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.

Health law in Australia

Health Law in Australia is the first book to deal with health law on a comprehensive national basis. In a field of law that is becoming increasingly important and where the demand for expertise is rapidly expanding, Health Law in Australia takes a logical, structured approach to an examination of the law in all Australian jurisdictions. By covering all the major areas in this diverse field of law, Health Law in Australia enhances the understanding of the discipline as a whole. Beginning with an exploration of the general principles of health law, including chapters on “Medical Negligence”, “Children and Consent”, and “Confidentiality, Privacy, and Access to Health Records”, the book goes on to consider beginning-of-life and end-of-life issues before concluding with chapters on emerging areas in health law, such as biotechnology and medical research. The contributing authors include national leaders in the field who are specialists in these areas of health law and who can therefore reveal to readers the results of their research. Health Law in Australia has been written for those with a legal background and is essential reading for undergraduate law students, postgraduate law students, researchers and scholars in the disciplines of law, health and medicine, as well as legal practitioners, government departments and bodies in the health area, and private health providers.

Health law : scope, sources and forces

• For the purposes of this chapter, “health law” encapsulates regulation of the medical and health professions, the administration of health services and the maintenance of public health to the extent that it is connected to the provision of health services. • There are diverging views as to whether health law can be regarded as a discrete “area of law”. • Health law draws on other areas of law such as tort law, criminal law and family law. It is also draws upon other disciplines, most notably medical and health ethics. • Social and economic forces have influenced the development and direction of health law, and these forces may become even more influential as the century develops. • The increasingly globalised world has implications for Australia’s health systems and raises questions and creates commitments in respect of the international community. • Technological developments, including in respect of treatment, diagnosis and information management, create ongoing challenges for health law. • Patient rights, human rights and consumerism are increasingly key drivers in the development of health law. • Health law is significant to contemporary Australian society because of the gravity of the topics that fall within its ambit, its social relevance to so many aspects of human existence and endeavour, the important role it plays in protecting the vulnerable, and the extent to which it engages with fundamental principles of justice.

Everyday life and the edges of existence : wrongs with no name or the wrong name?

Actions for wrongful life, as they have come unfortunately to be styled, encompass various types of claim. These include claims for alleged negligence after conception, those based on negligent advice or diagnosis prior to conception concerning possible effects of treatment given to the child's mother, contraception or sterilisation, or genetic disability. This distinguishes such claims from those for so called wrongful birth, which are claims by parents for the cost of raising either a healthy or a disabled child where the unplanned birth imposes costs on the parents as a result of clinical negligence. Two of the more controversial cases to have reached the High Court of Australia which are if interest to us here in the past decade are Cattanach v Melchior where the court, by a narrow majority (McHugh, Gummow, Kirby and Callinan JJ; Gleeson CJ, Hayne and Heydon dissenting) acknowledged recovery for wrongful birth. In the second joined appeals of Harriton v Stephens and Waller v James; Waller v Hoolahan the court overwhelmingly precluded a ‘wrongful life’ claim (Gleeson CJ, Gummow, Hayne, Callinan, Heydon and Crennan JJ; Kirby J dissenting). Both cases raised issues around the sanctity and value of life and the nature of harm and the assessment of damages, and this brief note affords us the opportunity to consider the way in which the ‘life as legal loss’ arguments were treated by the various judges in both cases.

Drugs, dental professionals and the law

Dentists have the privilege of possessing, administering and prescribing drugs, including highly addictive medications, to their patients. But because drugs are often vulnerable to being abused by all members of society, including dentists and their patients, and because drugs can be dangerous, they are tightly regulated in Canada by the federal and provincial/territorial governments. Regulatory and professional dental bodies also provide guidance for their members about how to best administer and prescribe drugs. This chapter outlines the regulation by federal and provincial/territorial governments in this area, examines the professional practice requirements set out by regulatory/professional bodies and the issue of drug abuse by dental professional and patients. It is important to note from the outset that governmental and professional regulations, policies and practices differ from province to province and territory to territory. This chapter aims to alert dentists to possible legal and professional issues surrounding the possession, administration and prescription of drugs. For detailed specific information about regulation, policies, ethical standards and professional practice standards in Canada or their province/ territory, dentists should contact their insurer or professional association.

