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.

Governing depression in law students and the shaping of legal personae

Since a recent Australian study found that university law students experience higher rates of depression than medical students and legal professionals (Kelk et al. 2009), the mental health of law students has increasingly become a target of government. To date, however, there has been no attempt to analyse these practices as an activity of government in advanced liberal societies. This paper addresses this imbalance by providing an initial analytics of the government of depression in law schools. It demonstrates how students are responsibilised to manage the risks and uncertainties of legal education by constructing resilient forms of personal and professional personae. It highlights that, in order to avoid depression, students are encouraged to shape not just their minds and bodies according to psychological and biomedical discourses, but are also to govern their ethical dispositions and become virtuous persons. This paper also argues that these forms of government are tied to advanced liberal forms of rule, as they position the law student as the locus of responsibility for depression, imply that depression is caused by an individual failing, and entrench students within responsibilising and entrepreneurial forms of subjectivity.

Managing Wetlands Sustainably as Ecosystems: The Contribution of the Law (Part 2)

In this Part 2 attention is turned towards the legal arrangements in nation states for managing wetlands. These national arrangements have effect within the international arrangements already mentioned and any regional arrangements that are relevant. However, each national system is a reflection of its own historical, cultural, political and constitutional background. It is the purpose of this Part 2 to review and assess the national approaches to wetlands management. This involves an analysis of a range of instruments. These are: constitutional rules; strategic rules; regulatory rules; and management rules. Each of these sets of rules performs different functions, assumes different forms and is differentially capable of enforcement.

Enduring documents : improving the forms, improving the outcomes

Most Australian states have introduced legislation to provide for enduring documents for financial, personal and health care decision making in the event of incapacity. Since the introduction of Enduring Powers of Attorney (EPAs) and Advance Health Directives (AHDs) in Queensland in 1998, concerns have continued to be raised by service providers, professionals and individuals about the uptake, understanding and appropriate use of these documents. In response to these concerns, the Department of Justice and Attorney-General (DJAG) convened a Practical Guardianship Initiatives Working Party. This group identified the limited evidence base available to address these concerns. In 2009, a multidisciplinary research team from the University of Queensland and the Queensland University of Technology was awarded $90,000 from the Legal Practitioners Interest on Trust Account Fund to undertake a review of the current EPA and AHD forms. The goal of the research was to gather data on the content and useability of the forms from the perspectives of a range of stakeholders, particularly those completing the EPA and AHD, witnesses of these documents, attorneys appointed under an EPA, and health professionals involved in the completion of an AHD or dealing with it in a clinical context. The researchers also sought to gather information from the perspective of Aboriginal and Torres Strait Islander (ATSI) individuals as well people from culturally and linguistically diverse (CALD) groups. Although the focus of the research was on the forms and the extent to which the current design, content and format represents a barrier to uptake, in the course of the research, some broader issues were identified which have an impact on the effectiveness of the EPA and AHD in achieving the goals of planning for financial and personal and health care in advance of losing capacity. The data gathered enabled the researchers to achieve the primary goal of the research: to make recommendations to improve the content and useability of the forms which hopefully will lead to an increased uptake and appropriate use of the forms. However, the researchers thought it was important not to ignore broader policy issues that were identified in the course of the research. These broader issues have been highlighted in this Report, and the researchers have responded to them in a variety of ways. For some issues, the researchers have suggested alterations that could be made to the forms to address the particular concerns. For other issues, the researchers have suggested that Government may need to take specific action such as educating the broader community with some attention to strategies that engage particular groups within communities. Other concerns raised can only be dealt with by legislative reform and, in some of these cases, the researchers have identified issues that Government may wish to consider further. We do note, however, that it is beyond the scope of this Report to recommend changes to the law. This three stage mixed methods project aimed to provide systematic evidence from a broad range of stakeholders in regard to: (i) which groups use and do not use these documents and why, (ii) the contribution of the length/complexity/format/language of the forms as barriers to their completion and/or effective use, and (iii) the issues raised by the current documents for witnesses and attorneys. Understanding and use of EPAs and AHDs were generally explored in separate but parallel processes. A purposive sampling strategy included users of the documents as principals and attorneys, and professionals, witnesses and service providers who assist others to execute or use the forms. The first component of this study built on existing knowledge using a Critical Reference Group and material provided by the DJAG Practical Guardianship Initiatives Working Party. This assisted in the development of the data collection tools for subsequent stages. The second component comprised semi-structured interviews and focus groups with a targeted sample of current users of the forms, potential users, witnesses and other professionals to provide in-depth information on critical issues. Outreach to Aboriginal and Torres Strait Islander Elders and individuals and workers with CALD groups ensured a broad sample of potential users of the two documents. Fifty individual interviews and three focus groups were completed. Most interviews and focus groups focused on perceptions of, and experiences with, either the EPA or the AHD form. In the interviews with Indigenous people and the CALD focus groups, however, respondents provided their perceptions and experiences of both documents. In general, these respondents had not used the forms and were responding to the documents made available in the interview or focus group. In total, seventy-seven individuals were involved in interviews or focus groups. The final component comprised on-line surveys for EPA principals, EPA attorneys, AHD principals, witnesses of EPAs and AHDs and medical practitioners with experience of AHDs as nominated and/or treating doctors. The surveys were developed from the initial component and the qualitative analysis of the interview and focus group data. A total of 116 surveys were returned from major cities and regional Queensland. The survey data was analysed descriptively for patterns and trends. It is important to note that the aim of the survey was to gain insight into issues and concerns relating to the documents and not to make generalisations to the broader population.

