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.

An accuracy assessment of ASTER stereo images-derived digital elevation model by using rational polynomial coefficient model

The along-track stereo images of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor with 15 m resolution were used to generate Digital Elevation Model (DEM) on an area with low and near Mean Sea Level (MSL) elevation in Johor, Malaysia. The absolute DEM was generated by using the Rational Polynomial Coefficient (RPC) model which was run on ENVI 4.8 software. In order to generate the absolute DEM, 60 Ground Control Pointes (GCPs) with almost vertical accuracy less than 10 meter extracted from topographic map of the study area. The assessment was carried out on uncorrected and corrected DEM by utilizing dozens of Independent Check Points (ICPs). Consequently, the uncorrected DEM showed the RMSEz of ± 26.43 meter which was decreased to the RMSEz of ± 16.49 meter for the corrected DEM after post-processing. Overall, the corrected DEM of ASTER stereo images met the expectations.

Cognitive behaviour therapy vs rational-emotive education : impact on children's self-talk, self-esteem and irrational beliefs

This study investigated the impact of Cognitive-Behavioural Therapy (CBT) and Rational~Emotive Education (REE) self-enhancement programs on children's self-talk, self-esteem and irrational beliefs. A total of 116 children (50.9% girls) with a mean age of 9.8 years attending Years 4 and 6 at two primary schools participated in the study. eBT resulted in a reduction in negative self-talk while REE seemed to enhance independence beliefs. Both programs were associated with increased positive self-talk and with having increased rationality in Conformity and Discomfort Intolerance beliefs.

Introduction

The title of this book, Hard Lesson: Reflections on Crime control in Late Modernity, contains a number of clues about its general theoretical direction. It is a book concerned, fist and foremost, with the vagaries of crime control in western neo-liberal and English speaking countries. More specifically, Hard Lessons draws attention to a number of examples in which discrete populations – those who have in one way or another offended against the criminal law - have become the subjects of various forms of stare intervention, regulation and control. We are concerned most of all with the ways in which recent criminal justice policies and practices have resulted in what are variously described as unintended consequences, unforeseen outcomes, unanticipated results, counter-productive effects or negative side effects. At their simplest, such terms refer to the apparent gulf between intention and outcome; they often form the basis for considerable amount of policy reappraisal, soul searching and even nihilistic despair among the mamandirns of crime control. Unintended consequences can, of course, be both positive and negative. Occasionally, crime control measures may result in beneficial outcomes, such as the use of DNA to acquit wrongly convicted prisoners. Generally, however, unforeseen effects tend to be negative and even entirely counterproductive, and/or directly opposite to what were originally intended. All this, of course, presupposes some sort of rational, well meaning and transparent policy making process so beloved by liberal social policy theorists. Yet, as Judith Bessant points out in her chapter, this view of policy formulation tends to obscure the often covert, regulatory and downright malevolent intentions contained in many government policies and practices. Indeed, history is replete with examples of governments seeking to mask their real aims from a prying public eye. Denials and various sorts of ‘techniques of neutralisation’ serve to cloak the real or ‘underlying’ aims of the powerful (Cohen 2000). The latest crop of ‘spin doctors’ and ‘official spokespersons’ has ensured that the process of governmental obfuscation, distortion and concealment remains deeply embedded in neo-liberal forms of governance. There is little new or surprising in this; nor should we be shocked when things ‘go wrong’ in the domain of crime control since many unintended consequences are, more often than not, quite predictable. Prison riots, high rates of recidivism and breaches of supervision orders, expansion rather than contraction of control systems, laws that create the opposite of what was intended – all these are normative features of western crime control. Indeed, without the deep fault lines running between policy and outcome it would be hard to imagine what many policy makers, administrators and practitioners would do: their day to day work practices and (and incomes) are directly dependent upon emergent ‘service delivery’ problems. Despite recurrent howls of official anguish and occasional despondency it is apparent that those involved in the propping up the apparatus of crime control have a vested interest in ensuring that polices and practices remain in an enduring state of review and reform.

