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.

Transitions

Transitions represents a selection of works presented by 3rd year QUT design students undertaken as part of their coursework entitled "Environments in Transitions". The work focuses upon the migration of ideas and aesthetics from East to West, with particular consideration for the influence of Japanese woodblock prints, Wabi-Sabi themes and decorative motifs upon European design during the turn of the 19th century. The works exhibited included design artifacts of various themes, and associated print work which informed the design process. A small exhibition publication accompanied the exhibition and talk.

Dark humour invigorates familiar fables ; a review

THEATRE: Grimm Tales. By Carol Ann Duffy and Tim Supple. Queensland Theatre Company, Brisbane. November 16. QUEENSLAND Theatre Company concludes its season with Grimm Tales, Carol Ann Duffy and Tim Supple's adaptation of classic cautionary tales as set down by the Brothers Grimm in the 19th century. This programming decision is clearly designed to present fun family entertainment as Christmas approaches. In Grimm Tales, well-known stories such as Hansel and Gretel, Snow White and Rumpelstiltskin pack a little more punch than in your standard picture book. Duffy and Supple's play is by no means the sort of poetic, postmodern or politicised adaptation of the fairytale we see from writers such as Angela Carter, and it is not intended to be subversive or to question the social and gender assumptions that underpin the tales. Start of sidebar. Skip to end of sidebar. End of sidebar. Return to start of sidebar. Rather, a return to the grislier original incarnations of the tales - the wicked stepsisters who lop off parts of their feet to fit the slipper and win the prince, or the hare so confused by the hedgehog's stratagem to make him think he is losing the race, he runs himself to death - has a comic effect. In this production, directed by Michael Futcher, heightened performances from some of Brisbane's best comic and physical actors, live music and an open, acknowledged relationship with the audience establish the atmosphere for the piece. While the production is a little sombre and slow to start with the first tale, Hansel and Gretel, the knowingness and almost slapstick quality with which the cast plays out the gruesome, scatological or silly moments in the other tales are well pitched to carry the comedy. The action is supported by a fantastic set by Greg Clarke of wooden planked walls, stairs and walkways which, with the help of David Walter's lighting design, is transformed into forests, ballrooms and castles as the cast moves up, over and under it. The overall highlight is probably the cast Futcher has brought together. Established QTC actors Eugene Gilfedder, Lucas Stibbard and Scott Witt, and emerging QTC actor Melanie Zanetti, join Liz Buchanan, Dan Crestani and Emma Pursey, all well known for their independent work in Brisbane but making their mainstage debut for the QTC. Every one of them metamorphoses with ease from character to character, human to animal, and central player to support. There is nothing particularly new in Grimm Tales, and it doesn't try to do anything more (or, indeed, less) than entertain, but skilful direction and a strong cast ensure it succeeds on those terms.

ICT for blended learning Queensland University of Technology, Australia

This report focuses on blended learning within the Queensland University of Technology (QUT) which is one of Australia’s largest public universities. Although the university in its current format was established in 1989, it contains several previous institutions that can be traced to the earliest forms of technical and teacher education in Queensland in the 19th century (Kyle et al., 1999). The focal point of the report is the experience of QUT’s Faculty of Education which was formed from the amalgamation of several teacher training colleges servicing pre-school and kindergarten, primary and secondary teacher education. While the broader university currently employs approximately 4,000 staff and has about 40,000 students, QUT’s Faculty of Education employs around 170 staff and has approximately 5,000 enrolled students. The Faculty of Education at QUT is the largest provider of pre-service teacher education in Australia and is one of the largest producers of educational research. A major theme of the Faculty of Education is its focus on education and research that provides teachers, schools and educational authorities with practical solutions to the multifaceted issues facing contemporary education.

Revolutionary self portrait

'Revolutionary Self Portrait' (2009) is a sculptural self-portrait. The work comprises a bust engulfed in hair and a scalloped pedestal stand. Historically, divine energy has frequently been depicted using fluid forms - drapery, clouds and occasionally hair. These forms and associations act as a departure point for this sculpture in which the figure is depicted in a state of inundation by billowing tufts hair. The work was also inspired by the tendency of great 19th century utopian thinkers - for example Marx, Bakunin and Kropotkin - to wear large beards. Within both traditions, the language of heroic subjectivity is amplified by a sculptural extension of the body. In 'Revolutionary Self Portrait' however, this extension threatens to suffocate the subject - a gesture made all the more ironic due to the fact that the artist himself is incapable of growing a beard. The work was selected for the National Artists' Self Portrait Prize, University of Queensland Art Museum, 2009.