Knowledge management in law enforcement : knowledge views for patrolling police officers

This paper describes and classifies different types of knowledge that are a part of police patrol officer's practice. Even though an investigation usually forces a police officer to apply several different knowledge types, this paper discusses different forms of professional knowledge separately to enable categorisation.

Vulnerability : an issue for law and policy in pandemic planning?

The 2009 H!Nl 'swine flu' pandemic was the first influenza pandemic of the twenty-first centmy. Unlike the first influenza pandemic of the twentieth century, the so-called 'Spanish flu' which killed millions of people worldwide, the 2009 pandemic was relatively mild. While the mildness of the 2009 pandemic meant that the 'Yorld was spared from the impact of a high-mortality event that would cause widespread social and economic disruption, the 2009 pandemic did provide an opportunity to road-test pandemic readiness. In other work we have assessed Australia's pandemic plans and emergency management legislation, finding that both provide flexible and adaptive forms of regulation that are capable of adapting to the scale and severity of a pandemic or other public health emergency. 1 In this chapter we consider whether pandemic planning adequately addresses the needs of vulnerable individuals and groups, both within countries and between them. Central to this is the question of whether vulnerability is itself a useful concept for both law and policy, and if so, the implications of expressly incorporating the concept of vulnerability into pandemic planning.

Using law to identify, manage and prevent child maltreatment

This chapter identifies ways in which laws are capable of responding to child maltreatment, both as an immediate regulator of conduct, and as an influence on a society’s cultural development and approach to children’s welfare. Informed by practices and experiences in selected common law systems, the chapter provides examples of legal mechanisms that can inform discussion of optimal strategies to identify and manage child maltreatment in many different societies. Both positive and negative aspects of these mechanisms are noted. While controversies arise as to what kinds of laws are best in preventing and responding to child maltreatment, and even, more fundamentally, whether there is a role for law in protecting children, this chapter offers evidence that a variety of legal tools can be employed to address child abuse and neglect, for any cultural setting in which there is willingness to act to prevent and treat its various forms.

An elegy for Greg Ham: Copyright law, the Kookaburra case, and remix culture

The ‘Kookaburra’ case was a tragic and controversial copyright dispute, highlighting the need for copyright law reform by the Australian Parliament. In the Kookaburra case, a copyright action was brought by Larrikin Records against Men at Work’s song ‘Down Under’, alleging copyright infringement of the ‘Kookaburra’ song composed by Marion Sinclair. The dispute raised a host of doctrinal matters. There was disquiet over the length of the copyright term. There were fierce contests as to the copyright ownership of the ‘Kookaburra’ song. The litigation raised questions about copyright infringement and substantiality – particularly in relation to musical works. The ‘Kookaburra’ case highlighted frailties in Australia’s regime of copyright exceptions. The litigation should spur the Australian Law Reform Commission to make recommendations for law reform in its inquiry Copyright and the Digital Economy. This article provides a critical evaluation of the options of a defence for transformative use; a defence for fair use; and statutory licensing. The ‘Kookaburra’ case also examines the question of appropriate remedies in respect of copyright infringement. The conclusion considers the implications of the Kookaburra case for other forms of musical works – including digital sampling, mash-ups, and creative remixes. It finishes with an elegy for Greg Ham – paying tribute to the multi-instrumentalist for Men at Work.

Incentives for global public health: Patent law and access to essential medicines

This portrait of the global debate over patent law and access to essential medicines focuses on public health concerns about HIV/AIDS, malaria, tuberculosis, the SARS virus, influenza, and diseases of poverty. The essays explore the diplomatic negotiations and disputes in key international fora, such as the World Trade Organization, the World Health Organization and the World Intellectual Property Organization. Drawing upon international trade law, innovation policy, intellectual property law, health law, human rights and philosophy, the authors seek to canvass policy solutions which encourage and reward worthwhile pharmaceutical innovation while ensuring affordable access to advanced medicines. A number of creative policy options are critically assessed, including the development of a Health Impact Fund, prizes for medical innovation, the use of patent pools, open-source drug development and forms of 'creative capitalism'.

Australian Media Law [5th Edition]

Australian Media Law details and explains the complex case law, legislation and regulations governing media practice in areas as diverse as journalism, advertising, multimedia and broadcasting. It examines the issues affecting traditional forms of media such as television, radio, film and newspapers as well as for recent forms such as the internet, online forums and digital technology, in a clear and accessible format. New additions to the fifth edition include: - the implications of new anti-terrorism legislation for journalists; - developments in privacy law, including Law Reform recommendations for a statutory cause of action to protect personal privacy in Australia and the expanding privacy jurisprudence in the United Kingdom and New Zealand; - liability for defamation of internet search engines and service providers; - the High Court decision in Roadshow v iiNet and the position of internet service providers in relation to copyright infringement via their services; - new suppression order regimes; - statutory reforms providing journalists with a rebuttable presumption of non-disclosure when called upon to reveal their sources in a court of law; - recent developments regarding whether journalists can use electronic devices to collect and disseminate information about court proceedings; - contempt committed by jurors via social media; and an examination of recent decisions on defamation, confidentiality, vilification, copyright and contempt.