Modeling corneal surfaces with rational functions for high-speed videokeratoscopy data compression

High-speed videokeratoscopy is an emerging technique that enables study of the corneal surface and tear-film dynamics. Unlike its static predecessor, this new technique results in a very large amount of digital data for which storage needs become significant. We aimed to design a compression technique that would use mathematical functions to parsimoniously fit corneal surface data with a minimum number of coefficients. Since the Zernike polynomial functions that have been traditionally used for modeling corneal surfaces may not necessarily correctly represent given corneal surface data in terms of its optical performance, we introduced the concept of Zernike polynomial-based rational functions. Modeling optimality criteria were employed in terms of both the rms surface error as well as the point spread function cross-correlation. The parameters of approximations were estimated using a nonlinear least-squares procedure based on the Levenberg-Marquardt algorithm. A large number of retrospective videokeratoscopic measurements were used to evaluate the performance of the proposed rational-function-based modeling approach. The results indicate that the rational functions almost always outperform the traditional Zernike polynomial approximations with the same number of coefficients.

Ambivalence and the experience of China-educated nurses working in Australia

The last decade has seen an increase in research on the experience of immigrant nurses. There are two prevailing approaches in this body of work. One is a focus on the positive or negative aspects of the experience, and the other, a depiction of the experience as a linear movement from struggle to a comfortable state. Based on our study findings on the experience of China educated nurses working in Australia, this study proposes that the concept of ambivalence is more appropriate in portraying the experience of immigrant nurses. Several sources of ambivalence experienced by the participants are represented: a disparity between expectation and reality, conflicting social and cultural norms, the dual reference points of comparison, divergent interests within families, and a sense that although it is unsatisfactory, it is hard to go back. We argue that immigration generates various forms of ambivalence and immigrant nurses must live with more or less ambivalence. The notion of ambivalence can explain a range of behaviours and situations beyond the scope of rational-choice explanations. To date, ambivalence as a theoretical concept in understanding the experience of immigrant nurses has been either ignored or insufficiently addressed in the literature.

Vulnerability assessment of reinforced concrete columns subjected to vehicular impacts

Columns are one of the key load bearing elements that are highly susceptible to vehicle impacts. The resulting severe damages to columns may leads to failures of the supporting structure that are catastrophic in nature. However, the columns in existing structures are seldom designed for impact due to inadequacies of design guidelines. The impact behaviour of columns designed for gravity loads and actions other than impact is, therefore, of an interest. A comprehensive investigation is conducted on reinforced concrete column with a particular focus on investigating the vulnerability of the exposed columns and to implement mitigation techniques under low to medium velocity car and truck impacts. The investigation is based on non-linear explicit computer simulations of impacted columns followed by a comprehensive validation process. The impact is simulated using force pulses generated from full scale vehicle impact tests. A material model capable of simulating triaxial loading conditions is used in the analyses. Circular columns adequate in capacity for five to twenty story buildings, designed according to Australian standards are considered in the investigation. The crucial parameters associated with the routine column designs and the different load combinations applied at the serviceability stage on the typical columns are considered in detail. Axially loaded columns are examined at the initial stage and the investigation is extended to analyse the impact behaviour under single axis bending and biaxial bending. The impact capacity reduction under varying axial loads is also investigated. Effects of the various load combinations are quantified and residual capacity of the impacted columns based on the status of the damage and mitigation techniques are also presented. In addition, the contribution of the individual parameter to the failure load is scrutinized and analytical equations are developed to identify the critical impulses in terms of the geometrical and material properties of the impacted column. In particular, an innovative technique was developed and introduced to improve the accuracy of the equations where the other techniques are failed due to the shape of the error distribution. Above all, the equations can be used to quantify the critical impulse for three consecutive points (load combinations) located on the interaction diagram for one particular column. Consequently, linear interpolation can be used to quantify the critical impulse for the loading points that are located in-between on the interaction diagram. Having provided a known force and impulse pair for an average impact duration, this method can be extended to assess the vulnerability of columns for a general vehicle population based on an analytical method that can be used to quantify the critical peak forces under different impact durations. Therefore the contribution of this research is not only limited to produce simplified yet rational design guidelines and equations, but also provides a comprehensive solution to quantify the impact capacity while delivering new insight to the scientific community for dealing with impacts.

