Locking away the mysteries of fair basis : Lockwood v Doric in the High Court

This article updates a previous article on the Lockwood v Doric fair basing case in the Full Court of the Federal Court which was recently appealed to the High Court. The High Court's decision provides a new and welcome level of clarity in this difficult area of patent law. With this new clarity we can finally lock away some of the mysteries that have plagued the area for some time. Already, indications are that Lockwood's guidelines are being usefully applied in the Patent Office and Federal Court.

Teaching English as an additional language in senior high school : critical discourses in critical times

This paper presents a Critical Discourse Analysis (CDA) of four policy documents currently offering ‘sets of possibilities’ for the teaching of English as an additional or second language (hereafter EAL/ESL) in senior classrooms in Queensland, Australia. The aim is to identify the ways in which each document re-presents the notion of critical literacy. Leximancer software, and Fairclough’s textually-oriented discourse analysis method (2001, 2003) are used to interrogate the relevant sections of the documents for the ways in which they re-present (sic) and construct the discourses around critical language study. This paper presents the description, interpretation and explanation of the discourses in these documents which constitute part of a larger project in which teacher interviews and classroom teaching are also investigated for the ways in which ‘the critical’ is constructed and contested in knowledge and practice.

Case study 3. A subtropical urban community. Medium to high density residential typologies

Subtropical Urban Communities Project Urban design and residential buildings The Centre for Subtropical Design has researched design concepts for livable subtropical neighbourhoods characterised by higher-density, mixed-use, family oriented housing by conducting a design charrette and analysing the proposed designs to evaluate how well these typologies might support economic, environmental and social sustainability. http://www.subtropicaldesign.org.au/index.php?option=com_content&task=view&id=125&Itemid=163 The QUT Team produced designs (Case Study 3) within the research framework of the design charrette.

Chemical functionalities of high and low sulfur Australian coals : a case study using micro attenuated total reflectance–fourier transform infrared (ATR–FTIR) spectrometry

The macerals in bituminous coals with varying organic sulfur content from the Early Permian Greta Coal Measures at three locations (Southland Colliery, Drayton Colliery and the Cranky Corner Basin), in and around the Sydney Basin (Australia), have been studied using light-element electron microprobe (EMP) analysis and micro-ATR–FTIR. Electron microprobe analysis of individual macerals reveals that the vitrinite in both the Cranky Corner Basin and Drayton Colliery (Puxtrees seam) samples have similar carbon contents (ca. 78% C in telocollinite), suggesting that they are of equivalent rank. However, the Cranky Corner coals have anomalously low vitrinite reflectance (down to 0.45%) vs. the Drayton materials (ca. 0.7%). They also have very high organic S content (3–6.5%) and lower O content (ca. 10%) than the equivalent macerals in the Drayton sample (0.7% S and 15.6% O). A study was carried out to investigate the impacts of the high organic S on the functional groups of the macerals in these two otherwise iso-rank, stratigraphically-equivalent seams. An iso-rank low-S coal from the overlying Wittingham Coal Measures near Muswellbrook and coals of slightly higher rank from the Greta Coal Measures at Southland Colliery near Cessnock were also evaluated using the same techniques to extend the data set. Although the telocollinite in the Drayton and Cranky Corner coals have very similar carbon content (ca.78% C), the ATR–FTIR spectra of the vitrinite and inertinite macerals in these respectively low S and high S coals show some distinct differences in IR absorbance from various aliphatic and aromatic functional groups. The differences in absorbance of the aliphatic stretching bands (2800–3000 cm−1) and the aromatic carbon (CC) peak at 1606 cm−1 are very obvious. Compared to that of the Drayton sample (0.7% S and 15% O), the telocollinite of the Cranky Corner coal (6% S and 10% O) clearly shows: (i) less absorbance from OH groups, represented by a broad region around 3553 cm−1, (ii) much stronger aliphatic C–H absorbance (stretching modes around 3000–2800 cm−1 and bending modes around 1442 cm−1) and (iii) less absorbance from aromatic carbon functional groups (peaking at 1606 cm−1). Evaluation of the iso-rank Drayton and Cranky Corner coals shows that: (i) the aliphatic C–H absorbances decrease with increasing oxygen content but increase with increasing organic S content and (ii) the aromatic H to aliphatic H ratio (Har/Hali) for the telocollinite increases with (organic) O%, but decreases progressively with increasing organic S. The high organic S content in the maceral appears to be accompanied by a greater proportion of aliphatic functional groups, possibly as a result of some of the O within maceral ring structures in the high S coal samples being replaced.

