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.

A simple and systematic approach to assigning Denavit-Hartenberg Parameters

This paper presents a simple and intuitive approach to determining the kinematic parameters of a serial-link robot in Denavit– Hartenberg (DH) notation. Once a manipulator’s kinematics is parameterized in this form, a large body of standard algorithms and code implementations for kinematics, dynamics, motion planning, and simulation are available. The proposed method has two parts. The first is the “walk through,” a simple procedure that creates a string of elementary translations and rotations, from the user-defined base coordinate to the end-effector. The second step is an algebraic procedure to manipulate this string into a form that can be factorized as link transforms, which can be represented in standard or modified DH notation. The method allows for an arbitrary base and end-effector coordinate system as well as an arbitrary zero joint angle pose. The algebraic procedure is amenable to computer algebra manipulation and a Java program is available as supplementary downloadable material.

Damage detection for truss bridge structures using correlation-based structural modal strain energy

This paper presents the feasibility of using structural modal strain energy as a parameter employed in correlation- based damage detection method for truss bridge structures. It is an extension of the damage detection method adopting multiple damage location assurance criterion. In this paper, the sensitivity of modal strain energy to damage obtained from the analytical model is incorporated into the correlation objective function. Firstly, the sensitivity matrix of modal strain energy to damage is conducted offline, and for an arbitrary damage case, the correlation coefficient (objective function) is calculated by multiplying the sensitivity matrix and damage vector. Then, a genetic algorithm is used to iteratively search the damage vector maximising the correlation between the corresponding modal strain energy change (hypothesised) and its counterpart in measurement. The proposed method is simulated and compared with the conventional methods, e.g. frequency-error method, coordinate modal assurance criterion and multiple damage location assurance criterion using mode shapes on a numerical truss bridge structure. The result demonstrates the modal strain energy correlation method is able to yield acceptable damage detection outcomes with less computing efforts, even in a noise contaminated condition.

An analysis of the RC4 family of stream ciphers against algebraic attacks

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.

Novel analytical and numerical methods for solving fractional dynamical systems

During the past three decades, the subject of fractional calculus (that is, calculus of integrals and derivatives of arbitrary order) has gained considerable popularity and importance, mainly due to its demonstrated applications in numerous diverse and widespread fields in science and engineering. For example, fractional calculus has been successfully applied to problems in system biology, physics, chemistry and biochemistry, hydrology, medicine, and finance. In many cases these new fractional-order models are more adequate than the previously used integer-order models, because fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes that are governed by anomalous diffusion. Hence, there is a growing need to find the solution behaviour of these fractional differential equations. However, the analytic solutions of most fractional differential equations generally cannot be obtained. As a consequence, approximate and numerical techniques are playing an important role in identifying the solution behaviour of such fractional equations and exploring their applications. The main objective of this thesis is to develop new effective numerical methods and supporting analysis, based on the finite difference and finite element methods, for solving time, space and time-space fractional dynamical systems involving fractional derivatives in one and two spatial dimensions. A series of five published papers and one manuscript in preparation will be presented on the solution of the space fractional diffusion equation, space fractional advectiondispersion equation, time and space fractional diffusion equation, time and space fractional Fokker-Planck equation with a linear or non-linear source term, and fractional cable equation involving two time fractional derivatives, respectively. One important contribution of this thesis is the demonstration of how to choose different approximation techniques for different fractional derivatives. Special attention has been paid to the Riesz space fractional derivative, due to its important application in the field of groundwater flow, system biology and finance. We present three numerical methods to approximate the Riesz space fractional derivative, namely the L1/ L2-approximation method, the standard/shifted Gr¨unwald method, and the matrix transform method (MTM). The first two methods are based on the finite difference method, while the MTM allows discretisation in space using either the finite difference or finite element methods. Furthermore, we prove the equivalence of the Riesz fractional derivative and the fractional Laplacian operator under homogeneous Dirichlet boundary conditions – a result that had not previously been established. This result justifies the aforementioned use of the MTM to approximate the Riesz fractional derivative. After spatial discretisation, the time-space fractional partial differential equation is transformed into a system of fractional-in-time differential equations. We then investigate numerical methods to handle time fractional derivatives, be they Caputo type or Riemann-Liouville type. This leads to new methods utilising either finite difference strategies or the Laplace transform method for advancing the solution in time. The stability and convergence of our proposed numerical methods are also investigated. Numerical experiments are carried out in support of our theoretical analysis. We also emphasise that the numerical methods we develop are applicable for many other types of fractional partial differential equations.

