Faster group operations on elliptic curves

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 12M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA). Keywords: Efficient elliptic curve arithmetic,unified addition, side channel attack.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

A participative education program to reduce speeding in a group of work-related drivers

A number of intervention approaches have been developed to improve work-related driving safety. However, past interventions have been limited in that they have been data-driven, and have not been developed within a theoretical framework. The aim of this study is to present a theory-driven intervention. Based on the methodology developed by Ludwig and Geller (1991), this study evaluates the effectiveness of a participative education intervention on a group of work-related drivers (n = 28; experimental group n = 19, control n = 9). The results support the effectiveness of the intervention in reducing speeding over a six month period, while a non significant increase was found in the control group. The results of this study have important implications for organisations developing theory-driven interventions designed to improve work-related driving behaviour.

Report on Innovation Working Group : The Mathematics Education into the 21st Century Project. Dresden, Saxony

This document reports on the Innovations Working Group that met at the 10th International Conference “Models in Developing Mathematics Education” from the 11-17th September 2009 in Dresden, Saxony. It briefly describes the over arching and consistent themes that emerged from the numerous papers presented. The authors and titles of each of the papers presented will be listed in Table 2.

Writing together, learning together : the value and effectiveness of a research writing group for doctoral students

The high level of scholarly writing required for a doctoral thesis is a challenge for many research students. However, formal academic writing training is not a core component of many doctoral programs. Informal writing groups for doctoral students may be one method of contributing to the improvement of scholarly writing. In this paper, we report on a writing group that was initiated by an experienced writer and higher degree research supervisor to support and improve her doctoral students’ writing capabilities. Over time, this group developed a workable model to suit their varying needs and circumstances. The model comprised group sessions, an email group, and individual writing. Here, we use a narrative approach to explore the effectiveness and value of our research writing group model in improving scholarly writing. The data consisted of doctoral students’ reflections to stimulus questions about their writing progress and experiences. The stimulus questions sought to probe individual concerns about their own writing, what they had learned in the research writing group, the benefits of the group, and the disadvantages and challenges to participation. These reflections were analysed using thematic analysis. Following this analysis, the supervisor provided her perspective on the key themes that emerged. Results revealed that, through the writing group, members learned technical elements (e.g., paragraph structure), non-technical elements (e.g., working within limited timeframes), conceptual elements (e.g., constructing a cohesive arguments), collaborative writing processes, and how to edit and respond to feedback. In addition to improved writing quality, other benefits were opportunities for shared writing experiences, peer support, and increased confidence and motivation. The writing group provides a unique social learning environment with opportunities for: professional dialogue about writing, peer learning and review, and developing a supportive peer network. Thus our research writing group has proved an effective avenue for building doctoral students’ capability in scholarly writing. The proposed model for a research writing group could be applicable to any context, regardless of the type and location of the university, university faculty, doctoral program structure, or number of postgraduate students. It could also be used within a group of students with diverse research abilities, needs, topics and methodologies. However, it requires a group facilitator with sufficient expertise in scholarly writing and experience in doctoral supervision who can both engage the group in planned writing activities and also capitalise on fruitful lines of discussion related to students’ concerns as they arise. The research writing group is not intended to replace traditional supervision processes nor existing training. However it has clear benefits for improving scholarly writing in doctoral research programs particularly in an era of rapidly increasing student load.

Prediction of outcome with group cognitive therapy for depression

Tested a social–cognitive model of depressive episodes and their treatment within a predictive study of treatment response. 42 clinically depressed volunteers (aged 22–60 yrs) were given self-efficacy (SE) questionnaires and other measures before and after treatment with cognitive therapy. Results support the idea that SE and skills regarding control of negative cognition mediates a sustained response to cognitive treatment for depression. Not only did mood-control variables correlate highly with concurrent changes in depression scores during treatment, but the posttreatment SE measure discriminated Ss who relapsed over the next 12 mo.

