. The newer version of the bignumber package have been measured to have considerably better performance in its modular exponentation operation.</p>