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.

Spectroscopy of selected copper group minerals : chalcophyllite and chenevixite-implications for hydrogen bonding

NIR and IR spectroscopy has been applied for detection of chemical species and the nature of hydrogen bonding in arsenate complexes. The structure and spectral properties of copper(II) arsenate minerals chalcophyllite and chenevixite are compared with copper(II) sulphate minerals devilline, chalcoalumite and caledonite. Split NIR bands in the electronic spectrum of two ranges 11700-8500 cm-1 and 8500-7200 cm-1 confirm distortion of octahedral symmetry for Cu(II) in the arsenate complexes. The observed bands with maxima at 9860 and 7750 cm-1 are assigned to Cu(II) transitions 2B1g ® 2B2g and 2B1g ® 2A1g. Overlapping bands in the NIR region 4500-4000 cm-1 is the effect of multi anions OH-, (AsO4)3- and (SO4)2-. The observation of broad and diffuse bands in the range 3700-2900 cm-1 confirms strong hydrogen bonding in chalcophyllite relative to chenevixite. The position of the water bending vibrations indicates the water is strongly hydrogen bonded in the mineral structure. The strong absorption feature centred at 1644 cm-1 in chalcophyllite indicates water is strongly hydrogen bonded in the mineral structure. The H2O-bending vibrations shift to low wavenumbers in chenevixite and an additional band observed at 1390 cm-1 is related to carbonate impurity. The characterisation of IR spectra by ν3 antisymmetric stretching vibrations of (SO4)2- and (AsO4)3 ions near 1100 and 800 cm-1 respectively is the result of isomorphic substitution for arsenate by sulphate in both the minerals of chalcophyllite and chenevixite.

Spectroscopy of selected copper group minerals : Ktenasite, orthoserpierite and Kipushite

The near-infrared (NIR) and infrared (IR) spectroscopy has been applied for characterisation of three complex Cu-Zn sulphate/phosphate minerals, namely ktenasite, orthoserpierite and kipushite. The spectral signatures of the three minerals are quite distinct in relation to their composition and structure. The effect of structural cations substitution (Zn2+ and Cu2+) on band shifts is significant both in the electronic and vibrational spectra of these Cu-Zn minerals. The variable Cu:Zn ratio between Zn-rich and Cu-rich compositions shows a strong effect on Cu(II) bands in the electronic spectra. The Cu(II) spectrum is most significant in kipushite (Cu-rich) with bands displayed at high wavenumbers at11390 and 7545 cm-1. The isomorphic substitution of Cu2+ for Zn2+ is reflected in the NIR and IR spectroscopic signatures. The multiple bands for 3 and 4 (SO4)2- stretching vibrations in ktenasite and orthoserpierite are attributed to the reduction of symmetry to the sulphate ion from Td to C2V. The IR spectrum of kipushite is characterised by strong (PO4)3- vibrational modes at 1090 and 990 cm-1. The range of IR absorption is higher in Ktenasite than in kipushite while it is intermediate in orthoserpierite.

Generic one round group key exchange in the standard model

Minimizing complexity of group key exchange (GKE) protocols is an important milestone towards their practical deployment. An interesting approach to achieve this goal is to simplify the design of GKE protocols by using generic building blocks. In this paper we investigate the possibility of founding GKE protocols based on a primitive called multi key encapsulation mechanism (mKEM) and describe advantages and limitations of this approach. In particular, we show how to design a one-round GKE protocol which satisfies the classical requirement of authenticated key exchange (AKE) security, yet without forward secrecy. As a result, we obtain the first one-round GKE protocol secure in the standard model. We also conduct our analysis using recent formal models that take into account both outsider and insider attacks as well as the notion of key compromise impersonation resilience (KCIR). In contrast to previous models we show how to model both outsider and insider KCIR within the definition of mutual authentication. Our analysis additionally implies that the insider security compiler by Katz and Shin from ACM CCS 2005 can be used to achieve more than what is shown in the original work, namely both outsider and insider KCIR.