Children and the environment

Children and the environment cover a broad, interdisciplinary field of research and practice. The social sciences often use the word “environment” to mean the social, political, or economic context of children’s lives, but this bibliography covers physical settings. It focuses on a place-based scale that children can see, hear, taste, smell, touch, and navigate: not large, abstract scales such as national identities or population dynamics, or small scales such as environmental impacts on genes or cell functions. Attention to the everyday settings of children’s lives grew in the 18th century, when Romantic literature introduced the theme of children and nature. In the 19th century, concern for children’s welfare included an interest in conditions for children in burgeoning industrial cities, and justifications for early streetcar and railroad suburbs included claims that they would save children from the dangers of cities and provide the healthful benefits of natural surroundings. In the 20th century, academic disciplines developed different lines of inquiry about the impact of the physical environment on children and how children relate to places: ethnographic studies of children in different parts of the world in the fields of anthropology and geography; sociological studies of different populations of children in different settings; educational research on the learning opportunities that different school and out-of-school settings afford; medical research to understand disease vectors and the impact of pollutants on children; and efforts in the field of environment and behavior research more broadly, to understand how built and designed environments affect children physically, cognitively, socially, and emotionally. At the beginning of the 21st century, children and the environment is an active area of inquiry seeking to understand rapidly changing conditions for children as the world urbanizes, opportunities for free play outdoors and independent mobility erode in many parts of the world, media environments consume more of children’s time, and awareness grows that children need opportunities to contribute to creating sustainable societies.

Stage brothers slow to resurrect a Ned Kelly myth

JUST like the man, Ned Kelly dramas have had a chequered history. A century ago they were banned from the stage and screen. Following censorship law changes, Douglas Stewart's 4 1/2-hour long 1942 radio play was a hit on the airwaves but a flop onstage. Stewart's Ned was a menacing hero/villain. Little has been seen of Ned in mainstage plays since. Matthew Ryan's Kelly breaks the drought.

Dichotomy in the design studio : adapting to new blended learning environments

Since the architectural design studio learning environment was first established in the early 19th century at the École des Beaux-Arts in Paris, there has been a complete transformation in how the discipline of architecture is practiced and how students of architecture acquire information. Digital technologies allow students to access information instantly and learning is no longer confined to the rigid boundaries of a physical campus environment. In many schools of architecture in Australia, the physical design studio learning environments however, remain largely unchanged. Many learning environments could be mistaken for those last refurbished 30 years ago, being devoid of any significant technological intervention. While some teaching staff are eagerly embracing new digital technologies and attempting to modify their pedagogical approaches, the physical design studio learning environment is resistant to such efforts. In a study aimed at better understanding how staff and students adapt to new blended learning environments, a group of 165 second year architecture students at a large school of architecture in Australia were separated into two different design studio learning environments. 70% of students were allocated to a traditional design studio setting and 30% to a new, high technology embedded, prototype digital learning laboratory. The digital learning laboratory was purpose designed for the case-study users, adapted Student-Centred Active Learning Environment for Undergraduate Programs [SCALE-UP] principles, and built as part of a larger university research project. The architecture students attended the same lectures, followed the same studio curriculum and completed the same pieces of assessment; the only major differences were the teaching staff and physical environment within which the studios were conducted. At the end of the semester, all staff and students were asked to complete a questionnaire about their experiences and preferences within the two respective learning environments. The questionnaire response rate represented the opinions of 100% of the 10 teaching staff and over 70% of the students. Using a qualitative grounded theory approach, data were coded, extrapolated and compared, to reveal emerging key themes. The key themes formed the basis for in-depth interviews and focus groups of teaching staff and students, allowing the researchers to understand the data in more detail. The results of the data verified what had become increasingly evident during the course of the semester: an underlying negative resistance to the new digital studio learning environment, by both staff and students. Many participants openly exhibited a yearning for a return to the traditional design studio learning environments, particularly when the new technology caused frustration, by being unreliable or failing altogether. This paper reports on the study, discusses the negative resistance and explores the major contributors to resistance. The researchers are not aware of any similar previous studies across these particular settings and believe that it offers a necessary and important contribution to emergent research about adaptation to new digital learning environments.

Public policy, disaster risk management and climate change adaptation

Public policymakers are caught in a dilemma : there is a growing list of urgent issues to address, at the same time that public expenditure is being cut. Adding to this dilemma is a system of government designed in the 19th century and competing theories of policymaking dating back to the 1950s. The interlinked problems of disaster risk management and climate change adaptation are cases in point. As the climate changes, there will be more frequent, intense and/or prolonged disasters such as floods and bushfires. Clearly a well integrated whole of government response is needed, but how might this be achieved? Further, how could academic research contribute to resolving this dilemma in a way that would produce something of theoretical interest as well as practical outcomes for policymakers? These are the questions addressed by our research via a comparative analysis of the 2009 Victorian bushfires, the 2011 Perth Hills bushfires, and the 2011 Brisbane floods. Our findings suggest that there is a need to: improve community engagement and communication; refocus attention on resilience; improve interagency communication and collaboration; and, develop institutional arrangements that support continual improvement and policy learning. These findings have implications for all areas of public policy theory and practice.

