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 hybrid genetic algorithm for the optimal constrained web service selection problem in web service composition

Web service composition is an important problem in web service based systems. It is about how to build a new value-added web service using existing web services. A web service may have many implementations, all of which have the same functionality, but may have different QoS values. Thus, a significant research problem in web service composition is how to select a web service implementation for each of the web services such that the composite web service gives the best overall performance. This is so-called optimal web service selection problem. There may be mutual constraints between some web service implementations. Sometimes when an implementation is selected for one web service, a particular implementation for another web service must be selected. This is so called dependency constraint. Sometimes when an implementation for one web service is selected, a set of implementations for another web service must be excluded in the web service composition. This is so called conflict constraint. Thus, the optimal web service selection is a typical constrained ombinatorial optimization problem from the computational point of view. This paper proposes a new hybrid genetic algorithm for the optimal web service selection problem. The hybrid genetic algorithm has been implemented and evaluated. The evaluation results have shown that the hybrid genetic algorithm outperforms other two existing genetic algorithms when the number of web services and the number of constraints are large.

ERP systems implementation and organizational culture : the case of Jordan

Jordan is adopting Enterprise Resource Planning (ERP) systems in both its public and private sectors. Jordan's emerging private sector has historically close ties to the public sector; though a global market orientation requires a shift in its organizational culture. ERPs however embed business processes which do not necessarily fit with traditional cultural practices, and implementation success is not assured. This study looks at the perceptions of both public and private sector ERP implementations in Jordan and assesses these on various measures of success. There were few differences between public and private sectors, but the benefits actually realized in Jordanian ERPs fell short of claims made for the technology in other cultures.

secFleck: A Public Key Technology Platform for Wireless Sensor Networks

We describe the design and implementation of a public-key platform, secFleck, based on a commodity Trusted Platform Module (TPM) chip that extends the capability of a standard node. Unlike previous software public-key implementations this approach provides E- Commerce grade security; is computationally fast, energy efficient; and has low financial cost — all essential attributes for secure large-scale sen- sor networks. We describe the secFleck message security services such as confidentiality, authenticity and integrity, and present performance re- sults including computation time, energy consumption and cost. This is followed by examples, built on secFleck, of symmetric key management, secure RPC and secure software update.

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.

Enterprise systems in universities : a teaching case

This teaching case aims to contribute to understanding the phenomenon of Enterprise Systems (ES) implementations in universities. Through this case, students will gain understanding of the importance of ‘contextual elements’ for large scale information systems (IS) implementations, in particular ES. This teaching case illustrates how these contextual factors contribute to the success or failure of such implementations, and how they can influence the decisions that dictate the lifecycle of such systems. The case describes ES implementations at a leading Australian university, and presents a rich account of the institutional, national and industry-sector contexts that have influenced the directions and decisions taken. The journey encountered with the main Enterprise Systems that support Financials, Human Resources and Facilities are described suggesting the lifecycle phases, critical success factors and lessons learnt.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Accurate silhouettes for surveillance : improved motion segmentation using graph cuts

Silhouettes are common features used by many applications in computer vision. For many of these algorithms to perform optimally, accurately segmenting the objects of interest from the background to extract the silhouettes is essential. Motion segmentation is a popular technique to segment moving objects from the background, however such algorithms can be prone to poor segmentation, particularly in noisy or low contrast conditions. In this paper, the work of [3] combining motion detection with graph cuts, is extended into two novel implementations that aim to allow greater uncertainty in the output of the motion segmentation, providing a less restricted input to the graph cut algorithm. The proposed algorithms are evaluated on a portion of the ETISEO dataset using hand segmented ground truth data, and an improvement in performance over the motion segmentation alone and the baseline system of [3] is shown.