Disturbed appetite and nutrient intake in peritoneal dialysis patients

OBJECTIVE Malnutrition is common among peritoneal dialysis (PD) patients. Reduced nutrient intake contributes to this. It has long been assumed that this reflects disturbed appetite. We set out to define the appetite profiles of a group of PD patients using a novel technique. DESIGN Prospective, cross-sectional comparison of PD patients versus controls. SETTING Teaching hospital dialysis unit. PATIENTS 39 PD patients and 42 healthy controls. INTERVENTION Visual analog ratings were recorded at hourly intervals to generate daily profiles for hunger and fullness. Summary statistics were generated to compare the groups. Food intake was measured using 3-day dietary records. MAIN OUTCOME MEASURES Hunger and fullness profiles. Derived hunger and fullness scores. RESULTS Controls demonstrated peaks of hunger before mealtimes, with fullness scores peaking after meals. The PD profiles had much reduced premeal hunger peaks. A postmeal reduction in hunger was evident, but the rest of the trace was flat. The PD fullness profile was also flatter than in the controls. Mean scores were similar despite the marked discrepancy in the profiles. The PD group had lower peak hunger and less diurnal variability in their hunger scores. They also demonstrated much less change in fullness rating around mealtimes, while the mean and peak fullness scores were little different. The reported nutrient intake was significantly lower for PD. CONCLUSION The data suggest that PD patients normalize their mean appetite perception at a lower level of nutrient intake than controls, suggesting that patient-reported appetite may be misleading in clinical practice. There is a loss of the usual daily variation for the PD group, which may contribute to their reduced food intake. The technique described here could be used to assess the impact of interventions upon the abnormal PD appetite profile.

Effect of poly(acrylic acid) end-group functionality on inhibition of calcium oxalate crystal growth

A number of series of poly(acrylic acids) (PAA) of differing end-groups and molecular weights prepared using atom transfer radical polymerization were used as inhibitors for the crystallization of calcium oxalate at 23 and 80°C. As measured by turbidimetry and conductivity and as expected from previous reports, all PAA series were most effective for inhibition of crystallization at molecular weights of 1500–4000. However, the extent of inhibition was in general strongly dependent on the hydrophobicity and molecular weight of the end-group. These results may be explicable in terms of adsorption/desorption of PAA to growth sites on crystallites. The overall effectiveness of the series didn't follow a simple trend with end-group hydrophobicity, suggesting self-assembly behavior or a balance between adsorption and desorption rates to crystallite surfaces may be critical in the mechanism of inhibition of calcium oxalate crystallization.

Effect of poly(acrylic acid) molecular mass and end-group functionality on calcium oxalate crystal morphology and growth

A number of series of poly(acrylic acids) (PAA) of differing end-groups and molecular mass were used to study the inhibition of calcium oxalate crystallization. The effects of the end-group on crystal speciation and morphology were significant and dramatic, with hexyl-isobutyrate end groups giving preferential formation of calcium oxalate dihydrate (COD) rather than the more stable calcium oxalate monohydrate (COM), while both more hydrophobic end-groups and less-hydrophobic end groups led predominantly to formation of the least thermodynamically stable form of calcium oxalate, calcium oxalate trihydrate. Conversely, molecular mass had little impact on calcium oxalate speciation or crystal morphology. It is probable that the observed effects are related to the rate of desorption of the PAA moiety from the crystal (lite) surfaces and that the results point to a major role for end-group as well as molecular mass in controlling desorption rate.

Knowledge-based approach for planning healthy cities : the case of Logan-Beaudesert, Australia

Introduction - The planning for healthy cities faces significant challenges due to lack of effective information, systems and a framework to organise that information. Such a framework is critical in order to make accessible and informed decisions for planning healthy cities. The challenges for planning healthy cities have been magnified by the rise of the healthy cities movement, as a result of which, there have been more frequent calls for localised, collaborative and knowledge-based decisions. Some studies have suggested that the use of a ‘knowledge-based’ approach to planning will enhance the accuracy and quality decision-making by improving the availability of data and information for health service planners and may also lead to increased collaboration between stakeholders and the community. A knowledge-based or evidence-based approach to decision-making can provide an ‘out-of-the-box’ thinking through the use of technology during decision-making processes. Minimal research has been conducted in this area to date, especially in terms of evaluating the impact of adopting knowledge-based approach on stakeholders, policy-makers and decision-makers within health planning initiatives. Purpose – The purpose of the paper is to present an integrated method that has been developed to facilitate a knowledge-based decision-making process to assist health planning Methodology – Specifically, the paper describes the participatory process that has been adopted to develop an online Geographic Information System (GIS)-based Decision Support System (DSS) for health planners. Value – Conceptually, it is an application of Healthy Cities and Knowledge Cities approaches which are linked together. Specifically, it is a unique settings-based initiative designed to plan for and improve the health capacity of Logan-Beaudesert area, Australia. This setting-based initiative is named as the Logan-Beaudesert Health Coalition (LBHC). Practical implications - The paper outlines the application of a knowledge-based approach to the development of a healthy city. Also, it focuses on the need for widespread use of this approach as a tool for enhancing community-based health coalition decision making processes.