Communications and learning structures that facilitate transfer of knowledge at innovation transition points

Innovation processes are rarely smooth and disruptions often occur at transition points were one knowledge domain passes the technology on to another domain. At these transition points communication is a key component in assisting the smooth hand over of technologies. However for smooth transitions to occur we argue that appropriate structures have to be in place and boundary spanning activities need to be facilitated. This paper presents three case studies of innovation processes and the findings support the view that structures and boundary spanning are essential for smooth transitions. We have explained the need to pass primary responsibility between agents to successfully bring an innovation to market. We have also shown the need to combine knowledge through effective communication so that absorptive capacity is built in process throughout the organisation rather than in one or two key individuals.

Rational design of serine protease inhibitors

Proteases regulate a spectrum of diverse physiological processes, and dysregulation of proteolytic activity drives a plethora of pathological conditions. Understanding protease function is essential to appreciating many aspects of normal physiology and progression of disease. Consequently, development of potent and specific inhibitors of proteolytic enzymes is vital to provide tools for the dissection of protease function in biological systems and for the treatment of diseases linked to aberrant proteolytic activity. The studies in this thesis describe the rational design of potent inhibitors of three proteases that are implicated in disease development. Additionally, key features of the interaction of proteases and their cognate inhibitors or substrates are analysed and a series of rational inhibitor design principles are expounded and tested. Rational design of protease inhibitors relies on a comprehensive understanding of protease structure and biochemistry. Analysis of known protease cleavage sites in proteins and peptides is a commonly used source of such information. However, model peptide substrate and protein sequences have widely differing levels of backbone constraint and hence can adopt highly divergent structures when binding to a protease’s active site. This may result in identical sequences in peptides and proteins having different conformations and diverse spatial distribution of amino acid functionalities. Regardless of this, protein and peptide cleavage sites are often regarded as being equivalent. One of the key findings in the following studies is a definitive demonstration of the lack of equivalence between these two classes of substrate and invalidation of the common practice of using the sequences of model peptide substrates to predict cleavage of proteins in vivo. Another important feature for protease substrate recognition is subsite cooperativity. This type of cooperativity is commonly referred to as protease or substrate binding subsite cooperativity and is distinct from allosteric cooperativity, where binding of a molecule distant from the protease active site affects the binding affinity of a substrate. Subsite cooperativity may be intramolecular where neighbouring residues in substrates are interacting, affecting the scissile bond’s susceptibility to protease cleavage. Subsite cooperativity can also be intermolecular where a particular residue’s contribution to binding affinity changes depending on the identity of neighbouring amino acids. Although numerous studies have identified subsite cooperativity effects, these findings are frequently ignored in investigations probing subsite selectivity by screening against diverse combinatorial libraries of peptides (positional scanning synthetic combinatorial library; PS-SCL). This strategy for determining cleavage specificity relies on the averaged rates of hydrolysis for an uncharacterised ensemble of peptide sequences, as opposed to the defined rate of hydrolysis of a known specific substrate. Further, since PS-SCL screens probe the preference of the various protease subsites independently, this method is inherently unable to detect subsite cooperativity. However, mean hydrolysis rates from PS-SCL screens are often interpreted as being comparable to those produced by single peptide cleavages. Before this study no large systematic evaluation had been made to determine the level of correlation between protease selectivity as predicted by screening against a library of combinatorial peptides and cleavage of individual peptides. This subject is specifically explored in the studies described here. In order to establish whether PS-SCL screens could accurately determine the substrate preferences of proteases, a systematic comparison of data from PS-SCLs with libraries containing individually