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.

From the cathedral to the classroom : the emergence of new discourses on religious education

In 2009, Religious Education is a designated key learning area in Catholic schools in the Archdiocese of Brisbane and, indeed, across Australia. Over the years, though, different conceptualisations of the nature and purpose of religious education have led to the construction of different approaches to the classroom teaching of religion. By investigating the development of religious education policy in the Archdiocese of Brisbane from 1984 to 2003, the study seeks to trace the emergence of new discourses on religious education. The study understands religious education to refer to a lifelong process that occurs through a variety of forms (Moran, 1989). In Catholic schools, it refers both to co-curricula activities, such as retreats and school liturgies, and the classroom teaching of religion. It is the policy framework for the classroom teaching of religion that this study explores. The research was undertaken using a policy case study approach to gain a detailed understanding of how new conceptualisations of religious education emerged at a particular site of policy production, in this case, the Archdiocese of Brisbane. The study draws upon Yeatman’s (1998) description of policy as occurring “when social actors think about what they are doing and why in relation to different and alternative possible futures” (p. 19) and views policy as consisting of more than texts themselves. Policy texts result from struggles over meaning (Taylor, 2004) in which specific discourses are mobilised to support particular views. The study has a particular interest in the analysis of Brisbane religious education policy texts, the discursive practices that surrounded them, and the contexts in which they arose. Policy texts are conceptualised in the study as representing “temporary settlements” (Gale, 1999). Such settlements are asymmetrical, temporary and dependent on context: asymmetrical in that dominant actors are favoured; temporary because dominant actors are always under challenge by other actors in the policy arena; and context - dependent because new situations require new settlements. To investigate the official policy documents, the study used Critical Discourse Analysis (hereafter referred to as CDA) as a research tool that affords the opportunity for researchers to map and chart the emergence of new discourses within the policy arena. As developed by Fairclough (2001), CDA is a three-dimensional application of critical analysis to language. In the Brisbane religious education arena, policy texts formed a genre chain (Fairclough, 2004; Taylor, 2004) which was a focus of the study. There are two features of texts that form genre chains: texts are systematically linked to one another; and, systematic relations of recontextualisation exist between the texts. Fairclough’s (2005) concepts of “imaginary space” and “frameworks for action” (p. 65) within the policy arena were applied to the Brisbane policy arena to investigate the relationship between policy statements and subsequent guidelines documents. Five key findings emerged from the study. First, application of CDA to policy documents revealed that a fundamental reconceptualisation of the nature and purpose of classroom religious education in Catholic schools occurred in the Brisbane policy arena over the last twenty-five years. Second, a disjuncture existed between catechetical discourses that continued to shape religious education policy statements, and educational discourses that increasingly shaped guidelines documents. Third, recontextualisation between policy documents was evident and dependent on the particular context in which religious education occurred. Fourth, at subsequent links in the chain, actors created their own “imaginary space”, thereby altering orders of discourse within the policy arena, with different actors being either foregrounded or marginalised. Fifth, intertextuality was more evident in the later links in the genre chain (i.e. 1994 policy statement and 1997 guidelines document) than in earlier documents. On the basis of the findings of the study, six recommendations are made. First, the institutional Church should carefully consider the contribution that the Catholic school can make to the overall pastoral mission of the diocese in twenty-first century Australia. Second, policymakers should articulate a nuanced understanding of the relationship between catechesis and education with regard to the religion classroom. Third, there should be greater awareness of the connections among policies relating to Catholic schools – especially the connection between enrolment policy and religious education policy. Fourth, there should be greater consistency between policy documents. Fifth, policy documents should be helpful for those to whom they are directed (i.e. Catholic schools, teachers). Sixth, “imaginary space” (Fairclough, 2005) in policy documents needs to be constructed in a way that allows for multiple “frameworks for action” (Fairclough, 2005) through recontextualisation. The findings of this study are significant in a number of ways. For religious educators, the study highlights the need to develop a shared understanding of the nature and purpose of classroom religious education. It argues that this understanding must take into account the multifaith nature of Australian society and the changing social composition of Catholic schools themselves. Greater recognition should be given to the contribution that religious studies courses such as Study of Religion make to the overall religious development of a person. In view of the social composition of Catholic schools, there is also an issue of ecclesiological significance concerning the conceptualisation of the relationship between the institutional Catholic Church and Catholic schools. Finally, the study is of significance because of its application of CDA to religious education policy documents. Use of CDA reveals the foregrounding, marginalising, or excluding of various actors in the policy arena.

