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.

Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

Researching crime and violence: Untold stories from the field

Undertaking empirical research on crime and violence can be a tricky enterprise fraught with ethical, methodological, intellectual and legal implications. This chapter takes readers on a reflective journey through the qualitative methodologies I used to research sex work in Kings Cross, miscarriages of justice, female delinquency, sexual violence, and violence in rural and regional settings over a period of nearly 30 years. Reflecting on these experiences, the chapter explores and analyses the reality of doing qualitative field research, the role of the researcher, the politics of subjectivity, the exercise of power, and the ‘muddiness’ of the research process, which is often overlooked in sanitised accounts of the research process (Byrne-Armstrong, Higgs and Horsfall, 2001; Davies, 2000).

Art in early childhood : the discourse of 'proper' teaching

This thesis is a problematisation of the teaching of art to young children. To problematise a domain of social endeavour, is, in Michel Foucault's terms, to ask how we come to believe that "something ... can and must be thought" (Foucault, 1985:7). The aim is to document what counts (i.e., what is sayable, thinkable, feelable) as proper art teaching in Queensland at this point ofhistorical time. In this sense, the thesis is a departure from more recognisable research on 'more effective' teaching, including critical studies of art teaching and early childhood teaching. It treats 'good teaching' as an effect of moral training made possible through disciplinary discourses organised around certain epistemic rules at a particular place and time. There are four key tasks accomplished within the thesis. The first is to describe an event which is not easily resolved by means of orthodox theories or explanations, either liberal-humanist or critical ones. The second is to indicate how poststructuralist understandings of the self and social practice enable fresh engagements with uneasy pedagogical moments. What follows this discussion is the documentation of an empirical investigation that was made into texts generated by early childhood teachers, artists and parents about what constitutes 'good practice' in art teaching. Twenty-two participants produced text to tell and re-tell the meaning of 'proper' art education, from different subject positions. Rather than attempting to capture 'typical' representations of art education in the early years, a pool of 'exemplary' teachers, artists and parents were chosen, using "purposeful sampling", and from this pool, three videos were filmed and later discussed by the audience of participants. The fourth aspect of the thesis involves developing a means of analysing these texts in such a way as to allow a 're-description' of the field of art teaching by attempting to foreground the epistemic rules through which such teacher-generated texts come to count as true ie, as propriety in art pedagogy. This analysis drew on Donna Haraway's (1995) understanding of 'ironic' categorisation to hold the tensions within the propositions inside the categories of analysis rather than setting these up as discursive oppositions. The analysis is therefore ironic in the sense that Richard Rorty (1989) understands the term to apply to social scientific research. Three 'ironic' categories were argued to inform the discursive construction of 'proper' art teaching. It is argued that a teacher should (a) Teach without teaching; (b) Manufacture the natural; and (c) Train for creativity. These ironic categories work to undo modernist assumptions about theory/practice gaps and finding a 'balance' between oppositional binary terms. They were produced through a discourse theoretical reading of the texts generated by the participants in the study, texts that these same individuals use as a means of discipline and self-training as they work to teach properly. In arguing the usefulness of such approaches to empirical data analysis, the thesis challenges early childhood research in arts education, in relation to its capacity to deal with ambiguity and to acknowledge contradiction in the work of teachers and in their explanations for what they do. It works as a challenge at a range of levels - at the level of theorising, of method and of analysis. In opening up thinking about normalised categories, and questioning traditional Western philosophy and the grand narratives of early childhood art pedagogy, it makes a space for re-thinking art pedagogy as "a game oftruth and error" (Foucault, 1985). In doing so, it opens up a space for thinking how art education might be otherwise.