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.

Identifying programs to reduce road trauma to A.C.T. motorcyclists

A broad range of motorcycle safety programs and systems exist in Australia and New Zealand. These vary from statewide licensing and training systems run by government licensing and transport agencies to safety programs run in small communities and by individual rider groups. While the effectiveness of licensing and training has been reviewed and recommendations for improvement have been developed (e.g. Haworth & Mulvihill, 2005), little is known about many smaller or innovative programs, and their potential to improve motorcycle safety in the ACT.

Impacts of periodic tillage on soil C stocks : a synthesis

Long-term loss of soil C stocks under conventional tillage and accrual of soil C following adoption of no-tillage have been well documented. No-tillage use is spreading, but it is common to occasionally till within a no-till regime or to regularly alternate between till and no-till practices within a rotation of different crops. Short-term studies indicate that substantial amounts of C can be lost from the soil immediately following a tillage event, but there are few field studies that have investigated the impact of infrequent tillage on soil C stocks. How much of the C sequestered under no-tillage is likely to be lost if the soil is tilled? What are the longer-term impacts of continued infrequent no-tillage? If producers are to be compensated for sequestering C in soil following adoption of conservation tillage practices, the impacts of infrequent tillage need to be quantified. A few studies have examined the short-term impacts of tillage on soil C and several have investigated the impacts of adoption of continuous no-tillage. We present: (1) results from a modeling study carried out to address these questions more broadly than the published literature allows, (2) a review of the literature examining the short-term impacts of tillage on soil C, (3) a review of published studies on the physical impacts of tillage and (4) a synthesis of these components to assess how infrequent tillage impacts soil C stocks and how changes in tillage frequency could impact soil C stocks and C sequestration. Results indicate that soil C declines significantly following even one tillage event (1-11 % of soil C lost). Longer-term losses increase as frequency of tillage increases. Model analyses indicate that cultivating and ripping are less disruptive than moldboard plowing, and soil C for those treatments average just 6% less than continuous NT compared to 27% less for CT. Most (80%) of the soil C gains of NT can be realized with NT coupled with biannual cultivating or ripping. (C) 2007 Elsevier B.V. All rights reserved.

Stabilization mechanisms of soil organic matter: Implications for C-saturation of soils

The relationship between soil structure and the ability of soil to stabilize soil organic matter (SOM) is a key element in soil C dynamics that has either been overlooked or treated in a cursory fashion when developing SOM models. The purpose of this paper is to review current knowledge of SOM dynamics within the framework of a newly proposed soil C saturation concept. Initially, we distinguish SOM that is protected against decomposition by various mechanisms from that which is not protected from decomposition. Methods of quantification and characteristics of three SOM pools defined as protected are discussed. Soil organic matter can be: (1) physically stabilized, or protected from decomposition, through microaggregation, or (2) intimate association with silt and clay particles, and (3) can be biochemically stabilized through the formation of recalcitrant SOM compounds. In addition to behavior of each SOM pool, we discuss implications of changes in land management on processes by which SOM compounds undergo protection and release. The characteristics and responses to changes in land use or land management are described for the light fraction (LF) and particulate organic matter (POM). We defined the LF and POM not occluded within microaggregates (53-250 mum sized aggregates as unprotected. Our conclusions are illustrated in a new conceptual SOM model that differs from most SOM models in that the model state variables are measurable SOM pools. We suggest that physicochemical characteristics inherent to soils define the maximum protective capacity of these pools, which limits increases in SOM (i.e. C sequestration) with increased organic residue inputs.

Validation of the Chinese version of the Problem Areas in Diabetes (PAID-C) scale

OBJECTIVE To examine the psychometric properties of a Chinese version of the Problem Areas In Diabetes (PAID-C) scale. RESEARCH DESIGN AND METHODS The reliability and validity of the PAID-C were evaluated in a convenience sample of 205 outpatients with type 2 diabetes. Confirmatory factor analysis, Bland-Altman analysis, and Spearman's correlations facilitated the psychometric evaluation. RESULTS Confirmatory factor analysis confirmed a one-factor structure of the PAID-C (χ2/df ratio = 1.894, goodness-of-fit index = 0.901, comparative fit index = 0.905, root mean square error of approximation = 0.066). The PAID-C was associated with A1C (rs = 0.15; P < 0.05) and diabetes self-care behaviors in general diet (rs = −0.17; P < 0.05) and exercise (rs = −0.17; P < 0.05). The 4-week test-retest reliability demonstrated satisfactory stability (rs = 0.83; P < 0.01). CONCLUSIONS The PAID-C is a reliable and valid measure to determine diabetes-related emotional distress in Chinese people with type 2 diabetes.