Socially responsible investment in market downturns : implications for the fiduciary responsibilities of investment fund trustees

This paper investigates whether Socially Responsible Investment (SRI) is more or less sensitive to market downturns than conventional investment, and examines the legal implications for fund managers and trustees. Using a market model methodology, we find that over the past 15 years, the beta risk of SRI, both in Australia and internationally, increased more than that of conventional investment during economic downturns. This implies that companies acting as fund trustees, managed investment schemes and traditional institutional fund managers risk breaching their fiduciary or statutory duties if they go long - or remain long - in SRI funds during market downturns, unless perhaps relevant legislation is reformed. If reform is viewed as desirable, possible reforms could include explicitly overriding the common law to allow all traditional funds to invest in SRI; granting immunity to directors of trustee companies from potential personal liability under sections 197 or 588G et seq of the Corporations Act; allowing companies acting as trustees, managed investment schemes and traditional institutional fund managers and trustees to invest in SRI without triggering a substantial capital gains tax liability through trust resettlement; tax concessions for SRI (eg. introducing a 150% tax deduction or investment allowance for SRI); and allowing SRI sub-funds to obtain “deductible gift recipient” status or the equivalent from relevant taxation authorities. The research is important and original insofar as the assessment of risk in SRIs during market downturns is an area which has hitherto not been subjected to rigorous empirical investigation, despite its serious legal implications.

Safety-restraint use rate as function of law enforcement and other factors : preliminary analysis

Persistent use of safety restraints prevents deaths and reduces the severity and number of injuries resulting from motor vehicle crashes. However, safety-restraint use rates in the United States have been below those of other nations with safety-restraint enforcement laws. With a better understanding of the relationship between safety-restraint law enforcement and safety-restraint use, programs can be implemented to decrease the number of deaths and injuries resulting from motor vehicle crashes. Does safety-restraint use increase as enforcement increases? Do motorists increase their safety-restraint use in response to the general presence of law enforcement or to targeted law enforcement efforts? Does a relationship between enforcement and restraint use exist at the countywide level? A logistic regression model was estimated by using county-level safety-restraint use data and traffic citation statistics collected in 13 counties within the state of Florida in 1997. The model results suggest that safety-restraint use is positively correlated with enforcement intensity, is negatively correlated with safety-restraint enforcement coverage (in lanemiles of enforcement coverage), and is greater in urban than rural areas. The quantification of these relationships may assist Florida and other law enforcement agencies in raising safety-restraint use rates by allocating limited funds more efficiently either by allocating additional time for enforcement activities of the existing force or by increasing enforcement staff. In addition, the research supports a commonsense notion that enforcement activities do result in behavioral response.

Digital constitutionalism and the role of the rule of law in the governance of virtual communities

This project proposes a new conceptual framework for the regulation of social networks and virtual communities. By applying a model based upon the rule of law, this thesis addresses the growing tensions that revolve around the public use of private networks. This research examines the shortcomings of traditional contractual governance models and cyberlaw theory and provides a reconstituted approach that will allow public constitutional-type interests to be recognised in the interpretation and enforcement of contractual doctrine.

Encryption safe harbours and data breach notification laws

Data breach notification laws require organisations to notify affected persons or regulatory authorities when an unauthorised acquisition of personal data occurs. Most laws provide a safe harbour to this obligation if acquired data has been encrypted. There are three types of safe harbour: an exemption; a rebuttable presumption and factor-based analysis. We demonstrate, using three condition-based scenarios, that the broad formulation of most encryption safe harbours is based on the flawed assumption that encryption is the silver bullet for personal information protection. We then contend that reliance upon an encryption safe harbour should be dependent upon a rigorous and competent risk-based review that is required on a case-by-case basis. Finally, we recommend the use of both an encryption safe harbour and a notification trigger as our preferred choice for a data breach notification regulatory framework.

The mandatory notification of data breaches : issues arising for Australian and EU legal developments

Public and private sector organisations are now able to capture and utilise data on a vast scale, thus heightening the importance of adequate measures for protecting unauthorised disclosure of personal information. In this respect, data breach notification has emerged as an issue of increasing importance throughout the world. It has been the subject of law reform in the United States and in other jurisdictions. This article reviews US, Australian and EU legal developments regarding the mandatory notification of data breaches. The authors highlight areas of concern based on the extant US experience that require further consideration in Australia and in the EU.