An exploration of affine group laws for elliptic curves

Several forms of elliptic curves are suggested for an efficient implementation of Elliptic Curve Cryptography. However, a complete description of the group law has not appeared in the literature for most popular forms. This paper presents group law in affine coordinates for three forms of elliptic curves. With the existence of the proposed affine group laws, stating the projective group law for each form becomes trivial. This work also describes an automated framework for studying elliptic curve group law, which is applied internally when preparing this work.

Making sense of an everyday science text : linguistic, visual and spatial design

In this article, we take a close look at the literacy demands of one task from the ‘Marvellous Micro-organisms Stage 3 Life and Living’ Primary Connections unit (Australian Academy of Science, 2005). One lesson from the unit, ‘Exploring Bread’, (pp 4-8) asks students to ‘use bread labels to locate ingredient information and synthesise understanding of bread ingredients’. We draw upon a framework offered by the New London Group (2000), that of linguistic, visual and spatial design, to consider in more detail three bread wrappers and from there the complex literacies that students need to interrelate to undertake the required task. Our findings are that although bread wrappers are an example of an everyday science text, their linguistic, visual and spatial designs and their interrelationship are not trivial. We conclude by reinforcing the need for teachers of science to also consider how the complex design elements of everyday science texts and their interrelated literacies are made visible through instructional practice.

Socialising across channels : group multichannel communication

People increasingly communicate over multiple channels, such as SMS, email and IM. Choosing the channel for interaction is typically a considered action and shapes the message itself. In order to explore how people make sense of communication mediums and more generally, social group behaviour, we developed a multichannel communication prototype. Preliminary results indicate that multichannel communication was considered very useful in the group context even considering the increased quantity of messages while it was little used for person-to-person interaction.