Flexible high-power multi DC-DC converters for train systems

This thesis reports on the investigations, simulations and analyses of novel power electronics topologies and control strategies. The research is financed by an Australian Research Council (ARC) Linkage (07-09) grant. Therefore, in addition to developing original research and contributing to the available knowledge of power electronics, it also contributes to the design of a DC-DC converter for specific application to the auxiliary power supply in electric trains. Specifically, in this regard, it contributes to the design of a 7.5 kW DC-DC converter for the industrial partner (Schaffler and Associates Ltd) who supported this project. As the thesis is formatted as a ‘thesis by publication’, the contents are organized around published papers. The research has resulted in eleven papers, including seven peer reviewed and published conference papers, one published journal paper, two journal papers accepted for publication and one submitted journal paper (provisionally accepted subject to few changes). In this research, several novel DC-DC converter topologies are introduced, analysed, and tested. The similarity of all of the topologies devised lies in their ‘current circulating’ switching state, which allows them to store some energy in the inductor, as extra inductor current. The stored energy may be applied to enhance the performance of the converter in the occurrence of load current or input voltage disturbances. In addition, when there is an alternating load current, the ability to store energy allows the converter to perform satisfactorily despite frequently and highly varying load current. In this research, the capability of current storage has been utilised to design topologies for specific applications, and the enhancement of the performance of the considered applications has been illustrated. The simplest DC-DC converter topology, which has a ‘current circulating’ switching state, is the Positive Buck-Boost (PBB) converter (also known as the non-inverting Buck-Boost converter). Usually, the topology of the PBB converter is operating as a Buck or a Boost converter in applications with widely varying input voltage or output reference voltage. For example, in electric railways (the application of our industrial partner), the overhead line voltage alternates from 1000VDC to 500VDC and the required regulated voltage is 600VDC. In the course of this research, our industrial partner (Schaffler and Associates Ltd) industrialized a PBB converter–the ‘Mudo converter’–operating at 7.5 kW. Programming the onboard DSP and testing the PBB converter in experimental and nominal power and voltage was part of this research program. In the earlier stages of this research, the advantages and drawbacks of utilization of the ‘current circulating’ switching state in the positive Buck-Boost converter were investigated. In brief, the advantages were found to be robustness against input voltage and current load disturbances, and the drawback was extra conduction and switching loss. Although the robustness against disturbances is desirable for many applications, the price of energy loss must be minimized to attract attention to the utilization of the PBB converter. In further stages of this research, two novel control strategies for different applications were devised to minimise the extra energy loss while the advantages of the positive Buck-Boost converter were fully utilized. The first strategy is Smart Load Controller (SLC) for applications with pre-knowledge or predictability of input voltage and/or load current disturbances. A convenient example of these applications is electric/hybrid cars where a master controller commands all changes in loads and voltage sources. Therefore, the master controller has a pre-knowledge of the load and input voltage disturbances so it can apply the SLC strategy to utilize robustness of the PBB converter. Another strategy aiming to minimise energy loss and maximise the robustness in the face of disturbance is developed to cover applications with unexpected disturbances. This strategy is named Dynamic Hysteresis Band (DHB), and is used to manipulate the hysteresis band height after occurrence of disturbance to reduce dynamics of the output voltage. When no disturbance has occurred, the PBB converter works with minimum inductor current and minimum energy loss. New topologies based on the PBB converter have been introduced to address input voltage disturbances for different onboard applications. The research shows that the performance of applications of symmetrical/asymmetrical multi-level diode-clamped inverters, DC-networks, and linear-assisted RF amplifiers may be enhanced by the utilization of topologies based on the PBB converter. Multi-level diode-clamped inverters have the problem of DC-link voltage balancing when the power factor of their load closes to unity. This research has shown that this problem may be solved with a suitable multi-output DC-DC converter supplying DClink capacitors. Furthermore, the multi-level diode-clamped inverters supplied with asymmetrical DC-link voltages may improve the quality of load voltage and reduce the level of Electromagnetic Interference (EMI). Mathematical analyses and experiments on supplying symmetrical and asymmetrical multi-level inverters by specifically designed multi-output DC-DC converters have been reported in two journal papers. Another application in which the system performance can be improved by utilization of the ‘current circulating’ switching state is linear-assisted RF amplifiers in communicational receivers. The concept of ‘linear-assisted’ is to divide the signal into two frequency domains: low frequency, which should be amplified by a switching circuit; and the high frequency domain, which should be amplified by a linear amplifier. The objective is to minimize the overall power loss. This research suggests using the current storage capacity of a PBB based converter to increase its bandwidth, and to increase the domain of the switching converter. The PBB converter addresses the industrial demand for a DC-DC converter for the application of auxiliary power supply of a typical electric train. However, after testing the industrial prototype of the PBB converter, there were some voltage and current spikes because of switching. To attenuate this problem without significantly increasing the switching loss, the idea of Active Gate Signalling (AGS) is presented. AGS suggests a smart gate driver that selectively controls the switching process to reduce voltage/current spikes, without unacceptable reduction in the efficiency of switching.