Work health and safety and the criminal law in Australia

This paper analyses recent Australian debates about the use of the criminal law in work health and safety regulation. It argues that these debates have to be seen in the context of the historical development of work health and safety regulation in the United Kingdom and Australia. The first part of the paper shows that, since the late 19th century, contraventions against the Australian work health and safety statutes have not been regarded as 'really criminal', and have largely been addressed by informal measures and, since the 1980s, by administrative sanctions. When prosecutions have taken place, work health and safety issues have been individualised and decontextualised, so that defendants have been able to reduce their culpability in the eyes of the court. Significant legal barriers have undermined the use of the crime of gross negligence manslaughter against corporations and individuals. The second part of the paper analyses recent debates about restructuring gross negligence manslaughter and bolstering the 'criminality' of offences under the work health and safety statutes. It argues that the latter debate has been constrained by the historical forces examined in the first part of the paper, and that the current position, embodied in the recently harmonised Work Health and Safety Acts, favours attempting to recriminalise the work health and safety legislation. The debate about reforming gross negligence manslaughter has stalled.

Raewyn Connell: Hegemonic Masculinities and Men’s Health

This handbook offers a new perspective on the sociology of health, illness and medicine by stressing the importance of social theory, and giving due attention to theorists often overlooked in the healthcare field including Harriet Martineau and Raewyn Connell, as well as more widely known theorists such as Michel Foucault and Max Weber. This is a compendium of both male and female social theorists from the turn of the 19th century to the present day. Leading international sociologists from Europe, America, Britain, Australia, New Zealand and Canada investigate the key concepts and theories of a single theorist, looking at the way their ideas such as medicalisation, reflexivity, capitalism, hegemonic masculinity, the biomedical model and social stigma can be used to understand specific health issues including men's health, Indigenous health, disability, the health professions and chronic illness.

Epistemological lens : birth, death and ecology of documentary practices

This paper considers the epistemological life cycle of the camera lens in documentary practices. The 19th century industrial economies that manufactured and commercialised the camera lens have engendered political and economic contingencies on documentary practices to sustain a hegemonic and singular interpretive epistemology. Colonial documentary practices are considered from the viewpoint of manipulative hegemonic practices - all of which use the interpretive epistemology of the camera lens to capitalise a viewpoint which is singular and possesses the power to sustain its own status and economic privilege. I suggest that decolonising documentary practices can be nurtured in what Boaventura de Sousa Santos proposes as an 'ecology of knowledges' (Andreotti, Ahenakew, & Cooper 2011) - a way of including the epistemologies of cultures beyond the 'abyssal' (Santos), outside the limits of epistemological dominance. If an 'epistemicide' (Santos) of indigenous knowledges in the dominant limits has occurred then in an ecology of knowledges the limits become limitless and what were once invisible knowledges, come into their own ontological and epistemological being: as free agents and on their own terms. In an ecology of knowledges, ignorance and blindness may still exist but are not privileged. The decolonisation of documentary practices inevitably destabilises prevailing historicities and initiates ways for equal privilege to exist between multiple epistemologies.

Émile Durkheim and Thomas Luckmann: Religion, spirituality and mental health

This chapter examines connections between religion, spirituality and mental health. Religion and spirituality influence the way people conceive themselves, others and the world around them, as well as how they behave – and are strongly associated with numerous mental health outcomes. Religion and spirituality therefore demand the attention of those who seek a comprehensive understanding of the factors that affect mental health. Mental health professionals are increasingly being asked to consider their clients’ religious and/or spiritual beliefs when devising their treatment plans, making the study of religion and spirituality an essential area of learning for those working in the mental health field. Initial discussion in this chapter will focus on the different approaches taken by sociologists in studying mental health. Emile Durkheim, one of the founders of sociology, proposed that religion was fundamental to societal wellbeing and was the first to demonstrate a link between religion and mental health at a population level in the late 19th century. Durkheim’s classic theory of religion, together with the work of Thomas Luckmann and other contemporary social theorists who have sought to explain widespread religious change in Western countries since World War II will be examined. Two key changes during this period are the shift away from mainstream Christian religions and the widespread embracing of ‘spirituality’ as an alternative form of religious expression. In combination, the theories of Durkheim, Luckmann and other sociologists provide a platform from which to consider reasons for variations in rates of mental health problems observed in contemporary Western societies according to people’s religious/spiritual orientation. This analysis demonstrates the relevance of both classic and contemporary sociological theories to issues confronting societies in the present day.