Combinatorial design of key distribution mechanisms for wireless sensor networks

Key distribution is one of the most challenging security issues in wireless sensor networks where sensor nodes are randomly scattered over a hostile territory. In such a sensor deployment scenario, there will be no prior knowledge of post deployment configuration. For security solutions requiring pairwise keys, it is impossible to decide how to distribute key pairs to sensor nodes before the deployment. Existing approaches to this problem are to assign more than one key, namely a key-chain, to each node. Key-chains are randomly drawn from a key-pool. Either two neighboring nodes have a key in common in their key-chains, or there is a path, called key-path, among these two nodes where each pair of neighboring nodes on this path has a key in common. Problem in such a solution is to decide on the key-chain size and key-pool size so that every pair of nodes can establish a session key directly or through a path with high probability. The size of the key-path is the key factor for the efficiency of the design. This paper presents novel, deterministic and hybrid approaches based on Combinatorial Design for key distribution. In particular, several block design techniques are considered for generating the key-chains and the key-pools.

Adaptive stepsize based on control theory for stochastic differential equations

The numerical solution of stochastic differential equations (SDEs) has been focused recently on the development of numerical methods with good stability and order properties. These numerical implementations have been made with fixed stepsize, but there are many situations when a fixed stepsize is not appropriate. In the numerical solution of ordinary differential equations, much work has been carried out on developing robust implementation techniques using variable stepsize. It has been necessary, in the deterministic case, to consider the "best" choice for an initial stepsize, as well as developing effective strategies for stepsize control-the same, of course, must be carried out in the stochastic case. In this paper, proportional integral (PI) control is applied to a variable stepsize implementation of an embedded pair of stochastic Runge-Kutta methods used to obtain numerical solutions of nonstiff SDEs. For stiff SDEs, the embedded pair of the balanced Milstein and balanced implicit method is implemented in variable stepsize mode using a predictive controller for the stepsize change. The extension of these stepsize controllers from a digital filter theory point of view via PI with derivative (PID) control will also be implemented. The implementations show the improvement in efficiency that can be attained when using these control theory approaches compared with the regular stepsize change strategy.

High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations

The pioneering work of Runge and Kutta a hundred years ago has ultimately led to suites of sophisticated numerical methods suitable for solving complex systems of deterministic ordinary differential equations. However, in many modelling situations, the appropriate representation is a stochastic differential equation and here numerical methods are much less sophisticated. In this paper a very general class of stochastic Runge-Kutta methods is presented and much more efficient classes of explicit methods than previous extant methods are constructed. In particular, a method of strong order 2 with a deterministic component based on the classical Runge-Kutta method is constructed and some numerical results are presented to demonstrate the efficacy of this approach.

Order conditions of stochastic Runge-Kutta methods by B-series

In this paper, general order conditions and a global convergence proof are given for stochastic Runge Kutta methods applied to stochastic ordinary differential equations ( SODEs) of Stratonovich type. This work generalizes the ideas of B-series as applied to deterministic ordinary differential equations (ODEs) to the stochastic case and allows a completely general formalism for constructing high order stochastic methods, either explicit or implicit. Some numerical results will be given to illustrate this theory.

Expander graph based key distribution mechanisms in wireless sensor networks

Secure communications between large number of sensor nodes that are randomly scattered over a hostile territory, necessitate efficient key distribution schemes. However, due to limited resources at sensor nodes such schemes cannot be based on post deployment computations. Instead, pairwise (symmetric) keys are required to be pre-distributed by assigning a list of keys, (a.k.a. key-chain), to each sensor node. If a pair of nodes does not have a common key after deployment then they must find a key-path with secured links. The objective is to minimize the keychain size while (i) maximizing pairwise key sharing probability and resilience, and (ii) minimizing average key-path length. This paper presents a deterministic key distribution scheme based on Expander Graphs. It shows how to map the parameters (e.g., degree, expansion, and diameter) of a Ramanujan Expander Graph to the desired properties of a key distribution scheme for a physical network topology.

