Hardware processors for pairing-based cryptography

Bilinear pairings can be used to construct cryptographic systems with very desirable properties. A pairing performs a mapping on members of groups on elliptic and genus 2 hyperelliptic curves to an extension of the finite field on which the curves are defined. The finite fields must, however, be large to ensure adequate security. The complicated group structure of the curves and the expensive field operations result in time consuming computations that are an impediment to the practicality of pairing-based systems. The Tate pairing can be computed efficiently using the ɳT method. Hardware architectures can be used to accelerate the required operations by exploiting the parallelism inherent to the algorithmic and finite field calculations. The Tate pairing can be performed on elliptic curves of characteristic 2 and 3 and on genus 2 hyperelliptic curves of characteristic 2. Curve selection is dependent on several factors including desired computational speed, the area constraints of the target device and the required security level. In this thesis, custom hardware processors for the acceleration of the Tate pairing are presented and implemented on an FPGA. The underlying hardware architectures are designed with care to exploit available parallelism while ensuring resource efficiency. The characteristic 2 elliptic curve processor contains novel units that return a pairing result in a very low number of clock cycles. Despite the more complicated computational algorithm, the speed of the genus 2 processor is comparable. Pairing computation on each of these curves can be appealing in applications with various attributes. A flexible processor that can perform pairing computation on elliptic curves of characteristic 2 and 3 has also been designed. An integrated hardware/software design and verification environment has been developed. This system automates the procedures required for robust processor creation and enables the rapid provision of solutions for a wide range of cryptographic applications.

Learning curves: analysing pace and challenge in four successful puzzle games

The pace at which challenges are introduced in a game has long been identified as a key determinant of both the enjoyment and difficulty experienced by game players, and their ability to learn from game play. In order to understand how to best pace challenges in games, there is great value in analysing games already demonstrated as highly engaging. Play-through videos of four puzzle games (Portal, Portal 2 Co-operative mode, Braid and Lemmings), were observed and analysed using metrics derived from a behavioural psychology understanding of how people solve problems. Findings suggest that; 1) the main skills learned in each game are introduced separately, 2) through simple puzzles that require only basic performance of that skill, 3) the player has the opportunity to practice and integrate that skill with previously learned skills, and 4) puzzles increase in complexity until the next new skill is introduced. These data provide practical guidance for designers, support contemporary thinking on the design of learning structures in games, and suggest future directions for empirical research.