Cascading appearance-based features for visual voice activity detection

The detection of voice activity is a challenging problem, especially when the level of acoustic noise is high. Most current approaches only utilise the audio signal, making them susceptible to acoustic noise. An obvious approach to overcome this is to use the visual modality. The current state-of-the-art visual feature extraction technique is one that uses a cascade of visual features (i.e. 2D-DCT, feature mean normalisation, interstep LDA). In this paper, we investigate the effectiveness of this technique for the task of visual voice activity detection (VAD), and analyse each stage of the cascade and quantify the relative improvement in performance gained by each successive stage. The experiments were conducted on the CUAVE database and our results highlight that the dynamics of the visual modality can be used to good effect to improve visual voice activity detection performance.

A new multilevel converter configuration for high power and high quality applications

The Queensland University of Technology (QUT) allows the presentation of theses for the Degree of Doctor of Philosophy in the format of published or submitted papers, where such papers have been published, accepted or submitted during the period of candidature. This thesis is composed of ten published /submitted papers and book chapters of which nine have been published and one is under review. This project is financially supported by an Australian Research Council (ARC) Discovery Grant with the aim of investigating multilevel topologies for high quality and high power applications, with specific emphasis on renewable energy systems. The rapid evolution of renewable energy within the last several years has resulted in the design of efficient power converters suitable for medium and high-power applications such as wind turbine and photovoltaic (PV) systems. Today, the industrial trend is moving away from heavy and bulky passive components to power converter systems that use more and more semiconductor elements controlled by powerful processor systems. However, it is hard to connect the traditional converters to the high and medium voltage grids, as a single power switch cannot stand at high voltage. For these reasons, a new family of multilevel inverters has appeared as a solution for working with higher voltage levels. Besides this important feature, multilevel converters have the capability to generate stepped waveforms. Consequently, in comparison with conventional two-level inverters, they present lower switching losses, lower voltage stress across loads, lower electromagnetic interference (EMI) and higher quality output waveforms. These properties enable the connection of renewable energy sources directly to the grid without using expensive, bulky, heavy line transformers. Additionally, they minimize the size of the passive filter and increase the durability of electrical devices. However, multilevel converters have only been utilised in very particular applications, mainly due to the structural limitations, high cost and complexity of the multilevel converter system and control. New developments in the fields of power semiconductor switches and processors will favor the multilevel converters for many other fields of application. The main application for the multilevel converter presented in this work is the front-end power converter in renewable energy systems. Diode-clamped and cascade converters are the most common type of multilevel converters widely used in different renewable energy system applications. However, some drawbacks – such as capacitor voltage imbalance, number of components, and complexity of the control system – still exist, and these are investigated in the framework of this thesis. Various simulations using software simulation tools are undertaken and are used to study different cases. The feasibility of the developments is underlined with a series of experimental results. This thesis is divided into two main sections. The first section focuses on solving the capacitor voltage imbalance for a wide range of applications, and on decreasing the complexity of the control strategy on the inverter side. The idea of using sharing switches at the output structure of the DC-DC front-end converters is proposed to balance the series DC link capacitors. A new family of multioutput DC-DC converters is proposed for renewable energy systems connected to the DC link voltage of diode-clamped converters. The main objective of this type of converter is the sharing of the total output voltage into several series voltage levels using sharing switches. This solves the problems associated with capacitor voltage imbalance in diode-clamped multilevel converters. These converters adjust the variable and unregulated DC voltage generated by renewable energy systems (such as PV) to the desirable series multiple voltage levels at the inverter DC side. A multi-output boost (MOB) converter, with one inductor and series output voltage, is presented. This converter is suitable for renewable energy systems based on diode-clamped converters because it boosts the low output voltage and provides the series capacitor at the output side. A simple control strategy using cross voltage control with internal current loop is presented to obtain the desired voltage levels at the output voltage. The proposed topology and control strategy are validated by simulation and hardware results. Using the idea of voltage sharing switches, the circuit structure of different topologies of multi-output DC-DC converters – or multi-output voltage sharing (MOVS) converters – have been proposed. In order to verify the feasibility of this topology and its application, steady state and dynamic analyses have been carried out. Simulation and experiments using the proposed control strategy have verified the mathematical analysis. The