synthesised peptides (sparse matrix library; SML) was carried out. These SML libraries were designed to include all possible sequence combinations of the residues that were suggested to be preferred by a protease using the PS-SCL method. SML screening against the three serine proteases kallikrein 4 (KLK4), kallikrein 14 (KLK14) and plasmin revealed highly preferred peptide substrates that could not have been deduced by PS-SCL screening alone. Comparing protease subsite preference profiles from screens of the two types of peptide libraries showed that the most preferred substrates were not detected by PS SCL screening as a consequence of intermolecular cooperativity being negated by the very nature of PS SCL screening. Sequences that are highly favoured as result of intermolecular cooperativity achieve optimal protease subsite occupancy, and thereby interact with very specific determinants of the protease. Identifying these substrate sequences is important since they may be used to produce potent and selective inhibitors of protolytic enzymes. This study found that highly favoured substrate sequences that relied on intermolecular cooperativity allowed for the production of potent inhibitors of KLK4, KLK14 and plasmin. Peptide aldehydes based on preferred plasmin sequences produced high affinity transition state analogue inhibitors for this protease. The most potent of these maintained specificity over plasma kallikrein (known to have a very similar substrate preference to plasmin). Furthermore, the efficiency of this inhibitor in blocking fibrinolysis in vitro was comparable to aprotinin, which previously saw clinical use to reduce perioperative bleeding. One substrate sequence particularly favoured by KLK4 was substituted into the 14 amino acid, circular sunflower trypsin inhibitor (SFTI). This resulted in a highly potent and selective inhibitor (SFTI-FCQR) which attenuated protease activated receptor signalling by KLK4 in vitro. Moreover, SFTI-FCQR and paclitaxel synergistically reduced growth of ovarian cancer cells in vitro, making this inhibitor a lead compound for further therapeutic development. Similar incorporation of a preferred KLK14 amino acid sequence into the SFTI scaffold produced a potent inhibitor for this protease. However, the conformationally constrained SFTI backbone enforced a different intramolecular cooperativity, which masked a KLK14 specific determinant. As a consequence, the level of selectivity achievable was lower than that found for the KLK4 inhibitor. Standard mechanism inhibitors such as SFTI rely on a stable acyl-enzyme intermediate for high affinity binding. This is achieved by a conformationally constrained canonical binding loop that allows for reformation of the scissile peptide bond after cleavage. Amino acid substitutions within the inhibitor to target a particular protease may compromise structural determinants that support the rigidity of the binding loop and thereby prevent the engineered inhibitor reaching its full potential. An in silico analysis was carried out to examine the potential for further improvements to the potency and selectivity of the SFTI-based KLK4 and KLK14 inhibitors. Molecular dynamics simulations suggested that the substitutions within SFTI required to target KLK4 and KLK14 had compromised the intramolecular hydrogen bond network of the inhibitor and caused a concomitant loss of binding loop stability. Furthermore in silico amino acid substitution revealed a consistent correlation between a higher frequency of formation and the number of internal hydrogen bonds of SFTI-variants and lower inhibition constants. These predictions allowed for the production of second generation inhibitors with enhanced binding affinity toward both targets and highlight the importance of considering intramolecular cooperativity effects when engineering proteins or circular peptides to target proteases. The findings from this study show that although PS-SCLs are a useful tool for high throughput screening of approximate protease preference, later refinement by SML screening is needed to reveal optimal subsite occupancy due to cooperativity in substrate recognition. This investigation has also demonstrated the importance of maintaining structural determinants of backbone constraint and conformation when engineering standard mechanism inhibitors for new targets. Combined these results show that backbone conformation and amino acid cooperativity have more prominent roles than previously appreciated in determining substrate/inhibitor specificity and binding affinity. The three key inhibitors designed during this investigation are now being developed as lead compounds for cancer chemotherapy, control of fibrinolysis and cosmeceutical applications. These compounds form the basis of a portfolio of intellectual property which will be further developed in the coming years.

