Twisted Edwards curves revisited

This paper introduces fast algorithms for performing group operations on twisted Edwards curves, pushing the recent speed limits of Elliptic Curve Cryptography (ECC) forward in a wide range of applications. Notably, the new addition algorithm uses for suitably selected curve constants. In comparison, the fastest point addition algorithms for (twisted) Edwards curves stated in the literature use . It is also shown that the new addition algorithm can be implemented with four processors dropping the effective cost to . This implies an effective speed increase by the full factor of 4 over the sequential case. Our results allow faster implementation of elliptic curve scalar multiplication. In addition, the new point addition algorithm can be used to provide a natural protection from side channel attacks based on simple power analysis (SPA).

Faster group operations on elliptic curves

This paper improves implementation techniques of Elliptic Curve Cryptography. We introduce new formulae and algorithms for the group law on Jacobi quartic, Jacobi intersection, Edwards, and Hessian curves. The proposed formulae and algorithms can save time in suitable point representations. To support our claims, a cost comparison is made with classic scalar multiplication algorithms using previous and current operation counts. Most notably, the best speeds are obtained from Jacobi quartic curves which provide the fastest timings for most scalar multiplication strategies benefiting from the proposed 12M + 5S + 1D point doubling and 7M + 3S + 1D point addition algorithms. Furthermore, the new addition algorithm provides an efficient way to protect against side channel attacks which are based on simple power analysis (SPA). Keywords: Efficient elliptic curve arithmetic,unified addition, side channel attack.

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.

Beam polarization effects in the radiative production of lightest neutralinos in e(+)e(-) collisions in supersymmetric grand unified models

We study the production of the lightest neutralinos in the process e(+)e(-) -> chi(0)(1)chi(0)(1)gamma in supersymmetric grand unified models for the International Linear Collider energies with longitudinally polarized beams. We consider cases where the standard model gauge group is unified into the grand unified gauge groups SU(5), or SO(10). We have carried out a comprehensive study of this process in the SU(5) and SO(10) grand unified theories which includes the QED radiative corrections. We compare and contrast the dependence of the signal cross section on the grand unified gauge group, and on the different representations of the grand unified gauge group, when the electron and positron beams are longitudinally polarized. To assess the feasibility of experimentally observing the radiative production process, we have also considered in detail the background to this process coming from the radiative neutrino production process e(+)e(-)-> nu(nu) over bar gamma with longitudinally polarized electron and positron beams. In addition we have also considered the supersymmetric background coming from the radiative production of scalar neutrinos in the process e(+)e(-) -> (nu) over tilde(nu) over tilde*gamma with longitudinally polarized beams. The process can be a major background to the radiative production of neutralinos when the scalar neutrinos decay invisibly.

Unified modelling in support of organization design and change

The aim of this research is to provide a unified modelling-based method to help with the evaluation of organization design and change decisions. Relevant literature regarding model-driven organization design and change is described. This helps identify the requirements for a new modelling methodology. Such a methodology is developed and described. The three phases of the developed method include the following. First, the use of CIMOSA-based multi-perspective enterprise modelling to understand and capture the most enduring characteristics of process-oriented organizations and externalize various types of requirement knowledge about any target organization. Second, the use of causal loop diagrams to identify dynamic causal impacts and effects related to the issues and constraints on the organization under study. Third, the use of simulation modelling to quantify the effects of each issue in terms of organizational performance. The design and case study application of a unified modelling method based on CIMOSA (computer integrated manufacturing open systems architecture) enterprise modelling, causal loop diagrams, and simulation modelling, is explored to illustrate its potential to support systematic organization design and change. Further application of the proposed methodology in various company and industry sectors, especially in manufacturing sectors, would be helpful to illustrate complementary uses and relative benefits and drawbacks of the methodology in different types of organization. The proposed unified modelling-based method provides a systematic way of enabling key aspects of organization design and change. The case company, its relevant data, and developed models help to explore and validate the proposed method. The application of CIMOSA-based unified modelling method and integrated application of these three modelling techniques within a single solution space constitutes an advance on previous best practice. Also, the purpose and application domain of the proposed method offers an addition to knowledge. © IMechE 2009.

Laminar Cortical Dynamics of Cognitive and Motor Working Memory, Sequence Learning and Performance: Toward a Unified Theory of How the Cerebral Cortex Works

How do the layered circuits of prefrontal and motor cortex carry out working memory storage, sequence learning, and voluntary sequential item selection and performance? A neural model called LIST PARSE is presented to explain and quantitatively simulate cognitive data about both immediate serial recall and free recall, including bowing of the serial position performance curves, error-type distributions, temporal limitations upon recall, and list length effects. The model also qualitatively explains cognitive effects related to attentional modulation, temporal grouping, variable presentation rates, phonemic similarity, presentation of non-words, word frequency/item familiarity and list strength, distracters and modality effects. In addition, the model quantitatively simulates neurophysiological data from the macaque prefrontal cortex obtained during sequential sensory-motor imitation and planned performance. The article further develops a theory concerning how the cerebral cortex works by showing how variations of the laminar circuits that have previously clarified how the visual cortex sees can also support cognitive processing of sequentially organized behaviors.

