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.

Accidental amenity

Landscape in Australian multi-unit residential developments has passed through a number of phases. Can we make the successes more intentional than serendipitous? When did the block of flats become renamed "multi-unit residential"? Perhaps it coincided with a realization by Australians that medium - and high-density urban housing was neither an attack on the quarter-acre block nor a synonym for public housing. Higher densities allow people to participate in the city, and the expansion of unit-based housing represents Australians' growing love of cities for their urban and cosmopolitan values. As our attitude to the city has changed, so have the types of multi-unit residential stock changed - in their spatial qualities as well as their role in the landscape.

Implementation of an integrated, technology-based, discovery mode assessment item involving an incubation period to enhance learning outcomes for engineering maths students

In this paper we discuss our current efforts to develop and implement an exploratory, discovery mode assessment item into the total learning and assessment profile for a target group of about 100 second level engineering mathematics students. The assessment item under development is composed of 2 parts, namely, a set of "pre-lab" homework problems (which focus on relevant prior mathematical knowledge, concepts and skills), and complementary computing laboratory exercises which are undertaken within a fixed (1 hour) time frame. In particular, the computing exercises exploit the algebraic manipulation and visualisation capabilities of the symbolic algebra package MAPLE, with the aim of promoting understanding of certain mathematical concepts and skills via visual and intuitive reasoning, rather than a formal or rigorous approach. The assessment task we are developing is aimed at providing students with a significant learning experience, in addition to providing feedback on their individual knowledge and skills. To this end, a noteworthy feature of the scheme is that marks awarded for the laboratory work are primarily based on the extent to which reflective, critical thinking is demonstrated, rather than the amount of CBE-style tasks completed by the student within the allowed time. With regard to student learning outcomes, a novel and potentially critical feature of our scheme is that the assessment task is designed to be intimately linked to the overall course content, in that it aims to introduce important concepts and skills (via individual student exploration) which will be revisited somewhat later in the pedagogically more restrictive formal lecture component of the course (typically a large group plenary format). Furthermore, the time delay involved, or "incubation period", is also a deliberate design feature: it is intended to allow students the opportunity to undergo potentially important internal re-adjustments in their understanding, before being exposed to lectures on related course content which are invariably delivered in a more condensed, formal and mathematically rigorous manner. In our presentation, we will discuss in more detail our motivation and rationale for trailing such a scheme for the targeted student group. Some of the advantages and disadvantages of our approach (as we perceived them at the initial stages) will also be enumerated. In a companion paper, the theoretical framework for our approach will be more fully elaborated, and measures of student learning outcomes (as obtained from eg. student provided feedback) will be discussed.

Developing mathematics understanding and abstraction : the case of equivalence in the elementary years

Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data were gathered from multiple sources including interviews, videos of classroom teaching, and pre-and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.

Characterising anomalous events using change point correlation on unsolicited network traffic

Monitoring unused or dark IP addresses offers opportunities to extract useful information about both on-going and new attack patterns. In recent years, different techniques have been used to analyze such traffic including sequential analysis where a change in traffic behavior, for example change in mean, is used as an indication of malicious activity. Change points themselves say little about detected change; further data processing is necessary for the extraction of useful information and to identify the exact cause of the detected change which is limited due to the size and nature of observed traffic. In this paper, we address the problem of analyzing a large volume of such traffic by correlating change points identified in different traffic parameters. The significance of the proposed technique is two-fold. Firstly, automatic extraction of information related to change points by correlating change points detected across multiple traffic parameters. Secondly, validation of the detected change point by the simultaneous presence of another change point in a different parameter. Using a real network trace collected from unused IP addresses, we demonstrate that the proposed technique enables us to not only validate the change point but also extract useful information about the causes of change points.