The lived experience of families living with spinal cord disability in Northeast Thailand

The experience of disability in the global South remains relatively underreported in spite of the greater focus on disability as both an impediment to development and frequently as a result of development. This article reports a qualitative study using ethnographic techniques undertaken in the province of Khon Kaen in Northeast Thailand. The primary participants were men who had experienced a severe spinal cord injury at a time when they were breadwinners, a role which is significant in the context of a modernising state that is an active participant in a global economy. The experiences, constructions and beliefs of these men, their family carers, and other informants illustrate the complex ways in which social and cultural factors interact with the opportunities, challenges and constraints of transition to modernity. The findings, interpreted according to the 'three bodies' approach, illustrate the intersection of colonising effects, governmentality and resistance, and embodied experience in a cultural context.

Narratives for novices : is there a place for edgy texts in edgy NAPLAN communities?

The genre of narratives has become the genre of choice in many classrooms since the introduction of NAPLAN into Australian schools. Yet, Knapp and Watkins (2005) argue that narratives are the least understood of all the genres. Despite wide-spread acceptance that narratives serve the social purpose of entertaining, they can also be more edgy, offering a powerful social or information role. This paper considers the effects of exposing novices to less standard realms of social discourse and disciplinary knowledge vis-a-vis a more clinical treatment focused on ‘standard’ narratives. I argue that we should not shy away from the challenges of edgy narratives just because our students are novice readers. The same holds true for our work in communities on the edge, that is where poverty, multiculturalism or multilingualism and systemic failure are the norm. I am part of an Australian Research Council (ARC) Linkage Grant (LP 0990289) working in such a community. Like many such situations, teachers in these communities are caught in the fray of establishing a dialogue between the culture of federally mandated performance orientated reforms and the cultures and discourses of the lives and future needs of their students (see Exley & Singh, in press).

Genres of editorial photographs and patterns of photographic practice

Taking an 'action genre' approach (Lemke, 199**) this paper analyses representational strategies of three genres of photography: press photography, photojournalism and documentary photography. While there has been much written on editorial photography, there is no organised body of scholarship that distinguishes between these three very different modes of of editorial photography.

AIDS and pro-social television : industry, policy and Australian television drama

This thesis examines the intersection of popular cultural representations of HIV and AIDS and the discourses of public health campaigns. Part Two provides a comprehensive record of all HIV related storylines in Australian television drama from the first AIDS episode of The Flying Doctors in 1986 to the ongoing narrative of Pacific Drive, with its core HIV character, in 1996. Textual representations are examined alongside the agency of "cultural technicians" working within the television industry. The framework for this analysis is established in Part One of the thesis, which examines the discursive contexts for speaking about HIV and AIDS established through national health policy and the regulatory and industry framework for broadcasting in Australia. The thesis examines the dominant liberal democratic framework for representation of HIV I AIDS and adopts a Foucauldian understanding of the processes of governmentality to argue that during the period of the 1980s and 1990s a strand of social democratic discourse combined with practices of self management and the management of the Australian population. The actions of committed agents within both domains of popular culture and health education ensured that more challenging expressions of HIV found their way into public culture.

The candidate : a novella and examination of Australian Gothic crime fiction

Australia is a land without haunted castles or subterranean corridors, without ancient graveyards or decaying monasteries, a land whose climate is rarely gloomy. Yet, the literary landscape is splattered with shades of the Gothic genre. This Gothic heritage is especially evident within elements of nineteenth century Australian sensation fiction. Australian crime fiction in the twentieth century, in keeping with this lineage, repeatedly employs elements of the Gothic, adapting and appropriating these conventions for literary effect. I believe that a ‘mélange’ of historical Gothic crime traditions could produce an exciting new mode of Gothic crime writing in the Australian context. As such, I have written a contemporary literary experiment in a Gothic crime ‘hybrid’ style: this novella forms my creative practice. The accompanying exegesis is a critical study of a selection of Australian literary works that exhibit the characteristics of both Gothic and crime genres. Through an analysis of these creative works, this study argues that the interlacing of Gothic traditions with crime writing conventions has been a noteworthy practice in Australian fiction during both the nineteenth and twentieth centuries and these literary tropes are interwoven in the writing of ‘The Candidate’, a Gothic crime novella.