Looking through the corridor : Malaysia and the MSC

As part of a development plan-in-progress spanning a total of 25 years(1996 to 2020), Malaysia’s Multimedia Super Corridor (MSC) provides a unique opportunity to witness a brief and microcosmic unfolding of the reciprocally formative process between society and technology that Lewis Mumford lays out in exhaustive detail in Technics and Civilization (Mumford, 1963). The interlocking of national imagining, destiny and progress with a specific group of technologies, information and communication technologies (ICT) is, in itself, worthy of interest. However, what renders the MSC doubly remarkable is its introduction in Malaysia, one of the most well established of contemporary ethnocracies. This chapter reads the development and implementation of the MSC as the text through which the association between nation and ethnicity is examined. Broadly speaking I argue here that the MSC inflects the imagining(s) of Malaysia at two levels. At the first level where the MSC is understood to be the insertion of a new policy into Malaysia’s pre-existent ethnocratic climate, I contend the MSC inflects the nation through its incongruence with prevalent conditions. At the second level, where the MSC is viewed through the position of its Chinese populace, I suggest that the MSC inflects Malaysia (perhaps to a lesser degree) through the re-emphasis it lends to issues of transnationalism and belonging for the Malaysian Chinese.

Crowd counting using group tracking and local features

In public venues, crowd size is a key indicator of crowd safety and stability. In this paper we propose a crowd counting algorithm that uses tracking and local features to count the number of people in each group as represented by a foreground blob segment, so that the total crowd estimate is the sum of the group sizes. Tracking is employed to improve the robustness of the estimate, by analysing the history of each group, including splitting and merging events. A simplified ground truth annotation strategy results in an approach with minimal setup requirements that is highly accurate.

The Queensland Cancer Physics Collaborative and the Quantitative Biomedical Imaging & Characterisation (Q-BIC) Research Group

a presentation about immersive visualised simulation systems, image analysis and GPGPU Techonology

Designing ePortfolios for music postgraduate study : a practice-led inquiry

In this research I have examined how ePortfolios can be designed for Music postgraduate study through a practice led research enquiry. This process involved designing two Web 2.0 ePortfolio systems for a group of five post graduate music research students. The design process revolved around the application of an iterative methodology called Software Develop as Research (SoDaR) that seeks to simultaneously develop design and pedagogy. The approach to designing these ePortfolio systems applied four theoretical protocols to examine the use of digitised artefacts in ePortfolio systems to enable a dynamic and inclusive dialogue around representations of the students work. The research and design process involved an analysis of existing software and literature with a focus upon identifying the affordances of available Web 2.0 software and the applications of these ideas within 21st Century life. The five post graduate music students each posed different needs in relation to the management of digitised artefacts and the communication of their work amongst peers, supervisors and public display. An ePortfolio was developed for each of them that was flexible enough to address their needs within the university setting. However in this first SoDaR iteration data gathering phase I identified aspects of the university context that presented a negative case that impacted upon the design and usage of the ePortfolios and prevented uptake. Whilst the portfolio itself functioned effectively, the university policies and technical requirements prevented serious use. The negative case analysis of the case study found revealed that Access and Control and Implementation, Technical and Policy Constraints protocols where limiting user uptake. From the semistructured interviews carried out as part of this study participant feedback revealed that whilst the participants did not use the ePortfolio system I designed, each student was employing Web 2.0 social networking and storage processes in their lives and research. In the subsequent iterations I then designed a more ‘ideal’ system that could be applied outside of the University context that draws upon the employment of these resources. In conclusion I suggest recommendations about ePortfolio design that considers what the applications of the theoretical protocols reveal about creative arts settings. The transferability of these recommendations are of course dependent upon the reapplication of the theoretical protocols in a new context. To address the mobility of ePortfolio design between Institutions and wider settings I have also designed a prototype for a business card sized USB portal for the artists’ ePortfolio. This research project is not a static one; it stands as an evolving design for a Web 2.0 ePortfolio that seeks to refer to users needs, institutional and professional contexts and the development of software that can be incorporated within the design. What it potentially provides to creative artist is an opportunity to have a dialogue about art with artefacts of the artist products and processes in that discussion.