Encyclopedia contributions: entries C-G in Oxford Companion to Australian Gardens

Caulfield, Harold William; p.131 Cowan, Alexander; p.164 Cowley, Ebenezer; p.164 East Talgai Station; p.193 Eaves, S.H.; p.193-194 Edgar, J.S.; p.196 Everist, Selwyn; p.206 Experimental Farms and Gardens; pp.207-208 Government Houses - Queensland; pp.267-268

Automatic generation of assertions to detect potential security vulnerabilities in C programs that use union and pointer types

Type unions, pointer variables and function pointers are a long standing source of subtle security bugs in C program code. Their use can lead to hard-to-diagnose crashes or exploitable vulnerabilities that allow an attacker to attain privileged access over classified data. This paper describes an automatable framework for detecting such weaknesses in C programs statically, where possible, and for generating assertions that will detect them dynamically, in other cases. Exclusively based on analysis of the source code, it identifies required assertions using a type inference system supported by a custom made symbol table. In our preliminary findings, our type system was able to infer the correct type of unions in different scopes, without manual code annotations or rewriting. Whenever an evaluation is not possible or is difficult to resolve, appropriate runtime assertions are formed and inserted into the source code. The approach is demonstrated via a prototype C analysis tool.

Thermal studies of D.C. traction motors

This paper describes a thorough thermal study on a fleet of DC traction motors which were found to suffer from overheating after 3 years of full operation. Overheating of these traction motors is attributed partly because of the higher than expected number of starts and stops between train terminals. Another probable cause of overheating is the design of the traction motor and/or its control strategy. According to the motor manufacturer, a current shunt is permanently connected across the motor field winding. Hence, some of the armature current is bypassed into the current shunt. The motor then runs above its rated speed in the field weakening mode. In this study, a finite difference model has been developed to simulate the temperature profile at different parts inside the traction motor. In order to validate the simulation result, an empty vehicle loaded with drums of water was also used to simulate the full pay-load of a light rail vehicle experimentally. The authors report that the simulation results agree reasonably well with experimental data, and it is likely that the armature of the traction motor will run cooler if its field shunt is disconnected at low speeds

Influence of historic land use change on the biosphere-atmosphere-exchange of C and N trace gases in the humid, subtropical region of Queensland

Increases in atmospheric concentrations of the greenhouse gases (GHGs) carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) due to human activities have been linked to climate change. GHG emissions from land use change and agriculture have been identified as significant contributors to both Australia’s and the global GHG budget. This is expected to increase over the coming decades as rates of agriculture intensification and land use change accelerate to support population growth and food production. Limited data exists on CO2, CH4 and N2O trace gas fluxes from subtropical or tropical soils and land uses. To develop effective mitigation strategies a full global warming potential (GWP) accounting methodology is required that includes emissions of the three primary greenhouse gases. Mitigation strategies that focus on one gas only can inadvertently increase emissions of another. For this reason, detailed inventories of GHGs from soils and vegetation under individual land uses are urgently required for subtropical Australia. This study aimed to quantify GHG emissions over two consecutive years from three major land uses; a well-established, unfertilized subtropical grass-legume pasture, a 30 year (lychee) orchard and a remnant subtropical Gallery rainforest, all located near Mooloolah, Queensland. GHG fluxes were measured using a combination of high resolution automated sampling, coarser spatial manual sampling and laboratory incubations. Comparison between the land uses revealed that land use change can have a substantial impact on the GWP on a landscape long after the deforestation event. The conversion of rainforest to agricultural land resulted in as much as a 17 fold increase in GWP, from 251 kg CO2 eq. ha-1 yr-1 in the rainforest to 889 kg CO2 eq. ha-1 yr-1 in the pasture to 2538 kg CO2 eq. ha-1 yr-1 in the lychee plantation. This increase resulted from altered N cycling and a reduction in the aerobic capacity of the soil in the pasture and lychee systems, enhancing denitrification and nitrification events, and reducing atmospheric CH4 uptake in the soil. High infiltration, drainage and subsequent soil aeration under the rainforest limited N2O loss, as well as promoting CH4 uptake of 11.2 g CH4-C ha-1 day-1. This was among the highest reported for rainforest systems, indicating that aerated subtropical rainforests can act as substantial sink of CH4. Interannual climatic variation resulted in significantly higher N2O emission from the pasture during 2008 (5.7 g N2O-N ha day) compared to 2007 (3.9 g N2O-N ha day), despite receiving nearly 500 mm less rainfall. Nitrous oxide emissions from the pasture were highest during the summer months and were highly episodic, related more to the magnitude and distribution of rain events rather than soil moisture alone. Mean N2O emissions from the lychee plantation increased from an average of 4.0 g N2O-N ha-1 day-1, to 19.8 g N2O-N ha-1 day-1 following a split application of N fertilizer (560 kg N ha-1, equivalent to 1 kg N tree-1). The timing of the split application was found to be critical to N2O emissions, with over twice as much lost following an application in spring (emission factor (EF): 1.79%) compared to autumn (EF: 0.91%). This was attributed to the hot and moist climatic conditions and a reduction in plant N uptake during the spring creating conditions conducive to N2O loss. These findings demonstrate that land use change in subtropical Australia can be a significant source of GHGs. Moreover, the study shows that modifying the timing of fertilizer application can be an efficient way of reducing GHG emissions from subtropical horticulture.