second part of this thesis addresses the second problem of multilevel converters: the need to improve their quality with minimum cost and complexity. This is related to utilising asymmetrical multilevel topologies instead of conventional multilevel converters; this can increase the quality of output waveforms with a minimum number of components. It also allows for a reduction in the cost and complexity of systems while maintaining the same output quality, or for an increase in the quality while maintaining the same cost and complexity. Therefore, the asymmetrical configuration for two common types of multilevel converters – diode-clamped and cascade converters – is investigated. Also, as well as addressing the maximisation of the output voltage resolution, some technical issues – such as adjacent switching vectors – should be taken into account in asymmetrical multilevel configurations to keep the total harmonic distortion (THD) and switching losses to a minimum. Thus, the asymmetrical diode-clamped converter is proposed. An appropriate asymmetrical DC link arrangement is presented for four-level diode-clamped converters by keeping adjacent switching vectors. In this way, five-level inverter performance is achieved for the same level of complexity of the four-level inverter. Dealing with the capacitor voltage imbalance problem in asymmetrical diodeclamped converters has inspired the proposal for two different DC-DC topologies with a suitable control strategy. A Triple-Output Boost (TOB) converter and a Boost 3-Output Voltage Sharing (Boost-3OVS) converter connected to the four-level diode-clamped converter are proposed to arrange the proposed asymmetrical DC link for the high modulation indices and unity power factor. Cascade converters have shown their abilities and strengths in medium and high power applications. Using asymmetrical H-bridge inverters, more voltage levels can be generated in output voltage with the same number of components as the symmetrical converters. The concept of cascading multilevel H-bridge cells is used to propose a fifteen-level cascade inverter using a four-level H-bridge symmetrical diode-clamped converter, cascaded with classical two-level Hbridge inverters. A DC voltage ratio of cells is presented to obtain maximum voltage levels on output voltage, with adjacent switching vectors between all possible voltage levels; this can minimize the switching losses. This structure can save five isolated DC sources and twelve switches in comparison to conventional cascade converters with series two-level H bridge inverters. To increase the quality in presented hybrid topology with minimum number of components, a new cascade inverter is verified by cascading an asymmetrical four-level H-bridge diode-clamped inverter. An inverter with nineteen-level performance was achieved. This synthesizes more voltage levels with lower voltage and current THD, rather than using a symmetrical diode-clamped inverter with the same configuration and equivalent number of power components. Two different predictive current control methods for the switching states selection are proposed to minimise either losses or THD of voltage in hybrid converters. High voltage spikes at switching time in experimental results and investigation of a diode-clamped inverter structure raised another problem associated with high-level high voltage multilevel converters. Power switching components with fast switching, combined with hard switched-converters, produce high di/dt during turn off time. Thus, stray inductance of interconnections becomes an important issue and raises overvoltage and EMI issues correlated to the number of components. Planar busbar is a good candidate to reduce interconnection inductance in high power inverters compared with cables. The effect of different transient current loops on busbar physical structure of the high-voltage highlevel diode-clamped converters is highlighted. Design considerations of proper planar busbar are also presented to optimise the overall design of diode-clamped converters.

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.

Cluster-based Intrusion Detection (CBID) architecture for mobile ad hoc networks

The ad hoc networks are vulnerable to attacks due to distributed nature and lack of infrastructure. Intrusion detection systems (IDS) provide audit and monitoring capabilities that offer the local security to a node and help to perceive the specific trust level of other nodes. The clustering protocols can be taken as an additional advantage in these processing constrained networks to collaboratively detect intrusions with less power usage and minimal overhead. Existing clustering protocols are not suitable for intrusion detection purposes, because they are linked with the routes. The route establishment and route renewal affects the clusters and as a consequence, the processing and traffic overhead increases due to instability of clusters. The ad hoc networks are battery and power constraint, and therefore a trusted monitoring node should be available to detect and respond against intrusions in time. This can be achieved only if the clusters are stable for a long period of time. If the clusters are regularly changed due to routes, the intrusion detection will not prove to be effective. Therefore, a generalized clustering algorithm has been proposed that can run on top of any routing protocol and can monitor the intrusions constantly irrespective of the routes. The proposed simplified clustering scheme has been used to detect intrusions, resulting in high detection rates and low processing and memory overhead irrespective of the routes, connections, traffic types and mobility of nodes in the network. Clustering is also useful to detect intrusions collaboratively since an individual node can neither detect the malicious node alone nor it can take action against that node on its own.