Points of convergence and divergence : normative, institutional and operational relationships between R2P and POC

As an international norm, the Responsibility to Protect (R2P) has gained substantial influence and institutional presence—and created no small controversy—in the ten years since its first conceptualisation. Conversely, the Protection of Civilians in Armed Conflict (PoC) has a longer pedigree and enjoys a less contested reputation. Yet UN Security Council action in Libya in 2011 has thrown into sharp relief the relationship between the two. UN Security Council Resolutions 1970 and 1973 follow exactly the process envisaged by R2P in response to imminent atrocity crimes, yet the operative paragraphs of the resolutions themselves invoke only PoC. This article argues that, while the agendas of PoC and R2P converge with respect to Security Council action in cases like Libya, outside this narrow context it is important to keep the two norms distinct. Peacekeepers, humanitarian actors, international lawyers, individual states and regional organisations are required to act differently with respect to the separate agendas and contexts covered by R2P and PoC. While overlap between the two does occur in highly visible cases like Libya, neither R2P nor PoC collapses normatively, institutionally or operationally into the other.

Rational avoidance of accountability

Anthony Downs public choice theory proposes that every rational person would try to meet their own desires in preference to those of others, and that such rational persons would attempt to obtain these desires in the most efficient manner possible. This paper will demonstrate that the application of this theory would mean that public servants and politicians would perform acts of corruption and maladministration in order to efficiently meet their desires. As such action is unavoidable, political parties must appear to meet the public demand for accountability systems, but must not make these systems viable lest they expose the corruption and maladministration that would threaten the government’s chance or re-election. It is therefore logical for governments to display a commitment for accountability whilst simultaneously ensuring the systems would not be able to interfere with government control or expose its flaws.

The FAM deubiquitylating enzyme localizes to multiple points of protein trafficking in epithelia, where it associates with E-cadherin and β-catenin

Ubiquitylation is a necessary step in the endocytosis and lysosomal trafficking of many plasma membrane proteins and can also influence protein trafficking in the biosynthetic pathway. Although a molecular understanding of ubiquitylation in these processes is beginning to emerge, very little is known about the role deubiquitylation may play. Fat Facets in mouse (FAM) is substrate-specific deubiquitylating enzyme highly expressed in epithelia where it interacts with its substrate, β-catenin. Here we show, in the polarized intestinal epithelial cell line T84, FAM localized to multiple points of protein trafficking. FAM interacted with β-catenin and E-cadherin in T84 cells but only in subconfluent cultures. FAM extensively colocalized with β-catenin in cytoplasmic puncta but not at sites of cell-cell contact as well as immunoprecipitating with β-catenin and E-cadherin from a higher molecular weight complex (~500 kDa). At confluence FAM neither colocalized with, nor immunoprecipitated, β-catenin or E-cadherin, which were predominantly in a larger molecular weight complex (~2 MDa) at the cell surface. Overexpression of FAM in MCF-7 epithelial cells resulted in increased β-catenin levels, which localized to the plasma membrane. Expression of E-cadherin in L-cell fibroblasts resulted in the relocalization of FAM from the Golgi to cytoplasmic puncta. These data strongly suggest that FAM associates with E-cadherin and β-catenin during trafficking to the plasma membrane.

Roll the dice, rational agent : should extra-curial punishment mitigate an offender's sentence?

It was rugby league State of Origin night 2008 and a group of adults had descended upon a house in Eagleby, Brisbane to have some drinks and to celebrate the game. At 11pm that evening, Shane Thomas Davidson entered the bedroom of the homeowner’s 10-year-old son, TC. Davidson approached the bed and began to massage the boy’s penis under his clothing, which caused TC to wake. Davidson stated, ‘Show me how big your willy is and I’ll show you how big mine is’. TC refused the request and after a small period of time, left the bedroom and told his father what had happened...