High strong order methods for non-commutative stochastic ordinary differential equation systems and the Magnus formula

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary differential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the difficulty in representing the (possibly large number of) random variable approximations to the stochastic integrals. Although Burrage and Burrage [High strong order explicit Runge-Kutta methods for stochastic ordinary differential equations, Applied Numerical Mathematics 22 (1996) 81-101] were able to construct strong local order 1.5 stochastic Runge-Kutta methods for certain cases, it is known that all extant stochastic Runge-Kutta methods suffer an order reduction down to strong order 0.5 if there is non-commutativity between the functions associated with the multiple Wiener processes. This order reduction down to that of the Euler-Maruyama method imposes severe difficulties in obtaining meaningful solutions in a reasonable time frame and this paper attempts to circumvent these difficulties by some new techniques. An additional difficulty in solving SODEs arises even in the Linear case since it is not possible to write the solution analytically in terms of matrix exponentials unless there is a commutativity property between the functions associated with the multiple Wiener processes. Thus in this present paper first the work of Magnus [On the exponential solution of differential equations for a linear operator, Communications on Pure and Applied Mathematics 7 (1954) 649-673] (applied to deterministic non-commutative Linear problems) will be applied to non-commutative linear SODEs and methods of strong order 1.5 for arbitrary, linear, non-commutative SODE systems will be constructed - hence giving an accurate approximation to the general linear problem. Secondly, for general nonlinear non-commutative systems with an arbitrary number (d) of Wiener processes it is shown that strong local order I Runge-Kutta methods with d + 1 stages can be constructed by evaluated a set of Lie brackets as well as the standard function evaluations. A method is then constructed which can be efficiently implemented in a parallel environment for this arbitrary number of Wiener processes. Finally some numerical results are presented which illustrate the efficacy of these approaches. (C) 1999 Elsevier Science B.V. All rights reserved.

General order conditions for stochastic Runge-Kutta methods for both commuting and non-commuting stochastic ordinary differential equation systems

In many modeling situations in which parameter values can only be estimated or are subject to noise, the appropriate mathematical representation is a stochastic ordinary differential equation (SODE). However, unlike the deterministic case in which there are suites of sophisticated numerical methods, numerical methods for SODEs are much less sophisticated. Until a recent paper by K. Burrage and P.M. Burrage (1996), the highest strong order of a stochastic Runge-Kutta method was one. But K. Burrage and P.M. Burrage (1996) showed that by including additional random variable terms representing approximations to the higher order Stratonovich (or Ito) integrals, higher order methods could be constructed. However, this analysis applied only to the one Wiener process case. In this paper, it will be shown that in the multiple Wiener process case all known stochastic Runge-Kutta methods can suffer a severe order reduction if there is non-commutativity between the functions associated with the Wiener processes. Importantly, however, it is also suggested how this order can be repaired if certain commutator operators are included in the Runge-Kutta formulation. (C) 1998 Elsevier Science B.V. and IMACS. All rights reserved.

Games for change and transformative learning : an ethnographic case study

This thesis aims to contribute to a better understanding of how serious games/games for change function as learning frameworks for transformative learning in an educational setting. This study illustrates how the meaning-making processes and learning with and through computer gameplay are highly contingent, and are significantly influenced by the uncertainties of the situational context. The study focuses on SCAPE, a simulation game that addresses urban planning and sustainability. SCAPE is based on the real-world scenario of Kelvin Grove Urban Village, an inner city redevelopment area in Brisbane, Queensland, Australia. The game is embedded within an educational program, and I thus account for the various gameplay experiences of different school classes participating in this program. The networks emerging from the interactions between students/players, educators, facilitators, the technology, the researcher, as well as the setting, result in unanticipated, controversial, and sometimes unintended gameplay experiences and outcomes. To unpack play, transformative learning and games, this study adopts an ecological approach that considers the magic circle of gameplay in its wider context. Using Actor-Network Theory as the ontological lens for inquiry, the methods for investigation include an extensive literature review, ethnographic participant observation of SCAPE, as well as student and teacher questionnaires, finishing with interviews with the designers and facilitators of SCAPE. Altogether, these methods address my research aim to better understand how the heterogeneous actors engage in the relationships in and around gameplay, and illustrate how their conflicting understandings enable, shape or constrain the (transformative) learning experience. To disentangle these complexities, my focus continuously shifts between the following modes of inquiry into the aims „h To describe and analyse the game as a designed artefact. „h To examine the gameplay experiences of players/students and account for how these experiences are constituted in the relationships of the network. „h To trace the meaning-making processes emerging from the various relations of players/students, facilitators, teachers, designers, technology, researcher, and setting, and consider how the boundaries of the respective ecology are configured and negotiated. „h To draw out the implications for the wider research area of game-based learning by using the simulation game SCAPE as an example for introducing gameplay to educational settings. Accounting in detail for five school classes, these accounts represent, each in its own right, distinct and sometimes controversial forms of engagement in gameplay. The practices and negotiations of all the assembled human and non-human actors highlight the contingent nature of gameplay and learning. In their sum, they offer distinct but by no means exhaustive examples of the various relationships that emerge from the different assemblages of human and non-human actors. This thesis, hence, illustrates that game-based learning in an educational setting is accompanied by considerable unpredictability and uncertainty. As ordinary life spills and leaks into gameplay experiences, group dynamics and the negotiations of technology, I argue that overly deterministic assertions of the game¡¦s intention, as well as a too narrowly defined understanding of the transformative learning outcome, can constrain our inquiries and hinder efforts to further elucidate and understand the evolving uncertainties around game-based learning. Instead, this thesis posits that playing and transformative learning are relational effects of the respective ecology, where all actors are networked in their (partial) enrolment in the process of translation. This study thus attempts to foreground the rich opportunities for exploring how game-based learning is assembled as a network of practices.