Intrusion detection techniques in wireless local area networks

This research investigates wireless intrusion detection techniques for detecting attacks on IEEE 802.11i Robust Secure Networks (RSNs). Despite using a variety of comprehensive preventative security measures, the RSNs remain vulnerable to a number of attacks. Failure of preventative measures to address all RSN vulnerabilities dictates the need for a comprehensive monitoring capability to detect all attacks on RSNs and also to proactively address potential security vulnerabilities by detecting security policy violations in the WLAN. This research proposes novel wireless intrusion detection techniques to address these monitoring requirements and also studies correlation of the generated alarms across wireless intrusion detection system (WIDS) sensors and the detection techniques themselves for greater reliability and robustness. The specific outcomes of this research are: A comprehensive review of the outstanding vulnerabilities and attacks in IEEE 802.11i RSNs. A comprehensive review of the wireless intrusion detection techniques currently available for detecting attacks on RSNs. Identification of the drawbacks and limitations of the currently available wireless intrusion detection techniques in detecting attacks on RSNs. Development of three novel wireless intrusion detection techniques for detecting RSN attacks and security policy violations in RSNs. Development of algorithms for each novel intrusion detection technique to correlate alarms across distributed sensors of a WIDS. Development of an algorithm for automatic attack scenario detection using cross detection technique correlation. Development of an algorithm to automatically assign priority to the detected attack scenario using cross detection technique correlation.

Science and subjectivity

Science has been under attack in the last thirty years, and recently a number of prominent scientists have been busy fighting back. Here, an argument is presented that the `science wars' stem from an unreasonably strict adherence to the reductive method on the part of science, but that weakening this stance need not imply a lapse into subjectivity. One possible method for formalising the description of non-separable, contextually dependent complex systems is presented. This is based upon a quantum-like approach.

Telcagepant is a new oral treatment for migraine

Background : Migraine is a common cause of disability. Many subjects (30 – 40%) do not respond to the 5-HT 1B/1D agonists (the triptans) commonly used in the treatment of migraine attacks. Calcitonin gene-related protein (CGRP) receptor antagonism is a new approach to the treatment of migraine attacks. Objectives/methods : This evaluation is of a Phase III clinical trial comparing telcagepant, an orally active CGRP receptor antagonist, with zolmitriptan in subjects during an attack of migraine. Results : Telcagepant 300 mg has a similar efficacy to zolmitriptan in relieving pain, phonophobia, photophobia, and nausea. Telcagepant was better tolerated than zolmitriptan. Conclusions : The initial Phase III clinical trial results with telcagepant are promising but several further clinical trials are needed to determine the place of telcagepant in the treatment of migraine attacks

Detecting and characterising malicious executable payloads

Buffer overflow vulnerabilities continue to prevail and the sophistication of attacks targeting these vulnerabilities is continuously increasing. As a successful attack of this type has the potential to completely compromise the integrity of the targeted host, early detection is vital. This thesis examines generic approaches for detecting executable payload attacks, without prior knowledge of the implementation of the attack, in such a way that new and previously unseen attacks are detectable. Executable payloads are analysed in detail for attacks targeting the Linux and Windows operating systems executing on an Intel IA-32 architecture. The execution flow of attack payloads are analysed and a generic model of execution is examined. A novel classification scheme for executable attack payloads is presented which allows for characterisation of executable payloads and facilitates vulnerability and threat assessments, and intrusion detection capability assessments for intrusion detection systems. An intrusion detection capability assessment may be utilised to determine whether or not a deployed system is able to detect a specific attack and to identify requirements for intrusion detection functionality for the development of new detection methods. Two novel detection methods are presented capable of detecting new and previously unseen executable attack payloads. The detection methods are capable of identifying and enumerating the executable payload’s interactions with the operating system on the targeted host at the time of compromise. The detection methods are further validated using real world data including executable payload attacks.