Automatic speaker recognition under adverse conditions

Speaker verification is the process of verifying the identity of a person by analysing their speech. There are several important applications for automatic speaker verification (ASV) technology including suspect identification, tracking terrorists and detecting a person’s presence at a remote location in the surveillance domain, as well as person authentication for phone banking and credit card transactions in the private sector. Telephones and telephony networks provide a natural medium for these applications. The aim of this work is to improve the usefulness of ASV technology for practical applications in the presence of adverse conditions. In a telephony environment, background noise, handset mismatch, channel distortions, room acoustics and restrictions on the available testing and training data are common sources of errors for ASV systems. Two research themes were pursued to overcome these adverse conditions: Modelling mismatch and modelling uncertainty. To directly address the performance degradation incurred through mismatched conditions it was proposed to directly model this mismatch. Feature mapping was evaluated for combating handset mismatch and was extended through the use of a blind clustering algorithm to remove the need for accurate handset labels for the training data. Mismatch modelling was then generalised by explicitly modelling the session conditions as a constrained offset of the speaker model means. This session variability modelling approach enabled the modelling of arbitrary sources of mismatch, including handset type, and halved the error rates in many cases. Methods to model the uncertainty in speaker model estimates and verification scores were developed to address the difficulties of limited training and testing data. The Bayes factor was introduced to account for the uncertainty of the speaker model estimates in testing by applying Bayesian theory to the verification criterion, with improved performance in matched conditions. Modelling the uncertainty in the verification score itself met with significant success. Estimating a confidence interval for the "true" verification score enabled an order of magnitude reduction in the average quantity of speech required to make a confident verification decision based on a threshold. The confidence measures developed in this work may also have significant applications for forensic speaker verification tasks.

Learning to win process-control games watching game-masters

The present paper focuses on some interesting classes of process-control games, where winning essentially means successfully controlling the process. A master for one of these games is an agent who plays a winning strategy. In this paper we investigate situations in which even a complete model (given by a program) of a particular game does not provide enough information to synthesize—even incrementally—a winning strategy. However, if in addition to getting a program, a machine may also watch masters play winning strategies, then the machine is able to incrementally learn a winning strategy for the given game. Studied are successful learning from arbitrary masters and from pedagogically useful selected masters. It is shown that selected masters are strictly more helpful for learning than are arbitrary masters. Both for learning from arbitrary masters and for learning from selected masters, though, there are cases where one can learn programs for winning strategies from masters but not if one is required to learn a program for the master's strategy itself. Both for learning from arbitrary masters and for learning from selected masters, one can learn strictly more by watching m+1 masters than one can learn by watching only m. Last, a simulation result is presented where the presence of a selected master reduces the complexity from infinitely many semantic mind changes to finitely many syntactic ones.

Estimation of the depth focus from wavefront measurements

It is possible to estimate the depth of focus (DOF) of the eye directly from wavefront measurements using various retinal image quality metrics (IQMs). In such methods, DOF is defined as the range of defocus error that degrades the retinal image quality calculated from IQMs to a certain level of the maximum value. Although different retinal image quality metrics are used, currently there have been two arbitrary threshold levels adopted, 50% and 80%. There has been limited study of the relationship between these threshold levels and the actual measured DOF. We measured the subjective DOF in a group of 17 normal subjects, and used through-focus augmented visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM. For each subject, a VSOTF threshold level was derived that would match the subjectively measured DOF. Significant correlation was found between the subject’s estimated threshold level and the HOA RMS (Pearson’s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual’s DOF from a single measurement of their wavefront aberrations.