Decentralized detector generation in cooperative intrusion detection system

We consider Cooperative Intrusion Detection System (CIDS) which is a distributed AIS-based (Artificial Immune System) IDS where nodes collaborate over a peer-to-peer overlay network. The AIS uses the negative selection algorithm for the selection of detectors (e.g., vectors of features such as CPU utilization, memory usage and network activity). For better detection performance, selection of all possible detectors for a node is desirable but it may not be feasible due to storage and computational overheads. Limiting the number of detectors on the other hand comes with the danger of missing attacks. We present a scheme for the controlled and decentralized division of detector sets where each IDS is assigned to a region of the feature space. We investigate the trade-off between scalability and robustness of detector sets. We address the problem of self-organization in CIDS so that each node generates a distinct set of the detectors to maximize the coverage of the feature space while pairs of nodes exchange their detector sets to provide a controlled level of redundancy. Our contribution is twofold. First, we use Symmetric Balanced Incomplete Block Design, Generalized Quadrangles and Ramanujan Expander Graph based deterministic techniques from combinatorial design theory and graph theory to decide how many and which detectors are exchanged between which pair of IDS nodes. Second, we use a classical epidemic model (SIR model) to show how properties from deterministic techniques can help us to reduce the attack spread rate.

Key distribution mechanisms for wireless sensor networks : a survey

Advances in technology introduce new application areas for sensor networks. Foreseeable wide deployment of mission critical sensor networks creates concerns on security issues. Security of large scale densely deployed and infrastructure less wireless networks of resource limited sensor nodes requires efficient key distribution and management mechanisms. We consider distributed and hierarchical wireless sensor networks where unicast, multicast and broadcast type of communications can take place. We evaluate deterministic, probabilistic and hybrid type of key pre-distribution and dynamic key generation algorithms for distributing pair-wise, group-wise and network-wise keys.

Combinatorial design of key distribution mechanisms for wireless sensor networks

Key distribution is one of the most challenging security issues in wireless sensor networks where sensor nodes are randomly scattered over a hostile territory. In such a sensor deployment scenario, there will be no prior knowledge of post deployment configuration. For security solutions requiring pair wise keys, it is impossible to decide how to distribute key pairs to sensor nodes before the deployment. Existing approaches to this problem are to assign more than one key, namely a key-chain, to each node. Key-chains are randomly drawn from a key-pool. Either two neighbouring nodes have a key in common in their key-chains, or there is a path, called key-path, among these two nodes where each pair of neighbouring nodes on this path has a key in common. Problem in such a solution is to decide on the key-chain size and key-pool size so that every pair of nodes can establish a session key directly or through a path with high probability. The size of the key-path is the key factor for the efficiency of the design. This paper presents novel, deterministic and hybrid approaches based on Combinatorial Design for key distribution. In particular, several block design techniques are considered for generating the key-chains and the key-pools. Comparison to probabilistic schemes shows that our combinatorial approach produces better connectivity with smaller key-chain sizes.