Using honeypots to analyse anomalous Internet activities

Monitoring Internet traffic is critical in order to acquire a good understanding of threats to computer and network security and in designing efficient computer security systems. Researchers and network administrators have applied several approaches to monitoring traffic for malicious content. These techniques include monitoring network components, aggregating IDS alerts, and monitoring unused IP address spaces. Another method for monitoring and analyzing malicious traffic, which has been widely tried and accepted, is the use of honeypots. Honeypots are very valuable security resources for gathering artefacts associated with a variety of Internet attack activities. As honeypots run no production services, any contact with them is considered potentially malicious or suspicious by definition. This unique characteristic of the honeypot reduces the amount of collected traffic and makes it a more valuable source of information than other existing techniques. Currently, there is insufficient research in the honeypot data analysis field. To date, most of the work on honeypots has been devoted to the design of new honeypots or optimizing the current ones. Approaches for analyzing data collected from honeypots, especially low-interaction honeypots, are presently immature, while analysis techniques are manual and focus mainly on identifying existing attacks. This research addresses the need for developing more advanced techniques for analyzing Internet traffic data collected from low-interaction honeypots. We believe that characterizing honeypot traffic will improve the security of networks and, if the honeypot data is handled in time, give early signs of new vulnerabilities or breakouts of new automated malicious codes, such as worms. The outcomes of this research include: • Identification of repeated use of attack tools and attack processes through grouping activities that exhibit similar packet inter-arrival time distributions using the cliquing algorithm; • Application of principal component analysis to detect the structure of attackers’ activities present in low-interaction honeypots and to visualize attackers’ behaviors; • Detection of new attacks in low-interaction honeypot traffic through the use of the principal component’s residual space and the square prediction error statistic; • Real-time detection of new attacks using recursive principal component analysis; • A proof of concept implementation for honeypot traffic analysis and real time monitoring.

Mitigating sandwich attacks against a secure key management scheme in wireless sensor networks for PCS/SCADA

Alzaid et al. proposed a forward & backward secure key management scheme in wireless sensor networks for Process Control Systems (PCSs) or Supervisory Control and Data Acquisition (SCADA) systems. The scheme, however, is still vulnerable to an attack called the sandwich attack that can be launched when the adversary captures two sensor nodes at times t1 and t2, and then reveals all the group keys used between times t1 and t2. In this paper, a fix to the scheme is proposed in order to limit the vulnerable time duration to an arbitrarily chosen time span while keeping the forward and backward secrecy of the scheme untouched. Then, the performance analysis for our proposal, Alzaid et al.’s scheme, and Nilsson et al.’s scheme is given.

H-house

The author's approach to the problems associated with building in bushfire prone landscapes comes from 12 years of study of the biophysical and cultural landscapes in the Great Southern Region of Western Australia - research which resulted in the design and construction of the H-house at Bremer Bay. The house was developed using a 'ground up' approach whereby Dr Weir conducted topographical surveys and worked with a local botanist and a bushfire risk consultant to ascertain the level of threat that fire presented to this particular site. The intention from the outset however, was not to design a bushfire resistant house per se, but to develop a design which would place the owners in close proximity to the highly biodiverse heath vegetation of their site. The research aim was to find ways - through architectural design-to link the patterns of usage of the house with other site specific conditions related to the prevailing winds, solar orientation and seasonal change. The H-house has a number of features which increase the level of bushfire safety. These include: Fire rated roller shutters (tested by the CSIRO for ember attack and radiant heat), Fire resistant double glazing (on windows not protected by the shutters), Fibre-cement sheet cladding of the underside of the elevated timber floor structure, Manually operated high pressure sprinkler system on exposed timber decks, A fire refuge (an enlarged laundry, shower area) within the house with a dedicated cabinet for fire fighting equipment) and A low pressure solar powered domestic water supply system.

Uncertainty based MDO of UAS using HAPMOEA

CFD has been successfully used in the optimisation of aerodynamic surfaces using a given set of parameters such as Mach numbers and angle of attack. While carrying out a multidisciplinary design optimisation one deals with situations where the parameters have some uncertain attached. Any optimisation carried out for fixed values of input parameters gives a design which may be totally unacceptable under off-design conditions. The challenge is to develop a robust design procedure which takes into account the fluctuations in the input parameters. In this work, we attempt this using a modified Taguchi approach. This is incorporated into an evolutionary algorithm with many features developed in house. The method is tested for an UCAV design which simultaneously handles aerodynamics, electromagnetics and maneuverability. Results demonstrate that the method has considerable potential.

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.