The Conceptualization and Exploration of Place Allegiance: Towards a Unified Model of Person-Place Relationships within Outdoor Recreation

The academic study of place has been generally defined by two distinct and highly refined discourses within outdoor recreation research: place attachment and sense of place. Place attachment generally describes the intensity of the place relationship, whereas sense of place approaches place from a more holistic and intimate orientation. This study bridges these two methodological and theoretical separate areas of place research together by re-conceptualizing the way in which place relationships are viewed within outdoor recreation research. The Psychological Continuum Model is used to extend the language of place attachment to incorporate more of the philosophy of sense of place while attending to the empirical strength and utility of place attachment. This extension results in the term place allegiance being coined to depict the strong and profound relationships outdoor recreationists build with their places of outdoor recreation. Using a concurrent mixed methods research design, this study explored place allegiance via an online survey (n = 437) and thirteen in-depth qualitative interviews with outdoor recreationists. Results indicate that place allegiance can be measured through a multi-dimensional model of place allegiance that incorporates behaviours, importance, resistance, knowledge and symbolic value. In addition, place allegiance was found to be related to an individual's influence on life course and his/her willingness to exhibit preservation and protection tendencies. Place allegiance plays an important role in acknowledging the importance of authentic place relationships in an effort to confront placelessness. Wilderness recreation is an important avenue for outdoor recreationists to build strong place relationships.

Unified framework for construction of rule based classification systems

Automatic generation of classification rules has been an increasingly popular technique in commercial applications such as Big Data analytics, rule based expert systems and decision making systems. However, a principal problem that arises with most methods for generation of classification rules is the overfit-ting of training data. When Big Data is dealt with, this may result in the generation of a large number of complex rules. This may not only increase computational cost but also lower the accuracy in predicting further unseen instances. This has led to the necessity of developing pruning methods for the simplification of rules. In addition, classification rules are used further to make predictions after the completion of their generation. As efficiency is concerned, it is expected to find the first rule that fires as soon as possible by searching through a rule set. Thus a suit-able structure is required to represent the rule set effectively. In this chapter, the authors introduce a unified framework for construction of rule based classification systems consisting of three operations on Big Data: rule generation, rule simplification and rule representation. The authors also review some existing methods and techniques used for each of the three operations and highlight their limitations. They introduce some novel methods and techniques developed by them recently. These methods and techniques are also discussed in comparison to existing ones with respect to efficient processing of Big Data.

A unified framework for linear function approximation of value functions in stochastic control

This paper contributes with a unified formulation that merges previ- ous analysis on the prediction of the performance ( value function ) of certain sequence of actions ( policy ) when an agent operates a Markov decision process with large state-space. When the states are represented by features and the value function is linearly approxi- mated, our analysis reveals a new relationship between two common cost functions used to obtain the optimal approximation. In addition, this analysis allows us to propose an efficient adaptive algorithm that provides an unbiased linear estimate. The performance of the pro- posed algorithm is illustrated by simulation, showing competitive results when compared with the state-of-the-art solutions.

COOPER-framework:a unified process for non-parametric projects

Practitioners assess performance of entities in increasingly large and complicated datasets. If non-parametric models, such as Data Envelopment Analysis, were ever considered as simple push-button technologies, this is impossible when many variables are available or when data have to be compiled from several sources. This paper introduces by the 'COOPER-framework' a comprehensive model for carrying out non-parametric projects. The framework consists of six interrelated phases: Concepts and objectives, On structuring data, Operational models, Performance comparison model, Evaluation, and Result and deployment. Each of the phases describes some necessary steps a researcher should examine for a well defined and repeatable analysis. The COOPER-framework provides for the novice analyst guidance, structure and advice for a sound non-parametric analysis. The more experienced analyst benefits from a check list such that important issues are not forgotten. In addition, by the use of a standardized framework non-parametric assessments will be more reliable, more repeatable, more manageable, faster and less costly. © 2010 Elsevier B.V. All rights reserved.

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.

Contemporary issues in Australian family law: Do we need a more unified and interventionist judicial model

Recent decisions of the Family Court of Australian reflect concerns over the adversarial nature of the legal process. The processes and procedures of the judicial system militate against a detailed examination of the issues and rights of the parties in dispute. The limitations of the family law framework are particularly demonstrated in disputes over the custody of children where the Court has tended to neglect the rights and interests of the primary carer. An alternative "unified family court" framework will be examined in which the Court pursues a more active and interventionist approach in the determination of family law disputes.

Chinese young children’s strategies on basic addition facts

Kindergartens in China offer structured full-day programs for children aged 3-6. Although formal schooling does not commence until age 7, the mathematics program in kindergartens is specifically focused on developing young children’s facility with simple addition and subtraction. This study explored young Chinese children’s strategies for solving basic addition facts as well as their intuitive understanding of addition via interview methods. Results indicate a strong impact that teacher-directed teaching methods have on young children’s cognitions in relation to addition.