Design and analysis of key management schemes for distributed wireless sensor networks

Secure communications in distributed Wireless Sensor Networks (WSN) operating under adversarial conditions necessitate efficient key management schemes. In the absence of a priori knowledge of post-deployment network configuration and due to limited resources at sensor nodes, key management schemes cannot be based on post-deployment computations. Instead, a list of keys, called a key-chain, is distributed to each sensor node before the deployment. For secure communication, either two nodes should have a key in common in their key-chains, or they should establish a key through a secure-path on which every link is secured with a key. We first provide a comparative survey of well known key management solutions for WSN. Probabilistic, deterministic and hybrid key management solutions are presented, and they are compared based on their security properties and re-source usage. We provide a taxonomy of solutions, and identify trade-offs in them to conclude that there is no one size-fits-all solution. Second, we design and analyze deterministic and hybrid techniques to distribute pair-wise keys to sensor nodes before the deployment. We present novel deterministic and hybrid approaches based on combinatorial design theory and graph theory for deciding how many and which keys to assign to each key-chain before the sensor network deployment. Performance and security of the proposed schemes are studied both analytically and computationally. Third, we address the key establishment problem in WSN which requires key agreement algorithms without authentication are executed over a secure-path. The length of the secure-path impacts the power consumption and the initialization delay for a WSN before it becomes operational. We formulate the key establishment problem as a constrained bi-objective optimization problem, break it into two sub-problems, and show that they are both NP-Hard and MAX-SNP-Hard. Having established inapproximability results, we focus on addressing the authentication problem that prevents key agreement algorithms to be used directly over a wireless link. We present a fully distributed algorithm where each pair of nodes can establish a key with authentication by using their neighbors as the witnesses.

On the prediction of simultaneous inbreeding coefficients at multiple loci

A new deterministic method for predicting simultaneous inbreeding coefficients at three and four loci is presented. The method involves calculating the conditional probability of IBD (identical by descent) at one locus given IBD at other loci, and multiplying this probability by the prior probability of the latter loci being simultaneously IBD. The conditional probability is obtained applying a novel regression model, and the prior probability from the theory of digenic measures of Weir and Cockerham. The model was validated for a finite monoecious population mating at random, with a constant effective population size, and with or without selfing, and also for an infinite population with a constant intermediate proportion of selfing. We assumed discrete generations. Deterministic predictions were very accurate when compared with simulation results, and robust to alternative forms of implementation. These simultaneous inbreeding coefficients were more sensitive to changes in effective population size than in marker spacing. Extensions to predict simultaneous inbreeding coefficients at more than four loci are now possible.

Power of QTL detection using association tests with family controls

The power of testing for a population-wide association between a biallelic quantitative trait locus and a linked biallelic marker locus is predicted both empirically and deterministically for several tests. The tests were based on the analysis of variance (ANOVA) and on a number of transmission disequilibrium tests (TDT). Deterministic power predictions made use of family information, and were functions of population parameters including linkage disequilibrium, allele frequencies, and recombination rate. Deterministic power predictions were very close to the empirical power from simulations in all scenarios considered in this study. The different TDTs had very similar power, intermediate between one-way and nested ANOVAs. One-way ANOVA was the only test that was not robust against spurious disequilibrium. Our general framework for predicting power deterministically can be used to predict power in other association tests. Deterministic power calculations are a powerful tool for researchers to plan and evaluate experiments and obviate the need for elaborate simulation studies.

Distributed data acquisition unit with microsecond-accurate wireless clock synchronisation

This paper describes the implementation of the first portable, embedded data acquisition unit (BabelFuse) that is able to acquire and timestamp generic sensor data and trigger General Purpose I/O (GPIO) events against a microsecond-accurate wirelessly-distributed ‘global’ clock. A significant issue encountered when fusing data received from multiple sensors is the accuracy of the timestamp associated with each piece of data. This is particularly important in applications such as Simultaneous Localisation and Mapping (SLAM) where vehicle velocity forms an important part of the mapping algorithms; on fast-moving vehicles, even millisecond inconsistencies in data timestamping can produce errors which need to be compensated for. The timestamping problem is compounded in a robot swarm environment especially if non-deterministic communication hardware (such as IEEE-802.11-based wireless) and inaccurate clock synchronisation protocols are used. The issue of differing timebases makes correlation of data difficult and prevents the units from reliably performing synchronised operations or manoeuvres. By utilising hardware-assisted timestamping, clock synchronisation protocols based on industry standards and firmware designed to minimise indeterminism, an embedded data acquisition unit capable of microsecond-level clock synchronisation is presented.