Smart Grid Test Bed Design and Implementation

Given there is currently a migration trend from traditional electrical supervisory control and data acquisition (SCADA) systems towards a smart grid based approach to critical infrastructure management. This project provides an evaluation of existing and proposed implementations for both traditional electrical SCADA and smart grid based architectures, and proposals a set of reference requirements which test bed implementations should implement. A high-level design for smart grid test beds is proposed and initial implementation performed, based on the proposed design, using open source and freely available software tools. The project examines the move towards smart grid based critical infrastructure management and illustrates the increased security requirements. The implemented test bed provides a basic framework for testing network requirements in a smart grid environment, as well as a platform for further research and development. Particularly to develop, implement and test network security related disturbances such as intrusion detection and network forensics. The project undertaken proposes and develops an architecture of the emulation of some smart grid functionality. The Common Open Research Emulator (CORE) platform was used to emulate the communication network of the smart grid. Specifically CORE was used to virtualise and emulate the TCP/IP networking stack. This is intended to be used for further evaluation and analysis, for example the analysis of application protocol messages, etc. As a proof of concept, software libraries were designed, developed and documented to enable and support the design and development of further smart grid emulated components, such as reclosers, switches, smart meters, etc. As part of the testing and evaluation a Modbus based smart meter emulator was developed to provide basic functionality of a smart meter. Further code was developed to send Modbus request messages to the emulated smart meter and receive Modbus responses from it. Although the functionality of the emulated components were limited, it does provide a starting point for further research and development. The design is extensible to enable the design and implementation of additional SCADA protocols. The project also defines an evaluation criteria for the evaluation of the implemented test bed, and experiments are designed to evaluate the test bed according to the defined criteria. The results of the experiments are collated and presented, and conclusions drawn from the results to facilitate discussion on the test bed implementation. The discussion undertaken also present possible future work.

Grade A Taipei junior high school principals’ self-reported leadership practices

The principal’s leadership and curriculum development are considered the core elements for creating a high performing junior high school. In Taiwan, mathematics curriculum reform has been an ongoing topic since 1994. The pedagogy, classroom interactions, and the underlying philosophy of mathematics education have varied with different versions of guidelines. These changes inevitably increase the requirement for principals’ leadership in order to effectively implement the curriculum reform. Principals’ leadership is essential to the success of the implementation in their school. This study aimed to explore and identify the leadership of junior high school principals whose schools had been judged by the Taipei City Government as Grade A junior high schools. Principals’ implementations of the reformed mathematics curriculum were used as examples to generate insights of their leadership. This study drew upon a multiple-case study approach. Data were collected from interviews, observations, and documentations. Bass and Avolio’s (1997) full range leadership theory provided a structure for gaining insight into these principals’ leadership practices. Five Grade A Taipei junior high school principals participated and shared their leadership concepts and experiences. Findings revealed that the leadership preferences of the five principles varied considerably. Management by exception-active, contingent reward, individualised consideration, and idealised influence were Grade A Taipei junior high school principals’ preferred leadership practices. In addition, principals’ leadership strategies associated with these practices were identified. These principals had adopted a range of leadership strategies according to the staff and school needs. Results of this study have implications for both Taiwanese principals and education departments. Principals can enhance their leadership by gaining more understanding about the Grade A principals’ leadership practices and strategies. Taiwanese education departments can improve school leadership training programs by focusing on these practices and strategies, which may also lead to more effective strategies for implementing national curriculum reform.

Design of a model-generated repository as a service for USDL

SAP and its research partners have been developing a lan- guage for describing details of Services from various view- points called the Unified Service Description Language (USDL). At the time of writing, version 3.0 describes technical implementation aspects of services, as well as stakeholders, pricing, lifecycle, and availability. Work is also underway to address other business and legal aspects of services. This language is designed to be used in service portfolio management, with a repository of service descriptions being available to various stakeholders in an organisation to allow for service prioritisation, development, deployment and lifecycle management. The structure of the USDL metadata is specified using an object-oriented metamodel that conforms to UML, MOF and EMF Ecore. As such it is amenable to code gener-ation for implementations of repositories that store service description instances. Although Web services toolkits can be used to make these programming language objects available as a set of Web services, the practicalities of writing dis- tributed clients against over one hundred class definitions, containing several hundred attributes, will make for very large WSDL interfaces and highly inefficient “chatty” implementations. This paper gives the high-level design for a completely model-generated repository for any version of USDL (or any other data-only metamodel), which uses the Eclipse Modelling Framework’s Java code generation, along with several open source plugins to create a robust, transactional repository running in a Java application with a relational datastore. However, the repository exposes a generated WSDL interface at a coarse granularity, suitable for distributed client code and user-interface creation. It uses heuristics to drive code generation to bridge between the Web service and EMF granularities.