Color and texture feature fusion using kernel PCA with application to object-based vegetation species classification

A good object representation or object descriptor is one of the key issues in object based image analysis. To effectively fuse color and texture as a unified descriptor at object level, this paper presents a novel method for feature fusion. Color histogram and the uniform local binary patterns are extracted from arbitrary-shaped image-objects, and kernel principal component analysis (kernel PCA) is employed to find nonlinear relationships of the extracted color and texture features. The maximum likelihood approach is used to estimate the intrinsic dimensionality, which is then used as a criterion for automatic selection of optimal feature set from the fused feature. The proposed method is evaluated using SVM as the benchmark classifier and is applied to object-based vegetation species classification using high spatial resolution aerial imagery. Experimental results demonstrate that great improvement can be achieved by using proposed feature fusion method.

Ethical fashion : the human stories driving a fashion movement

This paper examines and compares two stories, the novel Helen Fleetwood (Elizabeth, 1841) and the film China Blue (Teddy Bear Films, 2005), in relation to the Ethical Fashion movement. In 2005, more than 50 designers from around the world took part in The Ethical Fashion Show in Paris. This movement dictates that designers ensure that their garments are produced in an ethical manner, rather than support the ‘sweatshop’ environments of some industrialists determined to make a profit at the expense of workers rights. The momentum of the Ethical Fashion movement suggests that it is possible for fashion to be ethical, desirable and profitable in the 21st century. In 1841, after extensive research, Charlotte Elizabeth Tonna (using the pseudonym Charlotte Elizabeth) began to write about the atrocities of the factory system in industrialised England. Her novel, Helen Fleetwood, is one of the earliest examples of this kind of work, providing the reader with an extensive insight into the life of English factory workers in the mid-19th century. The story is about the Widow Green and her orphan dependents who are led, through circumstance, to leave their rural home and take up employment in the cotton mills of Manchester, with the hope of having an independent existence. Instead they discover the realities of factory life – extremely long hours, unsafe conditions, poor wages and a steady decline into extreme poverty. In his film China Blue (Teddy Bear Films, 2005), director Micha X. Peled tells an alarmingly similar tale set in 21st century China. This ‘docu-drama’ (a recreation from actual interviews and diary entries) tells the story of ‘Little Jasmine’ who leaves her family’s farm to pursue an independent life in Southern China’s manufacturing district. It is not long before the realities of modern factory life are revealed to the teenage ‘heroine’ – crowded dormitories, long working hours, arbitrary fines and wages that do not compare with those of workers in the Western world. While much of the human story remains unchanged, there have been significant improvements in technology and safety in the last 165 years that result in the reality that not all clothing manufacture is performed in ‘sweatshop’ conditions. After a recent visit to a manufacturing plant in China, consultation with peers in the industry and having worked in the Australian fashion industry for many years, the author compares these stories with her own experiences.

Heat effects of promoters and determination of burn criterion in promoted combustion testing

Promoted ignition testing (NASA) Test 17) [1] is used to determine the relative flammability of metal rods in oxygen-enriched atmospheres. A promotor is used to ignite a metal sample rod, initiating sample burning. If a predetermined length of the sample burns, beyond the promotor, the material is considered flammable at the condition tested. Historically, this burn length has been somewhat arbitrary. Experiments were performed to better understand this test by obtaining insight into the effect a burning promotor has on the preheating of a test sample. Test samples of several metallic materials were prepared and coupled to fast-responding thermocouples along their length. Thermocouple measurements and test video were synchronized to determine temperature increase with respect to time and length along each test sample. A recommended flammability burn length, based on a sample preheat of 500 degrees fahrenheit, was determined based on the preheated zone measured from these tests. This length was determined to be 30 mm (1.18 in.). Validation of this length and its rationale are presented.

Discovering characteristics of stochastic collections of process models

Process models in organizational collections are typically modeled by the same team and using the same conventions. As such, these models share many characteristic features like size range, type and frequency of errors. In most cases merely small samples of these collections are available due to e.g. the sensitive information they contain. Because of their sizes, these samples may not provide an accurate representation of the characteristics of the originating collection. This paper deals with the problem of constructing collections of process models, in the form of Petri nets, from small samples of a collection for accurate estimations of the characteristics of this collection. Given a small sample of process models drawn from a real-life collection, we mine a set of generation parameters that we use to generate arbitrary-large collections that feature the same characteristics of the original collection. In this way we can estimate the characteristics of the original collection on the generated collections.We extensively evaluate the quality of our technique on various sample datasets drawn from both research and industry.