Performance analysis of unified enterprise application security framework

Unified Enterprise application security is a new emerging approach for providing protection against application level attacks. Conventional application security approach that consists of embedding security into each critical application leads towards scattered security mechanism that is not only difficult to manage but also creates security loopholes. According to the CSIIFBI computer crime survey report, almost 80% of the security breaches come from authorized users. In this paper, we have worked on the concept of unified security model, which manages all security aspect from a single security window. The basic idea is to keep business functionality separate from security components of the application. Our main focus was on the designing of frame work for unified layer which supports single point of policy control, centralize logging mechanism, granular, context aware access control, and independent from any underlying authentication technology and authorization policy.

TCP-DR an effective protocol for infrastructure based wireless networks

TCP is a dominant protocol for consistent communication over the internet. It provides flow, congestion and error control mechanisms while using wired reliable networks. Its congestion control mechanism is not suitable for wireless links where data corruption and its lost rate are higher. The physical links are transparent from TCP that takes packet losses due to congestion only and initiates congestion handling mechanisms by reducing transmission speed. This results in wasting already limited available bandwidth on the wireless links. Therefore, there is no use to carry out research on increasing bandwidth of the wireless links until the available bandwidth is not optimally utilized. This paper proposed a hybrid scheme called TCP Detection and Recovery (TCP-DR) to distinguish congestion, corruption and mobility related losses and then instructs the data sending host to take appropriate action. Therefore, the link utilization is optimal while losses are either due to high bit error rate or mobility.

Using accelerometer, high sample rate GPS and magnetometer data to develop a cattle movement and behaviour model

The study described in this paper developed a model of animal movement, which explicitly recognised each individual as the central unit of measure. The model was developed by learning from a real dataset that measured and calculated, for individual cows in a herd, their linear and angular positions and directional and angular speeds. Two learning algorithms were implemented: a Hidden Markov model (HMM) and a long-term prediction algorithm. It is shown that a HMM can be used to describe the animal's movement and state transition behaviour within several “stay” areas where cows remained for long periods. Model parameters were estimated for hidden behaviour states such as relocating, foraging and bedding. For cows’ movement between the “stay” areas a long-term prediction algorithm was implemented. By combining these two algorithms it was possible to develop a successful model, which achieved similar results to the animal behaviour data collected. This modelling methodology could easily be applied to interactions of other animal species.

High dynamic range stereo vision for outdoor mobile robotics

We present a technique for high-dynamic range stereo for outdoor mobile robot applications. Stereo pairs are captured at a number of different exposures (exposure bracketing), and combined by projecting the 3D points into a common coordinate frame, and building a 3D occupancy map. We present experimental results for static scenes with constant and dynamic lighting as well as outdoor operation with variable and high contrast lighting conditions.

A secure architecture for Australia’s index based e-health environment

This paper proposes a security architecture for the basic cross indexing systems emerging as foundational structures in current health information systems. In these systems unique identifiers are issued to healthcare providers and consumers. In most cases, such numbering schemes are national in scope and must therefore necessarily be used via an indexing system to identify records contained in pre-existing local, regional or national health information systems. Most large scale electronic health record systems envisage that such correlation between national healthcare identifiers and pre-existing identifiers will be performed by some centrally administered cross referencing, or index system. This paper is concerned with the security architecture for such indexing servers and the manner in which they interface with pre-existing health systems (including both workstations and servers). The paper proposes two required structures to achieve the goal of a national scale, and secure exchange of electronic health information, including: (a) the employment of high trust computer systems to perform an indexing function, and (b) the development and deployment of an appropriate high trust interface module, a Healthcare Interface Processor (HIP), to be integrated into the connected workstations or servers of healthcare service providers. This proposed architecture is specifically oriented toward requirements identified in the Connectivity Architecture for Australia’s e-health scheme as outlined by NEHTA and the national e-health strategy released by the Australian Health Ministers.

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.