Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Thomas Young's contribution to visual optics : the Bakerian lecture "On the mechanism of the eye"

Thomas Young (1773-1829) carried out major pioneering work in many different subjects. In 1800 he gave the Bakerian Lecture of the Royal Society on the topic of the “mechanism of the eye”: this was published in the following year (Young, 1801). Young used his own design of optometer to measure refraction and accommodation, and discovered his own astigmatism. He considered the different possible origins of accommodation and confirmed that it was due to change in shape of the lens rather than to change in shape of the cornea or an increase in axial length. However, the paper also dealt with many other aspects of visual and ophthalmic optics, such as biometric parameters, peripheral refraction, longitudinal chromatic aberration, depth-of-focus and instrument myopia. These aspects of the paper have previously received little attention. We now give detailed consideration to these and other less-familiar features of Young’s work and conclude that his studies remain relevant to many of the topics which currently engage visual scientists.

An analysis of parliamentary questions raised by Opposition in the Uttar Pradesh (India) State Legislative Assembly

The use of parliamentary questions is the most popular and visible tool in the hands of the Opposition as a means to make government accountable. Their main purpose is to seek information or press for action. Contemporary parliamentary literature from the UK, Canada, and Australia, however, suggests that parliamentary questions have lost their effectiveness. The literature points out that Question Time in parliaments has become a battle ground between Ruling and Opposition parties in their fight to gain maximum political advantage. In this context, the effectiveness of parliamentary questions in the Indian state legislatures has not been investigated. The aim of this study, therefore, is to analyse the use, purpose and effectiveness of parliamentary questions in the State Legislative Assembly of Uttar Pradesh (India) to explore differences, if any, between Ruling and Opposition parties. In this study, 4023 parliamentary questions asked in the Uttar Pradesh State Legislative Assembly were analysed. The effectiveness of answers was also analysed qualitatively. The results show that half of the total members of the Assembly used this device, out of which 60% of the questions were asked by the Opposition party members. 31% of the questions from the Opposition were seeking information and 69% were pressing for action. The government provided the required information in 96% of the questions in the former category and took action in only 35% of the latter category. Furthermore, 60% of the questions raised by the Opposition were related to constituency matters and the remaining 40% were related to policy issues or public welfare. Comparing the data with the ruling party, the results indicate that the use,purpose and effectiveness of parliamentary questions were similar to that of the Opposition except some minor differences. Surprisingly, there was no evidence of any ‘Dorothy Dix’ questions. The study concludes parliamentary question is an effective device in the Indian state of Uttar Pradesh.

Early Intervention Program Final Evaluation Report

The Early Intervention Program aims to facilitate contact between children and their non-residential parent as soon as practicable after breakdown and separation of the immediate family unit. The Program is auspiced by the Sunshine Coast Family Contact Centre Association. The Program has been offered since late 2007 following receipt of a grant from the National Community Crime Prevention Program [NCCP] for Domestic Violence Prevention. This external evaluator report summarised main achievements with respect to meeting program objectives and also makes recommentations in view the of the continuation of this innovative program.

Australian ePortfolio Project–Stage 2 ePortfolio use by university students in Australia : Developing a sustainable community of practice Case studies extracted from the final project report December 2009

Fourteen sase studies extracted from the final project report - December 2009 Australian Flexible Learning Framework: E-portfolios Community of Practice (Aus) Personal learning plans and ePortfolio (Aus) RMIT University: Introducing ePortfolios (Aus) ePortfolio Practice: ALTC Exchange (Aus) Australian PebblePad User Group (APpUG) (Aus) ePortfolios in the library and information services sector (Aus) PDP and ePortfolios UK (UK) SURF NL Portfolio (Netherlands) University of Canterbury ePortfolio (NZ) AAEEBL: Association for Authentic, Experiential and Evidence-Based Learning (USA) Midlands Eportfolio Group, West Midlands(UK) EPAC: Electronic Portfolio Action and Communication (USA) Scottish Higher Education PDP Forum (UK) Centre for Recording Achievement (CRA)(UK)

Cognitive load and assembly tasks : effect of instructional formats on learning assembly procedures

The study investigated the effect on learning of four different instructional formats used to teach assembly procedures. Cognitive load and spatial information processing theories were used to generate the instructional material. The first group received a physical model to study, the second an isometric drawing, the third an isometric drawing plus a model and the fourth an orthographic drawing. Forty secondary school students were presented with the four different instructional formats and subsequently tested on an assembly task. The findings indicated that there may be evidence to argue that the model format which only required encoding of an already constructed three dimensional representation, caused less extraneous cognitive load compared to the isometric and the orthographic formats. No significant difference was found between the model and the isometric-plus-model formats on all measures because 80% of the students in the isometric-plus-model format chose to use the model format only. The model format also did not differ significantly from other groups in total time taken to complete the assembly, in number of correctly assembled pieces and in time spent on studying the tasks. However, the model group had significantly more correctly completed models and required fewer extra looks than the other groups.