Punitiveness and the criminalisation of the other : State wards, unlawful non-citizens and Indigenous youth

This paper explores the genealogies of bio-power that cut across punitive state interventions aimed at regulating or normalising several distinctive ‘problem’ or ‘suspect’ deviant populations, such as state wards, non-lawful citizens and Indigenous youth. It begins by making some general comments about the theoretical approach to bio-power taken in this paper. It then outlines the distinctive features of bio-power in Australia and how these intersected with the emergence of penal welfarism to govern the unruly, unchaste, unlawful, and the primitive. The paper draws on three examples to illustrate the argument – the gargantuan criminalisation rates of Aboriginal youth, the history of incarcerating state wards in state institutions, and the mandatory detention of unlawful non-citizens and their children. The construction of Indigenous people as a dangerous presence, alongside the construction of the unruly neglected children of the colony — the larrikin descendants of convicts as necessitating special regimes of internal controls and institutions, found a counterpart in the racial and other exclusionary criteria operating through immigration controls for much of the twentieth century. In each case the problem child or population was expelled from the social body through forms of bio-power, rationalised as strengthening, protecting or purifying the Australian population.

Using text-spotting to query the world

The world we live in is well labeled for the benefit of humans but to date robots have made little use of this resource. In this paper we describe a system that allows robots to read and interpret visible text and use it to understand the content of the scene. We use a generative probabilistic model that explains spotted text in terms of arbitrary search terms. This allows the robot to understand the underlying function of the scene it is looking at, such as whether it is a bank or a restaurant. We describe the text spotting engine at the heart of our system that is able to detect and parse wild text in images, and the generative model, and present results from images obtained with a robot in a busy city setting.

User profiling based on folksonomy information in Web 2.0 for personalized recommender systems

Information overload has become a serious issue for web users. Personalisation can provide effective solutions to overcome this problem. Recommender systems are one popular personalisation tool to help users deal with this issue. As the base of personalisation, the accuracy and efficiency of web user profiling affects the performances of recommender systems and other personalisation systems greatly. In Web 2.0, the emerging user information provides new possible solutions to profile users. Folksonomy or tag information is a kind of typical Web 2.0 information. Folksonomy implies the users‘ topic interests and opinion information. It becomes another source of important user information to profile users and to make recommendations. However, since tags are arbitrary words given by users, folksonomy contains a lot of noise such as tag synonyms, semantic ambiguities and personal tags. Such noise makes it difficult to profile users accurately or to make quality recommendations. This thesis investigates the distinctive features and multiple relationships of folksonomy and explores novel approaches to solve the tag quality problem and profile users accurately. Harvesting the wisdom of crowds and experts, three new user profiling approaches are proposed: folksonomy based user profiling approach, taxonomy based user profiling approach, hybrid user profiling approach based on folksonomy and taxonomy. The proposed user profiling approaches are applied to recommender systems to improve their performances. Based on the generated user profiles, the user and item based collaborative filtering approaches, combined with the content filtering methods, are proposed to make recommendations. The proposed new user profiling and recommendation approaches have been evaluated through extensive experiments. The effectiveness evaluation experiments were conducted on two real world datasets collected from Amazon.com and CiteULike websites. The experimental results demonstrate that the proposed user profiling and recommendation approaches outperform those related state-of-the-art approaches. In addition, this thesis proposes a parallel, scalable user profiling implementation approach based on advanced cloud computing techniques such as Hadoop, MapReduce and Cascading. The scalability evaluation experiments were conducted on a large scaled dataset collected from Del.icio.us website. This thesis contributes to effectively use the wisdom of crowds and expert to help users solve information overload issues through providing more accurate, effective and efficient user profiling and recommendation approaches. It also contributes to better usages of taxonomy information given by experts and folksonomy information contributed by users in Web 2.0.