Jacobi quartic curves revisited

This paper provides new results about efficient arithmetic on Jacobi quartic form elliptic curves, y 2 = d x 4 + 2 a x 2 + 1. With recent bandwidth-efficient proposals, the arithmetic on Jacobi quartic curves became solidly faster than that of Weierstrass curves. These proposals use up to 7 coordinates to represent a single point. However, fast scalar multiplication algorithms based on windowing techniques, precompute and store several points which require more space than what it takes with 3 coordinates. Also note that some of these proposals require d = 1 for full speed. Unfortunately, elliptic curves having 2-times-a-prime number of points, cannot be written in Jacobi quartic form if d = 1. Even worse the contemporary formulae may fail to output correct coordinates for some inputs. This paper provides improved speeds using fewer coordinates without causing the above mentioned problems. For instance, our proposed point doubling algorithm takes only 2 multiplications, 5 squarings, and no multiplication with curve constants when d is arbitrary and a = ±1/2.

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.

Faster pairings on special Weierstrass curves

This paper presents efficient formulas for computing cryptographic pairings on the curve y 2 = c x 3 + 1 over fields of large characteristic. We provide examples of pairing-friendly elliptic curves of this form which are of interest for efficient pairing implementations.

Distribution of respiratory droplets in enclosed environments under different air distribution methods

Dispersion characteristics of respiratory droplets in indoor environments are of special interest in controlling transmission of airborne diseases. This study adopts an Eulerian method to investigate the spatial concentration distribution and temporal evolution of exhaled and sneezed/coughed droplets within the range of 1.0~10.0μm in an office room with three air distribution methods, i.e. mixing ventilation (MV), displacement ventilation (DV), and under-floor air distribution (UFAD). The diffusion, gravitational settling, and deposition mechanism of particulate matters are well accounted in the one-way coupling Eulerian approach. The simulation results find that exhaled droplets with diameters up to 10.0μm from normal respiration process are uniformly distributed in MV, while they are trapped in the breathing height by thermal stratifications in DV and UFAD, resulting in a high droplet concentration and a high exposure risk to other occupants. Sneezed/coughed droplets are diluted much slower in DV/UFAD than in MV. Low air speed in the breathing zone in DV/UFAD can lead to prolonged residence of droplets in the breathing zone.

Deposition of combustion aerosols in the human respiratory tract : comparison of theoretical predictions with experimental data

Total deposition of petrol, diesel and environmental tobacco smoke (ETS) aerosols in the human respiratory tract for nasal breathing conditions was computed for 14 nonsmoking volunteers, considering the specific anatomical and respiratory parameters of each volunteer and the specific size distribution for each inhalation experiment. Theoretical predictions were 34.6% for petrol, 24.0% for diesel, and 18.5% for ETS particles. Compared to the experimental results, predicted deposition values were consistently smaller than the measured data (41.4% for petrol, 29.6% for diesel, and 36.2% for ETS particles). The apparent discrepancy between experimental data on total deposition and modeling results may be reconciled by considering the non-spherical shape of the test aerosols by diameter-dependent dynamic shape factors to account for differences between mobility-equivalent and volume-equivalent or thermodynamic diameters. While the application of dynamic shape factors is able to explain the observed differences for petrol and diesel particles, additional mechanisms may be required for ETS particle deposition, such as the size reduction upon inspiration by evaporation of volatile compounds and/or condensation-induced restructuring, and, possibly, electrical charge effects.