Primary students' group metacognitive processes in a computer supported collaborative learning environment

The current understanding of students’ group metacognition is limited. The research on metacognition has focused mainly on the individual student. The aim of this study was to address the void by developing a conceptual model to inform the use of scaffolds to facilitate group metacognition during mathematical problem solving in computer supported collaborative learning (CSCL) environments. An initial conceptual framework based on the literature from metacognition, cooperative learning, cooperative group metacognition, and computer supported collaborative learning was used to inform the study. In order to achieve the study aim, a design research methodology incorporating two cycles was used. The first cycle focused on the within-group metacognition for sixteen groups of primary school students working together around the computer; the second cycle included between-group metacognition for six groups of primary school students working together on the Knowledge Forum® CSCL environment. The study found that providing groups with group metacognitive scaffolds resulted in groups planning, monitoring, and evaluating the task and team aspects of their group work. The metacognitive scaffolds allowed students to focus on how their group was completing the problem-solving task and working together as a team. From these findings, a revised conceptual model to inform the use of scaffolds to facilitate group metacognition during mathematical problem solving in computer supported collaborative learning (CSCL) environments was generated.

Sex offenders in denial : a study into a group of forensic psychologists' attitudes regarding the corresponding impact upon risk assessment calculations and parole eligibility

A considerable proportion of convicted sex offenders maintain a stance of innocence and thus do not engage in recommended treatment programs. As a result, such offenders are often deemed to have outstanding criminogenic needs which may negatively impact upon risk assessment procedures and parole eligibility. This paper reports on a study that aimed to investigate a group of forensic psychologists’ attitudes regarding the impact of denial on risk assessment ratings as well as parole eligibility. Participants completed a confidential open-ended questionnaire. Analysis indicated that considerable variability exists among forensic psychologists in regards to their beliefs about the origins of denial and what impact such denial should have on post-prison release eligibility. In contrast, there was less disparity regarding beliefs about the percentage of innocent yet incarcerated sex offenders. This paper also reviews current understanding regarding the impact of denial on recidivism as well as upon general forensic assessments.

Emergency department surge capacity : Recommendations of the Australasian surge strategy working group

Background For more than a decade emergency medicine organizations have produced guidelines, training and leadership for disaster management. However to date, there have been limited guidelines for emergency physicians needing to provide a rapid response to a surge in demand. The aim of this study is to identify strategies which may guide surge management in the Emergency Department. Method A working group of individuals experienced in disaster medicine from the Australasian College for Emergency Medicine Disaster Medicine Subcommittee (the Australasian Surge Strategy Working Group) was established to undertake this work. The Working Group used a modified Delphi technique to examine response actions in surge situations. The Working Group identified underlying assumptions from epidemiological and empirical understanding and then identified remedial strategies from literature and from personal experience and collated these within domains of space, staff, supplies, and system operation. Findings These recommendations detail 22 potential actions available to an emergency physician working in the context of surge. The Working Group also provides detailed guidance on surge recognition, triage, patient flow through the emergency department and clinical goals and practices. Discussion These strategies provide guidance to emergency physicians confronting the challenges of a surge in demand. The paper also identifies areas that merit future research including the measurement of surge capacity, constraints to strategy implementation, validation of surge strategies and measurement of strategy impacts on throughput, cost, and quality of care.

Three-dimensional hydrogen-bonded structures in the 1:1 proton-transfer compounds of L-tartaric acid with the associative-group monosubstituted pyridines 3-minopyridine, 3-carboxypyridine (nicotinic acid) and 2-carboxypyridine (picolinic acid).