Modular transactional memory

Software transactional memory has the potential to greatly simplify development of concurrent software, by supporting safe composition of concurrent shared-state abstractions. However, STM semantics are defined in terms of low-level reads and writes on individual memory locations, so implementations are unable to take advantage of the properties of user-defined abstractions. Consequently, the performance of transactions over some structures can be disappointing. ----- ----- We present Modular Transactional Memory, our framework which allows programmers to extend STM with concurrency control algorithms tailored to the data structures they use in concurrent programs. We describe our implementation in Concurrent Haskell, and two example structures: a finite map which allows concurrent transactions to operate on disjoint sets of keys, and a non-deterministic channel which supports concurrent sources and sinks. ----- ----- Our approach is based on previous work by others on boosted and open-nested transactions, with one significant development: transactions are given types which denote the concurrency control algorithms they employ. Typed transactions offer a higher level of assurance for programmers reusing transactional code, and allow more flexible abstract concurrency control.

Efficient simulation of unsaturated flow using exponential time integration

We assess the performance of an exponential integrator for advancing stiff, semidiscrete formulations of the unsaturated Richards equation in time. The scheme is of second order and explicit in nature but requires the action of the matrix function φ(A) where φ(z) = [exp(z) - 1]/z on a suitability defined vector v at each time step. When the matrix A is large and sparse, φ(A)v can be approximated by Krylov subspace methods that require only matrix-vector products with A. We prove that despite the use of this approximation the scheme remains second order. Furthermore, we provide a practical variable-stepsize implementation of the integrator by deriving an estimate of the local error that requires only a single additional function evaluation. Numerical experiments performed on two-dimensional test problems demonstrate that this implementation outperforms second-order, variable-stepsize implementations of the backward differentiation formulae.

Overview of the INEX 2010 focused relevance feedback track

The INEX 2010 Focused Relevance Feedback track offered a refined approach to the evaluation of Focused Relevance Feedback algorithms through simulated exhaustive user feedback. As in traditional approaches we simulated a user-in-the loop by re-using the assessments of ad-hoc retrieval obtained from real users who assess focused ad-hoc retrieval submissions. The evaluation was extended in several ways: the use of exhaustive relevance feedback over entire runs; the evaluation of focused retrieval where both the retrieval results and the feedback are focused; the evaluation was performed over a closed set of documents and complete focused assessments; the evaluation was performed over executable implementations of relevance feedback algorithms; and �finally, the entire evaluation platform is reusable. We present the evaluation methodology, its implementation, and experimental results obtained for nine submissions from three participating organisations.

High resolution tiled display walls

Scalable high-resolution tiled display walls are becoming increasingly important to decision makers and researchers because high pixel counts in combination with large screen areas facilitate content rich, simultaneous display of computer-generated visualization information and high-definition video data from multiple sources. This tutorial is designed to cater for new users as well as researchers who are currently operating tiled display walls or 'OptiPortals'. We will discuss the current and future applications of display wall technology and explore opportunities for participants to collaborate and contribute in a growing community. Multiple tutorial streams will cover both hands-on practical development, as well as policy and method design for embedding these technologies into the research process. Attendees will be able to gain an understanding of how to get started with developing similar systems themselves, in addition to becoming familiar with typical applications and large-scale visualisation techniques. Presentations in this tutorial will describe current implementations of tiled display walls that highlight the effective usage of screen real-estate with various visualization datasets, including collaborative applications such as visualcasting, classroom learning and video conferencing. A feature presentation for this tutorial will be given by Jurgen Schulze from Calit2 at the University of California, San Diego. Jurgen is an expert in scientific visualization in virtual environments, human-computer interaction, real-time volume rendering, and graphics algorithms on programmable graphics hardware.