Applying data mining to assess crash risk on curves

The wide range of contributing factors and circumstances surrounding crashes on road curves suggest that no single intervention can prevent these crashes. This paper presents a novel methodology, based on data mining techniques, to identify contributing factors and the relationship between them. It identifies contributing factors that influence the risk of a crash. Incident records, described using free text, from a large insurance company were analysed with rough set theory. Rough set theory was used to discover dependencies among data, and reasons using the vague, uncertain and imprecise information that characterised the insurance dataset. The results show that male drivers, who are between 50 and 59 years old, driving during evening peak hours are involved with a collision, had a lowest crash risk. Drivers between 25 and 29 years old, driving from around midnight to 6 am and in a new car has the highest risk. The analysis of the most significant contributing factors on curves suggests that drivers with driving experience of 25 to 42 years, who are driving a new vehicle have the highest crash cost risk, characterised by the vehicle running off the road and hitting a tree. This research complements existing statistically based tools approach to analyse road crashes. Our data mining approach is supported with proven theory and will allow road safety practitioners to effectively understand the dependencies between contributing factors and the crash type with the view to designing tailored countermeasures.

Long-term exposure to gaseous air pollutants and cardio-respiratory mortality in Brisbane, Australia

Air pollution is ranked by the World Health Organisation as one of the top ten contributors to the global burden of disease and injury. Exposure to gaseous air pollutants, even at a low level, has been associated with cardiorespiratory diseases (Vedal, Brauer et al. 2003). Most recent epidemiological studies of air pollution have used time-series analyses to explore the relationship between daily mortality or morbidity and daily ambient air pollution concentrations based on the same day or previous days (Hajat, Armstrong et al. 2007). However, most of the previous studies have examined the association between air pollution and health outcomes using air pollution data from a single monitoring site or average values from a few monitoring sites to represent the whole population of the study area. In fact, for a metropolitan city, ambient air pollution levels may differ significantly among the different areas. There is increasing concern that the relationships between air pollution and mortality may vary with geographical area (Chen, Mengersen et al. 2007). Additionally, some studies have indicated that socio-economic status can act as a confounder when investigating the relation between geographical location and health (Scoggins, Kjellstrom et al. 2004). This study examined the spatial variation in the relationship between long-term exposure to gaseous air pollutants (including nitrogen dioxide (NO2), ozone (O3) and sulphur dioxide (SO2)), and cardiorespiratory mortality in Brisbane, Australia, during the period 1996 - 2004.

Mining patterns and factors contributing to crash severity on road curves

Road curves are an important feature of road infrastructure and many serious crashes occur on road curves. In Queensland, the number of fatalities is twice as many on curves as that on straight roads. Therefore, there is a need to reduce drivers’ exposure to crash risk on road curves. Road crashes in Australia and in the Organisation for Economic Co-operation and Development(OECD) have plateaued in the last five years (2004 to 2008) and the road safety community is desperately seeking innovative interventions to reduce the number of crashes. However, designing an innovative and effective intervention may prove to be difficult as it relies on providing theoretical foundation, coherence, understanding, and structure to both the design and validation of the efficiency of the new intervention. Researchers from multiple disciplines have developed various models to determine the contributing factors for crashes on road curves with a view towards reducing the crash rate. However, most of the existing methods are based on statistical analysis of contributing factors described in government crash reports. In order to further explore the contributing factors related to crashes on road curves, this thesis designs a novel method to analyse and validate these contributing factors. The use of crash claim reports from an insurance company is proposed for analysis using data mining techniques. To the best of our knowledge, this is the first attempt to use data mining techniques to analyse crashes on road curves. Text mining technique is employed as the reports consist of thousands of textual descriptions and hence, text mining is able to identify the contributing factors. Besides identifying the contributing factors, limited studies to date have investigated the relationships between these factors, especially for crashes on road curves. Thus, this study proposed the use of the rough set analysis technique to determine these relationships. The results from this analysis are used to assess the effect of these contributing factors on crash severity. The findings obtained through the use of data mining techniques presented in this thesis, have been found to be consistent with existing identified contributing factors. Furthermore, this thesis has identified new contributing factors towards crashes and the relationships between them. A significant pattern related with crash severity is the time of the day where severe road crashes occur more frequently in the evening or night time. Tree collision is another common pattern where crashes that occur in the morning and involves hitting a tree are likely to have a higher crash severity. Another factor that influences crash severity is the age of the driver. Most age groups face a high crash severity except for drivers between 60 and 100 years old, who have the lowest crash severity. The significant relationship identified between contributing factors consists of the time of the crash, the manufactured year of the vehicle, the age of the driver and hitting a tree. Having identified new contributing factors and relationships, a validation process is carried out using a traffic simulator in order to determine their accuracy. The validation process indicates that the results are accurate. This demonstrates that data mining techniques are a powerful tool in road safety research, and can be usefully applied within the Intelligent Transport System (ITS) domain. The research presented in this thesis provides an insight into the complexity of crashes on road curves. The findings of this research have important implications for both practitioners and academics. For road safety practitioners, the results from this research illustrate practical benefits for the design of interventions for road curves that will potentially help in decreasing related injuries and fatalities. For academics, this research opens up a new research methodology to assess crash severity, related to road crashes on curves.

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.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Molecular epidemiology of respiratory viruses in a paediatric cohort from Indonesia

Acute lower respiratory tract infections (ALRTIs) are a common cause of morbidity and mortality among children under 5 years of age and are found worldwide, with pneumonia as the most severe manifestation. Although the incidence of severe disease varies both between individuals and countries, there is still no clear understanding of what causes this variation. Studies of community-acquired pneumonia (CAP) have traditionally not focused on viral causes of disease due to a paucity of diagnostic tools. However, with the emergence of molecular techniques, it is now known that viruses outnumber bacteria as the etiological agents of childhood CAP, especially in children under 2 years of age. The main objective of this study was to investigate viruses contributing to disease severity in cases of childhood ALRTI, using a two year cohort study following 2014 infants and children enrolled in Bandung, Indonesia. A total of 352 nasopharyngeal washes collected from 256 paediatric ALRTI patients were used for analysis. A subset of samples was screened using a novel microarray pathogen detection method that identified respiratory syncytial virus (RSV), human metapneumovirus (hMPV) and human rhinovirus (HRV) in the samples. Real-time RT-PCR was used both for confirming and quantifying viruses found in the nasopharyngeal samples. Viral copy numbers were determined and normalised to the numbers of human cells collected with the use of 18S rRNA. Molecular epidemiology was performed for RSV A and hMPV using sequences to the glycoprotein gene and nucleoprotein gene respectively, to determine genotypes circulating in this Indonesian paediatric cohort. This study found that HRV (119/352; 33.8%) was the most common virus detected as the cause of respiratory tract infections in this cohort, followed by the viral pathogens RSV A (73/352; 20.7%), hMPV (30/352; 8.5%) and RSV B (12/352; 3.4%). Co-infections of more than two viruses were detected in 31 episodes (defined as an infection which occurred more than two weeks apart), accounting for 8.8% of the 352 samples tested or 15.4% of the 201 episodes with at least one virus detected. RSV A genotypes circulating in this population were predominantly GA2, GA5 and GA7, while hMPV genotypes circulating were mainly A2a (27/30; 90.0%), B2 (2/30; 6.7%) and A1 (1/30; 3.3%). This study found no evidence of disease severity associated either with a specific virus or viral strain, or with viral load. However, this study did find a significant association with co-infection of RSV A and HRV with severe disease (P = 0.006), suggesting that this may be a novel cause of severe disease.

Theoretical analysis of the motion and evaporation of exhaled respiratory droplets of mixed composition

The dynamics of droplets exhaled from the respiratory system during coughing or talking is addressed. A mathematical model is presented accounting for the motion of a droplet in conjunction with its evaporation. Droplet evaporation and motion are accounted for under two scenarios: 1) A well mixed droplet and 2) A droplet with inner composition variation. A multiple shells model was implemented to account for internal mass and heat transfer and for concentration and temperature gradients inside the droplet. The trajectories of the droplets are computed for a range of conditions and the spatial distribution and residence times of such droplets are evaluated.

Characterization of particle number concentrations and PM2.5 in a school : influence of outdoor air pollution on indoor air

Background, Aim and Scope The impact of air pollution on school children’s health is currently one of the key foci of international and national agencies. Of particular concern are ultrafine particles which are emitted in large quantities, contain large concentrations of toxins and are deposited deeply in the respiratory tract. Materials and methods In this study, an intensive sampling campaign of indoor and outdoor airborne particulate matter was carried out in a primary school in February 2006 to investigate indoor and outdoor particle number (PN) and mass concentrations (PM2.5), and particle size distribution, and to evaluate the influence of outdoor air pollution on the indoor air. Results For outdoor PN and PM2.5, early morning and late afternoon peaks were observed on weekdays, which are consistent with traffic rush hours, indicating the predominant effect of vehicular emissions. However, the temporal variations of outdoor PM2.5 and PN concentrations occasionally showed extremely high peaks, mainly due to human activities such as cigarette smoking and the operation of mower near the sampling site. The indoor PM2.5 level was mainly affected by the outdoor PM2.5 (r = 0.68, p<0.01), whereas the indoor PN concentration had some association with outdoor PN values (r = 0.66, p<0.01) even though the indoor PN concentration was occasionally influenced by indoor sources, such as cooking, cleaning and floor polishing activities. Correlation analysis indicated that the outdoor PM2.5 was inversely correlated with the indoor to outdoor PM2.5 ratio (I/O ratio) (r = -0.49, p<0.01), while the indoor PN had a weak correlation with the I/O ratio for PN (r = 0.34, p<0.01). Discussion and Conclusions The results showed that occupancy did not cause any major changes to the modal structure of particle number and size distribution, even though the I/O ratio was different for different size classes. The I/O curves had a maximum value for particles with diameters of 100 – 400 nm under both occupied and unoccupied scenarios, whereas no significant difference in I/O ratio for PM2.5 was observed between occupied and unoccupied conditions. Inspection of the size-resolved I/O ratios in the preschool centre and the classroom suggested that the I/O ratio in the preschool centre was the highest for accumulation mode particles at 600 nm after school hours, whereas the average I/O ratios of both nucleation mode and accumulation mode particles in the classroom were much lower than those of Aitken mode particles. Recommendations and Perspectives The findings obtained in this study are useful for epidemiological studies to estimate the total personal exposure of children, and to develop appropriate control strategies for minimizing the adverse health effects on school children.

Effects of dry density and grain size distribution on soil-water characteristic curves of sandy soils

The unsaturated soil mechanics is receiving increasing attention from researchers and as well as from practicing engineers. However, the requirement of sophisticated devices to measure unsaturated soil properties and time consumption have made the geotechnical engineers keep away from implication of the unsaturated soil mechanics for solving practical geotechnical problems. The application of the conventional laboratory devices with some modifications to measure unsaturated soil properties can promote the application of unsaturated soil mechanics into engineering practice. Therefore, in the present study, a conventional direct shear device was modified to measure unsaturated shear strength parameters at low suction. Specially, for the analysis of rain-induced slope failures, it is important to measure unsaturated shear strength parameters at low suction where slopes become unstable. The modified device was used to measure unsaturated shear strength of two silty soils at low suction values (0 ~ 50 kPa) that were achieved by following drying path and wetting path of soil-water characteristic curves (SWCCs) of soils. The results revealed that the internal friction angle of soil was not significantly affected by the suction and as well as the drying-wetting SWCCs of soils. The apparent cohesion of soil increased with a decreasing rate as the suction increased. Further, the apparent cohesion obtained from soil in wetting was greater than that obtained from soil in drying. Shear stress-shear displacement curves obtained from soil specimens subjected to the same net normal stress and different suction values showed a higher initial stiffness and a greater peak stress as the suction increased. In addition, it was observed that soil became more dilative with the increase of suction. A soil in wetting exhibited slightly higher peak shear stress and more contractive volume change behaviour than that of in drying at the same net normal stress and the suction.