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.

Governors highway safety associations and transportation planning: Exploratory factor analysis and structural equation modeling

The Intermodal Surface Transportation Efficiency Act (ISTEA) of 1991 mandated the consideration of safety in the regional transportation planning process. As part of National Cooperative Highway Research Program Project 8-44, "Incorporating Safety into the Transportation Planning Process," we conducted a telephone survey to assess safety-related activities and expertise at Governors Highway Safety Associations (GHSAs), and GHSA relationships with metropolitan planning organizations (MPOs) and state departments of transportation (DOTs). The survey results were combined with statewide crash data to enable exploratory modeling of the relationship between GHSA policies and programs and statewide safety. The modeling objective was to illuminate current hurdles to ISTEA implementation, so that appropriate institutional, analytical, and personnel improvements can be made. The study revealed that coordination of transportation safety across DOTs, MPOs, GHSAs, and departments of public safety is generally beneficial to the implementation of safety. In addition, better coordination is characterized by more positive and constructive attitudes toward incorporating safety into planning.

Framework for measuring corporate safety culture and its impact on construction safety performance

This paper presents the results of a structural equation model (SEM) that describes and quantifies the relationships between corporate culture and safety performance. The SEM is estimated using 196 individual questionnaire responses from three companies with better than average safety records. A multiattribute analysis of corporate safety culture characteristics resulted in a hierarchical description of corporate safety culture comprised of three major categories — people, process, and value. These three major categories were decomposed into 54 measurable questions and used to develop a questionnaire to quantify corporate safety culture. The SEM identified five latent variables that describe corporate safety culture: (1) a company’s safety commitment; (2) the safety incentives that are offered to field personal for safe performance; (3) the subcontractor involvement in the company culture; (4) the field safety accountability and dedication; and (5) the disincentives for unsafe behaviors. These characteristics of company safety culture serve as indicators for a company’s safety performance. Based on the findings from this limited sample of three companies, this paper proposes a list of practices that companies may consider to improve corporate safety culture and safety performance. A more comprehensive study based on a larger sample is recommended to corroborate the findings of this study.

Adoption Law and Practice [2nd ed.]

This book addresses the modern law relating to adoption. It comes at a time of fundamental change in adoption practice as, increasingly, Irish couples look outside the jurisdiction for the child that will make their family complete.---------- * Examines and explains the new regulatory framework and the law now governing domestic and intercountry adoption.---------- * Provides a guide to the changes outlined in the Adoption Bill 2008 which also consolidates the provisions of seven previous statutes and incorporates the Hague Convention into Irish statute law.---------- * Considers the responsibilities of the new Adoption Authority, and the roles of other administrative and legal bodies.---------- * Sets out the adoption process, explaining the complexities of intercountry adoption, giving consideration to the interface between adoption and children in care and dealing with the rights of the parties involved.

Empirical analysis of freeway traffic oscillation : its safety impact and evolution

Traffic oscillations are typical features of congested traffic flow that are characterized by recurring decelerations followed by accelerations. However, people have limited knowledge on this complex topic. In this research, 1) the impact of traffic oscillations on freeway crash occurrences has been measured using the matched case-control design. The results consistently reveal that oscillations have a more significant impact on freeway safety than the average traffic states. 2) Wavelet Transform has been adopted to locate oscillations' origins and measure their characteristics along their propagation paths using vehicle trajectory data. 3) Lane changing maneuver's impact on the immediate follower is measured and modeled. The knowledge and the new models generated from this study could provide better understanding on fundamentals of congested traffic; enable improvements to existing traffic control strategies and freeway crash countermeasures; and instigate people to develop new operational strategies with the objective of reducing the negative effects of oscillatory driving.

Legal ethics in a post-Westphalian world : building the international rule of law and otehr tasks

The emergence of strong sovereign states after the Treaty of Westphalia turned two of the most cosmopolitan professions (law and arms) into two of the least cosmopolitan. Sovereign states determined the content of the law within their borders – including which, if any, ecclesiastical law was to be applied; what form of economic regulation was adopted; and what, if any, international law applied. Similarly, states sought to ensure that all military force was at their disposal in national armies. The erosion of sovereignty in a post-Westphalian world may significantly reverse these processes. The erosion of sovereignty is likely to have profound consequences for the legal profession and the ethics of how, and for what ends, it is practised. Lawyers have played a major role in the civilization of sovereign states through the articulation and institutionalisation of key governance values – starting with the rule of law. An increasingly global profession must take on similar tasks. The same could be said of the military. This essay will review the concept of an international rule of law and its relationship to domestic conceptions and outline the task of building the international rule of law and the role that lawyers can and should play in it.

A sustainable approach to community based rehabilitation in rural and remote Australia

This paper presents a summary of an extensive review of the health, disability and rehabilitation literature conducted for the purposes of informing the formulation of a sustainable approach to community based rehabilitation in rural and remote Australia. It begins with a review of definitions of disability and rehabilitation, which is followed by differentiating 'rehabilitation in the community' and 'community based rehabilitation'. Finally, a network of community based rehabilitation coalitions is proposed as a sustainable approach to community based rehabilitation in rural and remote Australia. Each coalition would have a community rehabilitation facilitator and community specific database of resources, as well as a register of local community rehabilitation assistants who can support the work of health professionals by providing rehabilitation interventions under the latter's direction. In this approach, rehabilitation is conceptualised as being about people's lives rather than only a series of interventions provided by health care professionals. As such, rehabilitation becomes everybody's business.

Demand side response to mitigate electrical peak demand in Eastern and Southern Australia

The aim of this work is to develop a Demand-Side-Response (DSR) model, which assists electricity end-users to be engaged in mitigating peak demands on the electricity network in Eastern and Southern Australia. The proposed innovative model will comprise a technical set-up of a programmable internet relay, a router, solid state switches in addition to the suitable software to control electricity demand at user's premises. The software on appropriate multimedia tool (CD Rom) will be curtailing/shifting electric loads to the most appropriate time of the day following the implemented economic model, which is designed to be maximizing financial benefits to electricity consumers. Additionally the model is targeting a national electrical load be spread-out evenly throughout the year in order to satisfy best economic performance for electricity generation, transmission and distribution. The model is applicable in region managed by the Australian Energy Management Operator (AEMO) covering states of Eastern-, Southern-Australia and Tasmania.