Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Teachers’ conceptions of essential knowledge for integrated social education : a middle years of schooling perspective from Australia

Integrated social education in Australia is a divisive educational issue. The last decade has been marked by a controversial integrated social studies curriculum called Studies of Society and Environment (SOSE) where history, geography and environmental studies were integrated with civics and citizenship. The introduction of a compulsory K-10 Australian Curriculum from 2011, however, marks the return to history and geography and the abandonment of SOSE. Curriculum reform aside, what do teachers think is essential knowledge for middle years social education? The paper reports on a phenomenographical exploration of thirty-one middle school teachers’ conceptions of essential knowledge for SOSE. Framed by Shulman’s (1986, 1987) theoretical framework of the knowledge base for teaching, the research identified seven qualitatively different ways of understanding essential knowledge for integrated social education. The study indicates a practice-based theorization of integrated social education that justifies attention to disciplinary process and teacher identity in middle school social education.

Didiman: Australian agricultural extension officers in the territory of Papua and New Guinea, 1945-1975

Historically, the development philosophy for the two Territories of Papua and New Guinea (known as TPNG, formerly two territories, Papua and New Guinea) was equated with economic development, with a focus on agricultural development. To achieve the modification or complete change in indigenous farming systems the Australian Government’s Department of External Territories adopted and utilised a programme based on agricultural extension. Prior to World War II, under Australian administration, the economic development of these two territories, as in many colonies of the time, was based on the institution of the plantation. Little was initiated in agriculture development for indigenous people. This changed after World War II to a rationale based on the promotion and advancement of primary industry, but also came to include indigenous farmers. To develop agriculture within a colony it was thought that a modification to, or in some cases the complete transformation of, existing farming systems was necessary to improve the material welfare of the population. It was also seen to be a guarantee for the future national interest of the sovereign state after independence was granted. The Didiman and Didimisis became the frontline, field operatives of this theoretical model of development. This thesis examines the Didiman’s field operations, the structural organisation of agricultural administration and the application of policy in the two territories.

A first extension of geometric control theory to underwater vehicles

This paper serves as a first study on the implementation of control strategies developed using a kinematic reduction onto test bed autonomous underwater vehicles (AUVs). The equations of motion are presented in the framework of differential geometry, including external dissipative forces, as a forced affine connection control system. We show that the hydrodynamic drag forces can be included in the affine connection, resulting in an affine connection control system. The definitions of kinematic reduction and decoupling vector field are thus extended from the ideal fluid scenario. Control strategies are computed using this new extension and are reformulated for implementation onto a test-bed AUV. We compare these geometrically computed controls to time and energy optimal controls for the same trajectory which are computed using a previously developed algorithm. Through this comparison we are able to validate our theoretical results based on the experiments conducted using the time and energy efficient strategies.

Modified beam theories for bending properties of nanowires considering surface/intrinsic effects and axial extension effect

Several studies of the surface effect on bending properties of a nanowire (NW) have been conducted. However, these analyses are mainly based on theoretical predictions, and there is seldom integration study in combination between theoretical predictions and simulation results. Thus, based on the molecular dynamics (MD) simulation and different modified beam theories, a comprehensive theoretical and numerical study for bending properties of nanowires considering surface/intrinsic stress effects and axial extension effect is conducted in this work. The discussion begins from the Euler-Bernoulli beam theory and Timoshenko beam theory augmented with surface effect. It is found that when the NW possesses a relatively small cross-sectional size, these two theories cannot accurately interpret the true surface effect. The incorporation of axial extension effect into Euler-Bernoulli beam theory provides a nonlinear solution that agrees with the nonlinear-elastic experimental and MD results. However, it is still found inaccurate when the NW cross-sectional size is relatively small. Such inaccuracy is also observed for the Euler-Bernoulli beam theory augmented with both contributions from surface effect and axial extension effect. A comprehensive model for completely considering influences from surface stress, intrinsic stress, and axial extension is then proposed, which leads to good agreement with MD simulation results. It is thus concluded that, for NWs with a relatively small cross-sectional size, a simple consideration of surface stress effect is inappropriate, and a comprehensive consideration of the intrinsic stress effect is required.