Validation of FHWA crash models for rural intersections - Lessons learned

A national-level safety analysis tool is needed to complement existing analytical tools for assessment of the safety impacts of roadway design alternatives. FHWA has sponsored the development of the Interactive Highway Safety Design Model (IHSDM), which is roadway design and redesign software that estimates the safety effects of alternative designs. Considering the importance of IHSDM in shaping the future of safety-related transportation investment decisions, FHWA justifiably sponsored research with the sole intent of independently validating some of the statistical models and algorithms in IHSDM. Statistical model validation aims to accomplish many important tasks, including (a) assessment of the logical defensibility of proposed models, (b) assessment of the transferability of models over future time periods and across different geographic locations, and (c) identification of areas in which future model improvements should be made. These three activities are reported for five proposed types of rural intersection crash prediction models. The internal validation of the model revealed that the crash models potentially suffer from omitted variables that affect safety, site selection and countermeasure selection bias, poorly measured and surrogate variables, and misspecification of model functional forms. The external validation indicated the inability of models to perform on par with model estimation performance. Recommendations for improving the state of the practice from this research include the systematic conduct of carefully designed before-and-after studies, improvements in data standardization and collection practices, and the development of analytical methods to combine the results of before-and-after studies with cross-sectional studies in a meaningful and useful way.

Gemma Smith and the intuitive abstract

This article examines the work of Brisbane artist Gemma Smith. It investigates the artist's career and her developmental abstract paintings and sculptures. It argues that the artist is fundamentally intuitive in her approach to the genre and also employs mimicry of certain abstract styles as a means through which to develop her own creative outcomes.

Lift@Weimar : sustainable interaction with food, technology, and the city (Workshop)

This workshop explores innovative approaches to understanding and cultivating sustainable food culture in urban environments via human-computer-interaction (HCI) design and ubiquitous technologies. We perceive the city as an intersecting network of people, place, and technology in constant transformation. Our 2009 OZCHI workshop, Hungry 24/7? HCI Design for Sustainable Food Culture, opened a new space for discussion on this intersection amongst researchers and practitioners from diverse backgrounds including academia, government, industry, and non-for-profit organisations. Building on the past success, this new instalment of the workshop series takes a more refined view on mobile human-food interaction and the role of interactive media in engaging citizens to cultivate more sustainable everyday human-food interactions on the go. Interactive media in this sense is distributed, pervasive, and embedded in the city as a network. The workshop addresses environmental, health, and social domains of sustainability by bringing together insights across disciplines to discuss conceptual and design approaches in orchestrating mobility and interaction of people and food in the city as a network of people, place, technology, and food.

Important omitted spatial variables in safety models: Understanding contributing crash causes at intersections

Advances in safety research—trying to improve the collective understanding of motor vehicle crash causation—rests upon the pursuit of numerous lines of inquiry. The research community has focused on analytical methods development (negative binomial specifications, simultaneous equations, etc.), on better experimental designs (before-after studies, comparison sites, etc.), on improving exposure measures, and on model specification improvements (additive terms, non-linear relations, etc.). One might think of different lines of inquiry in terms of ‘low lying fruit’—areas of inquiry that might provide significant improvements in understanding crash causation. It is the contention of this research that omitted variable bias caused by the exclusion of important variables is an important line of inquiry in safety research. In particular, spatially related variables are often difficult to collect and omitted from crash models—but offer significant ability to better understand contributing factors to crashes. This study—believed to represent a unique contribution to the safety literature—develops and examines the role of a sizeable set of spatial variables in intersection crash occurrence. In addition to commonly considered traffic and geometric variables, examined spatial factors include local influences of weather, sun glare, proximity to drinking establishments, and proximity to schools. The results indicate that inclusion of these factors results in significant improvement in model explanatory power, and the results also generally agree with expectation. The research illuminates the importance of spatial variables in safety research and also the negative consequences of their omissions.

The impact of red light cameras on safety in Arizona

Red light cameras (RLCs) have been used in a number of US cities to yield a demonstrable reduction in red light violations; however, evaluating their impact on safety (crashes) has been relatively more difficult. Accurately estimating the safety impacts of RLCs is challenging for several reasons. First, many safety related factors are uncontrolled and/or confounded during the periods of observation. Second, “spillover” effects caused by drivers reacting to non-RLC equipped intersections and approaches can make the selection of comparison sites difficult. Third, sites selected for RLC installation may not be selected randomly, and as a result may suffer from the regression to the mean bias. Finally, crash severity and resulting costs need to be considered in order to fully understand the safety impacts of RLCs. Recognizing these challenges, a study was conducted to estimate the safety impacts of RLCs on traffic crashes at signalized intersections in the cities of Phoenix and Scottsdale, Arizona. Twenty-four RLC equipped intersections in both cities are examined in detail and conclusions are drawn. Four different evaluation methodologies were employed to cope with the technical challenges described in this paper and to assess the sensitivity of results based on analytical assumptions. The evaluation results indicated that both Phoenix and Scottsdale are operating cost-effective installations of RLCs: however, the variability in RLC effectiveness within jurisdictions is larger in Phoenix. Consistent with findings in other regions, angle and left-turn crashes are reduced in general, while rear-end crashes tend to increase as a result of RLCs.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites