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.

Experiments with underwater robot localization and tracking

This paper describes a novel experiment in which two very different methods of underwater robot localization are compared. The first method is based on a geometric approach in which a mobile node moves within a field of static nodes, and all nodes are capable of estimating the range to their neighbours acoustically. The second method uses visual odometry, from stereo cameras, by integrating scaled optical flow. The fundamental algorithmic principles of each localization technique is described. We also present experimental results comparing acoustic localization with GPS for surface operation, and a comparison of acoustic and visual methods for underwater operation.

Experiments in learning helicopter control from a pilot

This paper details the development of a machine learning system which uses the helicopter state and the actions of an instructing pilot to synthesise helicopter control modules online. Aggressive destabilisation/restabilisation sequences are used for training, such that a wide state space envelope is covered during training. The performance of heading, roll, pitch, height and lateral velocity control learning is presented using our Xcell 60 experimental platform. The helicopter is demonstrated to be stabilised on all axes using the “learning from a pilot” technique. To our knowledge, this is the first time a “learning from a pilot” technique has been successfully applied to all axes.

Specifying and enforcing a fine-grained information flow policy : model and experiments

In this paper we present a model for defining and enforcing a fine-grained information flow policy. We describe how the policy can be enforced on a typical computer and present experiments using the proposed model. A key feature of the model is that it allows the expression of rules which detail precisely which information elements are allowed to mix together. For example, the model allows the expression of a policy which forbids a doctor from mixing the personal medical details of the patients. The enforcement mechanisms tracks and records information flows within the system so that dynamic changes to the policy can be made with respect to information elements which may have propagated to different locations in the system.

Algebraic analysis of small scale LEX-BES

This paper examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this paper, experiments were conducted to find solution of the equation system describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the author knows, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

Clustered blind beamforming from ad-hoc microphone arrays

Microphone arrays have been used in various applications to capture conversations, such as in meetings and teleconferences. In many cases, the microphone and likely source locations are known \emph{a priori}, and calculating beamforming filters is therefore straightforward. In ad-hoc situations, however, when the microphones have not been systematically positioned, this information is not available and beamforming must be achieved blindly. In achieving this, a commonly neglected issue is whether it is optimal to use all of the available microphones, or only an advantageous subset of these. This paper commences by reviewing different approaches to blind beamforming, characterising them by the way they estimate the signal propagation vector and the spatial coherence of noise in the absence of prior knowledge of microphone and speaker locations. Following this, a novel clustered approach to blind beamforming is motivated and developed. Without using any prior geometrical information, microphones are first grouped into localised clusters, which are then ranked according to their relative distance from a speaker. Beamforming is then performed using either the closest microphone cluster, or a weighted combination of clusters. The clustered algorithms are compared to the full set of microphones in experiments on a database recorded on different ad-hoc array geometries. These experiments evaluate the methods in terms of signal enhancement as well as performance on a large vocabulary speech recognition task.

Experiments in visual localisation around underwater structures

Localisation of an AUV is challenging and a range of inspection applications require relatively accurate positioning information with respect to submerged structures. We have developed a vision based localisation method that uses a 3D model of the structure to be inspected. The system comprises a monocular vision system, a spotlight and a low-cost IMU. Previous methods that attempt to solve the problem in a similar way try and factor out the effects of lighting. Effects, such as shading on curved surfaces or specular reflections, are heavily dependent on the light direction and are difficult to deal with when using existing techniques. The novelty of our method is that we explicitly model the light source. Results are shown of an implementation on a small AUV in clear water at night.

Finding a way through the ethical and legal maze : withdrawing medical treatment and euthanasia

This article examines Finnis' and Keown's claim that the intention/foresight distinction should be used as the basis for the lawfulness of withholding and withdrawing medical treatment, rather than the act/omission distinction which is currently used. I argue that whilst the intention/foresight distinction is sound and can apply to palliative pain relief hastening death, it cannot be applied to withholding and withdrawing medical treatment. Instead, the act/omission distinction remains the better basis for the lawfulness of withholding and withdrawal, and law reform is consequently unnecessary.

Algebraic analysis of small Scale LEX-BES

This work examines the algebraic cryptanalysis of small scale variants of the LEX-BES. LEX-BES is a stream cipher based on the Advanced Encryption Standard (AES) block cipher. LEX is a generic method proposed for constructing a stream cipher from a block cipher, initially introduced by Biryukov at eSTREAM, the ECRYPT Stream Cipher project in 2005. The Big Encryption System (BES) is a block cipher introduced at CRYPTO 2002 which facilitates the algebraic analysis of the AES block cipher. In this article, experiments were conducted to find solutions of equation systems describing small scale LEX-BES using Gröbner Basis computations. This follows a similar approach to the work by Cid, Murphy and Robshaw at FSE 2005 that investigated algebraic cryptanalysis on small scale variants of the BES. The difference between LEX-BES and BES is that due to the way the keystream is extracted, the number of unknowns in LEX-BES equations is fewer than the number in BES. As far as the authors know, this attempt is the first at creating solvable equation systems for stream ciphers based on the LEX method using Gröbner Basis computations.

Reverse immigration

This book (256 pages, written in Korean) is a critical essay that reviews, questions, and criticises Korean and Eastern immigrants’ thinking and behaviour styles in Australia from their cultural perspectives, and discuss and proposes a creative cultural dimension for their better life in a multicultural context. Multiculturalism is not supportive of Eastern cultures because of individualistic collection of cultures, while transculturalism facilitates nurture of their culture in a community-oriented way within multicultural circumstances. Korean and Eastern immigrants, sharing oriental cultural systems and values, should approach to the Australian multicultural context with transculturalism which allows creating new cultural values in collaboration with and by participation into local communities. ------------------------------------------------------------ Many Eastern immigrants live in their own ethnic communities without or less interacting with Australian (communities). The author defines this phenomenon as “reverse immigration”. Reverse immigration refers to re-immigrating to their ethnic community in Australia or to their birth country despite they did not anticipate that this would happen to them before immigration to Australia. The author argues that Easterners’ collectivistic culture often devalues individuality and vice versa. Cultural clash between West and East often forces the immigrants to choose reverse immigration because of their lack of understanding of Western culture and their cultural characteristics such as low individuality, high power distance, and high uncertainty avoidance. For example, a vague boundary between individualist and collectivist in a collectivistic context (within their ethnic group) often leads to maladjustment to local communities and enhancement of cultural conservatism. The author proposes that the cultural clash can be overcome by cross-cultural activities named “transculturalism”. To Eastern immigrants, transculturalism can be achieved by acculturation of their two predominant cultures, the third-person perspective and generalised others. In a multicultural context, the former refers to the ability to share another person's feelings and emotions as if they were your own, and the latter does the ability to manage community and public expectations. When both cultural values are used for quality interactions between East and West, they allow Eastern immigrants to be more creative and critical and Australian to be more socially inclusive and culturally tolerant. With these discussions, the author discusses cultural differences throughout the book with four topics (chapters) and proposes transculturalism as a solution to the reverse immigration. ------------------------------------------------------------ Chapter 1 criticises Koreans’ attitudes and methods towards learning English that is less pragmatic and practical, but more likely to be a scholarly study. The author explains that Koreans’ non-pragmatic towards learning English has been firmly built based on their traditional systems and values that Koreans view English as a discipline and an aim of academic achievements rather than a means of communication. Within their cultural context, English can be perceived as more than a language, but something like vastly superior to their language and culture. Their collectivistic culture regards English as an unreachable and heterogeneous one that may threaten their cultural identity, so that “scholarly studying” is only the way to achieve (not learn) it. This discourages the immigrants to engage and involve in daily dialogues by “using” English as a second language. The author further advises the readers to be aware of Eastern collectivistic culture in communication and interaction that sometimes completely reverses private and public topics in a Western context. This leads them to feel that they have no content to talk to natives. ------------------------------------------------------------ Chapter 2 compares between Korea and Australia in terms of their educational systems and values, and proposes how Eastern overseas students can achieve critical and creative thinking within a Western educational setting. Interestingly, this chapter includes an explanation of why Eastern overseas students easily fail assessments including essay writing, oral presentations and discussions. One of the reasons the author explains is that Eastern students are not familiar to criticise others and think creatively, especially when they recognise that their words and ideas may harm the collectivistic harmony. Western educational systems focuses on enhancement of individuality such as self-confidence, self-esteem, and self-expression, while Eastern educational systems foster group-oriented values such as interpersonal relationship, and strong moral and spiritual values. Yet, the author argues that the collectivistic approach to criticism and creativity is often more critical and creative than Western individuals when they know what they are supposed to do for a group (or a community). Therefore, Eastern students need to think their cultural merits and demerits by using an individual perspective rather than generalised others’ perspective. The latter often discourages individual participation in a community, and the generalised others in a Western culture is weaker than Eastern. Furthermore, Western educational systems do not educate students to transform (loose) their individuality to fit into a group or a community. Rather they cultivate individuality for community prosperity. ------------------------------------------------------------ Chapter 3 introduces various cases of reverse immigration in workplaces that many immigrants return to their country or their ethnic community after many trials for acculturation. Reverse immigration is unexpected and not planned before immigration, so that its emotional embarrassment increases such severe social loneliness. Most Eastern immigrant workers have tried to adjust themselves in this new cultural environment at the early stages of immigration. However, their cultural features of collectivism, high power distance, high uncertainty avoidance, and long-term oriented cultures suppress individual initiative and eliminate the space for experiments in ways of acculturation. The author argues that returning to their ethnic community (physically and psychologically) leads to two significant problems: their distorted parenting and becoming more conservatives. The former leads the first generation of immigrants to pressure their children to pursue extrinsic or materialist values, such as financial success, fame and physical appearance, rather than on intrinsic values, while the latter refers to their isolated conservative characters because of their remoteness from the changes of their own country. The author also warns that their ethnic and religious groups actively strengthens immigrants’ social loneliness and systematically discourages immigrants’ interests and desire to be involving into local communities. The ethnic communities and leaders have not been interacting with Australian local communities and, as a result, are eager to conserve outdated cultural systems values. Even they have a tendency to weed out those people who wish to settle down within Australian local communities. They believe that those people can threaten their community’s survival and continuity. ------------------------------------------------------------ Chapter 4 titled multiculturalism argues that Korean and Eastern immigrants should more precisely understand Australia as a multicultural society in a way of collaboratively creating new cultural values. The author introduces multiculturalism with its definitions and history in Australia and argues the limitations of multiculturalism from an Easterner’s perspective. With well known tragedies of the second generations of U.S. immigrants, Cho Seung-Hui, a university student, massacred 32 people on the Virginia Tech before committing suicide and Hidal Hassan, an Army psychiatrist, killed 13 people at Fort Hood and the responses of ethnic community, the author explains that their mental illness may be derived from their parents’ (or ethnic group) culturally isolated attitude and socially static viewpoint of U.S. (Western system and values). The author insists that multiculturalism may restrict Eastern immigrants’ engagement and involvement in local communities. Multiculturalism has been systematically and historically developed based on Western systems and cultural values. In other words, multiculturalism requires high self-confidence and self-esteem that Eastern immigrants less prioritise them. It has been generally known that Easterners put more weight on human relationship than Westerners, but the author claims that this is not true. Within an individualistic culture, Westerners are more interested in building person-to-person connections and relationships. While Easterners are more interested in how individuals can achieve a sense of belonging within a group and a community. Therefore, multiculturalism is an ideology which forces Eastern immigrants to discard their strong desire to be part of a group and does not give a sense of belonging. In a consequence, the author advises that Eastern immigrants should aim towards “transculturalism” which allows them to actively participate in and contribute to their multicultural community. Transculturalism does not ask Easterners to discard their cultural values, but enables them to be a collectivistic individualist (a community leader) who is capable of developing new cultural values in a more creative and productive way. Furthermore, transculturalism encourages Western Australians in a multicultural context to collaborate with ethnic minorities to build a better community.

The mechanical heterogeneity of the hard callus influences local tissue strains during bone healing : a finite element study based on sheep experiments

During secondary fracture healing, various tissue types including new bone are formed. The local mechanical strains play an important role in tissue proliferation and differentiation. To further our mechanobiological understanding of fracture healing, a precise assessment of local strains is mandatory. Until now, static analyses using Finite Elements (FE) have assumed homogenous material properties. With the recent quantification of both the spatial tissue patterns (Vetter et al., 2010) and the development of elastic modulus of newly formed bone during healing (Manjubala et al., 2009), it is now possible to incorporate this heterogeneity. Therefore, the aim of this study is to investigate the effect of this heterogeneity on the strain patterns at six successive healing stages. The input data of the present work stemmed from a comprehensive cross-sectional study of sheep with a tibial osteotomy (Epari et al., 2006). In our FE model, each element containing bone was described by a bulk elastic modulus, which depended on both the local area fraction and the local elastic modulus of the bone material. The obtained strains were compared with the results of hypothetical FE models assuming homogeneous material properties. The differences in the spatial distributions of the strains between the heterogeneous and homogeneous FE models were interpreted using a current mechanobiological theory (Isakson et al., 2006). This interpretation showed that considering the heterogeneity of the hard callus is most important at the intermediate stages of healing, when cartilage transforms to bone via endochondral ossification.

The Canadian ‘Model Forest’ approach : a way forward for Tasmania?

Forest policy and forestry management in Tasmania have undergone a number of changes in the last thirty years, many explicitly aimed at improving industry sustainability, job security, and forest biodiversity conservation. Yet forestry remains a contentious issue in Tasmania, due to a number of interacting factors, most significant of which is the prevalence of a ‘command and control’ governance approach by policymakers and managers. New approaches such as multiple-stakeholder decision-making, adaptive management, and direct public participation in policymaking are needed. Such an approach has been attempted in Canada in the last decade, through the Canadian Model Forest Program, and may be suitable for Tasmania. This paper seeks to describe what the Canadian Model Forest approach is, how it may be implemented in Tasmania, and what role it may play in the shift to a new forestry paradigm. Until such a paradigm shift occurs contentions and confrontations are likely to continue.

Design of experiments for bivariate binary responses modelled by Copula functions

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

Sponsorship-linked marketing: The role of articulation in memory

Corporate sponsorship of events contributes significantly to marketing aims, including brand awareness as measured by recall and recognition of sponsor‐event pairings. Unfortunately, resultant advantages accrue disproportionately to brands having a natural or congruent fit with the available sponsorship properties. In three cued‐recall experiments, the effect of articulation of sponsorship fit on memory for sponsor‐event pairings is examined. While congruent sponsors have a natural memory advantage, results demonstrate that memory improvements via articulation are possible for incongruent sponsor‐event pairings. These improvements are, however, affected by the presence of competitor brands and the way in which memory is accessed.

Using a knowledge-based approach : the way healthy communities make decisions

The planning for Knowledge Cities faces significant challenges due to the lack of effective information tools. These challenges are magnified while planning healthy communities. The Australian Health Information Council (AHIC) concluded in its last report that health information needs to be shared more effectively (AHIC, 2008). Some research justifies the use of Decision Support Systems (DSS) as an E-planning tool, particularly in the context of healthy communities. However, very limited research has been conducted in this area to date, especially in terms of evaluating the impact of these tools on decision-makers within the health planning practice. The paper presents the methodological instruments which were developed to measure the impact of the E-planning tool (i.e., Health Decision Support System [HDSS])) on a group of health planners, namely, the Logan Beaudesert Health Coalition (LBHC). The paper is focused on the culture in which decisions were made before and after the intervention of the HDSS. Subsequently, the paper presents the observed impact of the HDSS tool, to facilitate a knowledge-based decision-making approach. This study is an attempt to make some contribution to the Knowledge Cities literature in the context of planning healthy communities by adopting E-planning tools.