A method for evaluating lean assembly process at design stage

Lean product design has the potential to reduce the overall product development time and cost and can improve the quality of a product. However, it has been found that no or little work has been carried out to provide an integrated framework of "lean design" and to quantitatively evaluate the effectiveness of lean practices/principles in product development process. This research proposed an integrated framework for lean design process and developed a dynamic decision making tool based on Methods Time Measurement (MTM) approach for assessing the impact of lean design on the assembly process. The proposed integrated lean framework demonstrates the lean processes to be followed in the product design and assembly process in order to achieve overall leanness. The decision tool consists of a central database, the lean design guidelines, and MTM analysis. Microsoft Access and C# are utilized to develop the user interface to use the MTM analysis as decision making tool. MTM based dynamic tool is capable of estimating the assembly time, costs of parts and labour of various alternatives of a design and hence is able to achieve optimum design. A case study is conducted to test and validate the functionality of the MTM Analysis as well as to verify the lean guidelines proposed for product development.

The WIL (Work Integrated Learning) report : a national scoping study [Final Report]

This report provides an account of the first large-scale scoping study of work integrated learning (WIL) in contemporary Australian higher education. The explicit aim of the project was to identify issues and map a broad and growing picture of WIL across Australia and to identify ways of improving the student learning experience in relation to WIL. The project was undertaken in response to high levels of interest in WIL, which is seen by universities both as a valid pedagogy and as a means to respond to demands by employers for work-ready graduates, and demands by students for employable knowledge and skills. Over a period of eight months of rapid data collection, 35 universities and almost 600 participants contributed to the project. Participants consistently reported the positive benefits of WIL and provided evidence of commitment and innovative practice in relation to enhancing student learning experiences. Participants provided evidence of strong partnerships between stakeholders and highlighted the importance of these relationships in facilitating effective learning outcomes for students. They also identified a range of issues and challenges that face the sector in growing WIL opportunities; these issues and challenges will shape the quality of WIL experiences. While the majority of comments focused on issues involved in ensuring quality placements, it was recognised that placements are just one way to ensure the integration of work with learning. Also, the WIL experience is highly contextualised and impacted by the expectations of students, employers, the professions, the university and government policy.

Exploiting the 1,2,3-triazolium motif in anion-templated formation of a bromide-selective rotaxane host assembly

Stimulated by the efficacy of copper (I) catalysed Huisgen-type 1,3-dipolar cycloaddition of terminal alkynes and organic azides to generate 1,4-disubstituted 1,2,3-triazole derivatives, the importance of ‘click’ chemistry in the synthesis of organic and biological molecular systems is ever increasing.[1] The mild reaction conditions have also led to this reaction gaining favour in the construction of interlocked molecular architectures.[2-4] In the majority of cases however, the triazole group simply serves as a covalent linkage with no function in the resulting organic molecular framework. More recently a renewed interest has been shown in the transition metal coordination chemistry of triazole ligands.[3, 5, 6] In addition novel aryl macrocyclic and acyclic triazole based oligomers have been shown to recognise halide anions via cooperative triazole C5-H….anion hydrogen bonds.[7] In light of this it is surprising the potential anion binding affinity of the positively charged triazolium motif has not, with one notable exception,[8] been investigated. With the objective of manipulating the unique topological cavities of mechanically bonded molecules for anion recognition purposes, we have developed general methods of using anions to template the formation of interpenetrated and interlocked structures.[9-13] Herein we report the first examples of exploiting the 1,2,3-triazolium group in the anion templated formation of pseudorotaxane and rotaxane assemblies. In an unprecedented discovery the bromide anion is shown to be a superior templating reagent to chloride in the synthesis of a novel triazolium axle containing [2]rotaxane. Furthermore the resulting rotaxane interlocked host system exhibits the rare selectivity preference for bromide over chloride...