The 1:1 proton-transfer compounds of L-tartaric acid with 3-aminopyridine [3-aminopyridinium hydrogen (2R,3R)-tartrate dihydrate, C5H7N2+·C4H5O6-·2H2O, (I)], pyridine-3-carboxylic acid (nicotinic acid) [anhydrous 3-carboxypyridinium hydrogen (2R,3R)-tartrate, C6H6NO2+·C4H5O6-, (II)] and pyridine-2-carboxylic acid [2-carboxypyridinium hydrogen (2R,3R)-tartrate monohydrate, C6H6NO2+·C4H5O6-·H2O, (III)] have been determined. In (I) and (II), there is a direct pyridinium-carboxyl N+-HO hydrogen-bonding interaction, four-centred in (II), giving conjoint cyclic R12(5) associations. In contrast, the N-HO association in (III) is with a water O-atom acceptor, which provides links to separate tartrate anions through Ohydroxy acceptors. All three compounds have the head-to-tail C(7) hydrogen-bonded chain substructures commonly associated with 1:1 proton-transfer hydrogen tartrate salts. These chains are extended into two-dimensional sheets which, in hydrates (I) and (III) additionally involve the solvent water molecules. Three-dimensional hydrogen-bonded structures are generated via crosslinking through the associative functional groups of the substituted pyridinium cations. In the sheet struture of (I), both water molecules act as donors and acceptors in interactions with separate carboxyl and hydroxy O-atom acceptors of the primary tartrate chains, closing conjoint cyclic R44(8), R34(11) and R33(12) associations. Also, in (II) and (III) there are strong cation carboxyl-carboxyl O-HO hydrogen bonds [OO = 2.5387 (17) Å in (II) and 2.441 (3) Å in (III)], which in (II) form part of a cyclic R22(6) inter-sheet association. This series of heteroaromatic Lewis base-hydrogen L-tartrate salts provides further examples of molecular assembly facilitated by the presence of the classical two-dimensional hydrogen-bonded hydrogen tartrate or hydrogen tartrate-water sheet substructures which are expanded into three-dimensional frameworks via peripheral cation bifunctional substituent-group crosslinking interactions.

Mechanisms of change in negative thinking and urinary monoamines in depressed patients during acute treatment with group cognitive behavior therapy and antidepressant medication

This naturalistic study investigated the mechanisms of change in measures of negative thinking and in 24-h urinary metabolites of noradrenaline (norepinephrine), dopamine and serotonin in a sample of 43 depressed hospital patients attending an eight-session group cognitive behavior therapy program. Most participants (91%) were taking antidepressant medication throughout the therapy period according to their treating Psychiatrists' prescriptions. The sample was divided into outcome categories (19 Responders and 24 Non-responders) on the basis of a clinically reliable change index [Jacobson, N.S., & Truax, P., 1991. Clinical significance: a statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12–19.] applied to the Beck Depression Inventory scores at the end of the therapy. Results of repeated measures analysis of variance [ANOVA] analyses of variance indicated that all measures of negative thinking improved significantly during therapy, and significantly more so in the Responders as expected. The treatment had a significant impact on urinary adrenaline and metadrenaline excretion however, these changes occurred in both Responders and Non-responders. Acute treatment did not significantly influence the six other monoamine metabolites. In summary, changes in urinary monoamine levels during combined treatment for depression were not associated with self-reported changes in mood symptoms.

Skydweller and representations of the adolescent crisis : group identity versus alienation

This document contains a creative work – the text of a young adult novel, Skydweller – and an exegesis discussing the ways in which identity and the adolescent crisis of group identity versus alienation are represented in young adult science fiction/fantasy novels.

A peptidomimetic inhibitor of matrix metalloproteinases containing a tetherable linker group

Successful wound repair and normal turnover of the extracellular matrix relies on a balance between matrix metalloproteinases (MMPs) and their natural inhibitors (the TIMPs). When over-expression of MMPs and abnormally high levels of activation or low expression of TIMPs are encountered, excessive degradation of connective tissue and the formation of chronic ulcers can occur. One strategy to rebalance MMPs and TIMPs is to use inhibitors. We have designed a synthetic pseudopeptide inhibitor with an amine linker group based on a known high-affinity peptidomimetic MMP inhibitor have demonstrated inhibition of MMP-1, -2, -3 and -9 activity in standard solutions. The inhibitor was also tethered to a polyethylene glycol hydrogel using a facile reaction between the linker unit on the inhibitor and the hydrogel precursors. After tethering, we observed inhibition of the MMPs although there was an increase in the IC50s which was attributed to poor diffusion of the MMPs into the hydrogels, reduced activity of the tethered inhibitor or incomplete incorporation of the inhibitor into the hydrogels. When the tethered inhibitors were tested against chronic wound fluid we observed significant inhibition in proteolytic activity suggesting our approach may prove useful in rebalancing MMPs within chronic wounds.

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.