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.

Frames of Anime: Culture and Image-Building

With the rising popularity of anime amongst animation students, audiences and scholars around the world, it has become increasingly important to critically analyse anime as being more than a ‘limited’ form of animation, and thematically as encompassing more than super robots and pocket monsters. Frames of Anime: Culture and Image-Building charts the development of Japanese animation from its indigenous roots within a native culture, through Japan’s experience of modernity and the impact of the Second World War. This text is the result of a rigorous study that recognises the heterogeneous and polymorphous background of anime. As such, Tze-Yue has adopted an ‘interdisciplinary and transnational’ (p. 7) approach to her enquiry, drawing upon face-to-face interviews, on-site visits and biographical writings of animators. Tze-Yue delineates anime from other forms of animation by linking its visual style to pre-modern Japanese art forms and demonstrating the connection it shares with an indigenous folk system of beliefs. Via the identification of traditional Japanese art forms and their visual connectedness to Japanese animation, Tze-Yue shows that the Japanese were already heavily engaged in what was destined to become anime once technology had enabled its production. Tze-Yue’s efforts to connect traditional Japanese art forms, and their artistic elements, to contemporary anime reveals that the Japanese already had a rich culture of visual storytelling that pre-dates modern animation. She identifies the Japanese form of the magic lantern at the turn of the 19th century, utsushi-e, as the pre-modern ancestor of Japanese animation, describing it as ‘Edo anime’ (p. 43). Along with utsushi-e, the Edo period also saw the woodblock print, ukiyo-e, being produced for the rising middle class (p. 32). Highlighting the ‘resurfacing’ of ‘realist’ approaches to Japanese art in ukiyo-e, Tze-Yue demonstrates the visual connection of ukiyo-e and anime in the …

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.

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.

Re-reading the reading lesson : episodes in the history of reading pedagogy

Reading pedagogy is constantly an object of discussion and debate in contemporary policy and practice but is rarely a matter for historical inquiry. This paper reports from a recent study of the history of reading pedagogy in Australia and beyond. It focuses on a recurring figure in the historical record—the ‘reading lesson’. Presented as a distinctive trope, the reading lesson is traced in its regularity in and through the discourse of reading pedagogy, starting in 1930s Australia and moving back into 19th-century Europe, and with specific reference to the UK and the USA. Teaching reading is expressly identified as a moral project—something that, it can be argued, clearly continues into the present.

The story of the men’s white shirt

The classic white dress shirt is familiar and omnipresent in men’s fashion. As a result, we tend to be unaware that for more than 200 years this singular item of apparel, which is essentially unadulterated in form from the late 19th century, has been able to define and represent status, wealth and fashion norms. The history underlying this garment is rich and, in the main part, untold.

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.

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.

Butterfly: the dark fluidity of suburban life

The American Association of Australasian Literary Studies (AAALS) Annual Conference, Forth Worth, Texas, 9–11 April 2015. The dark fluidity of Melbourne suburbia in Sonya Hartnett’s Butterfly Sonya Hartnett’s Butterfly (2009) is a fictional account of the suburban family life of the Coyles in 1980’s outer suburban Melbourne written from the perspective of teenager Plum Coyle. The Coyle family at first glance appear to be living a textbook example of the suburban lifestyle developed from the 19th century and sustained well into the twentieth century, in which housing design and gender roles were clearly defined and “connected with a normative heterosexuality” (Johnson 2000: 94). The Australian suburban space is also well documented as a place where people often have to contend with oppressive rigid social and cultural ideals (ie Rowse 1978, Johnson 1993, Turnbull 2008, and Flew 2011). There is a tendency to group “suburb” as one monolithic space but this paper will argue that Hartnett exposes the dark fluidity and the complexity of the term, just as she reveals that despite or perhaps because of the planned nature of suburbia, the lives that people live are often just as complex.

Good for the environment good for health

“First do no harm”. This phrase, attributed to the 19th century surgeon, Thomas Inman, 1 reflects an equivalent phrase found in Epidemics, Book I of the Hippocratic School, “Practise two things in your dealings with disease: either help or do not harm the patient”. Pharmacists have played, and continue to play, an important role in reducing patient harm from medication misadventures. Now, they have a new role to play. The delivery of pharmaceutical care contributes to climate change (e.g. through the embedded carbon in the manufacture and distribution of medicines, disposal of waste, and energy and water use),2 which in turn has a negative impact on health. 3,4 This paradox argues a moral and ethical obligation by pharmacists, to deliver pharmaceutical care more sustainably – do no harm. Sustainability “…. is concerned, on one hand, with resources and how we can preserve them, and, on the other hand, with waste products and how we can best reduce or dispose of them.” 5(p.37) It is about preserving and nurturing Earth’s resources and systems for this generation and future generations to enjoy. Pharmacists play an important role in preventative health strategies such as smoking cessation, promotion of healthier lifestyles and vaccination/immunisation programmes and have the potential to also play a significant role in delivering pharmaceutical care more sustainably. Sustainable pharmaceutical care may be considered a virtuous cycle - what is good for the environment is also good for our health. 5 The good news for community pharmacy owners and managers is that implementing sustainability initiatives in the pharmacy can also have significant financial co-benefits.

Gossip we can trust: Defamation law and non-fiction

Drawing on two case studies, this article considers the allegation of a disgruntled author: ’Defamation was framed to protect the reputations of 19th century gentlemen hypocrites'. The first case study considers the litigation over Bob Ellis' unreliable political memoir, ’Goodbye Jerusalem', published by Random House. The second case study focuses upon the litigation over the allegation by Media Watch that Richard Carleton had plagarised a documentary entitled ’Cry from the Grave'. The article considers the meaning of defamatory imputations, the range of defences, and the available remedies. It highlights the competing arguments over the protection of reputation and privacy, artistic expression, and the freedom of speech. This article concludes that defamation law should foster ’gossip we can trust'.