Modelling sea water intrusion in coastal aquifers using heterogeneous computing

The objective of this PhD research program is to investigate numerical methods for simulating variably-saturated flow and sea water intrusion in coastal aquifers in a high-performance computing environment. The work is divided into three overlapping tasks: to develop an accurate and stable finite volume discretisation and numerical solution strategy for the variably-saturated flow and salt transport equations; to implement the chosen approach in a high performance computing environment that may have multiple GPUs or CPU cores; and to verify and test the implementation. The geological description of aquifers is often complex, with porous materials possessing highly variable properties, that are best described using unstructured meshes. The finite volume method is a popular method for the solution of the conservation laws that describe sea water intrusion, and is well-suited to unstructured meshes. In this work we apply a control volume-finite element (CV-FE) method to an extension of a recently proposed formulation (Kees and Miller, 2002) for variably saturated groundwater flow. The CV-FE method evaluates fluxes at points where material properties and gradients in pressure and concentration are consistently defined, making it both suitable for heterogeneous media and mass conservative. Using the method of lines, the CV-FE discretisation gives a set of differential algebraic equations (DAEs) amenable to solution using higher-order implicit solvers. Heterogeneous computer systems that use a combination of computational hardware such as CPUs and GPUs, are attractive for scientific computing due to the potential advantages offered by GPUs for accelerating data-parallel operations. We present a C++ library that implements data-parallel methods on both CPU and GPUs. The finite volume discretisation is expressed in terms of these data-parallel operations, which gives an efficient implementation of the nonlinear residual function. This makes the implicit solution of the DAE system possible on the GPU, because the inexact Newton-Krylov method used by the implicit time stepping scheme can approximate the action of a matrix on a vector using residual evaluations. We also propose preconditioning strategies that are amenable to GPU implementation, so that all computationally-intensive aspects of the implicit time stepping scheme are implemented on the GPU. Results are presented that demonstrate the efficiency and accuracy of the proposed numeric methods and formulation. The formulation offers excellent conservation of mass, and higher-order temporal integration increases both numeric efficiency and accuracy of the solutions. Flux limiting produces accurate, oscillation-free solutions on coarse meshes, where much finer meshes are required to obtain solutions with equivalent accuracy using upstream weighting. The computational efficiency of the software is investigated using CPUs and GPUs on a high-performance workstation. The GPU version offers considerable speedup over the CPU version, with one GPU giving speedup factor of 3 over the eight-core CPU implementation.

Generalized-positioning for mixed-frequency of mixed-GNSS and its preliminary applications

Modernized GPS and GLONASS, together with new GNSS systems, BeiDou and Galileo, offer code and phase ranging signals in three or more carriers. Traditionally, dual-frequency code and/or phase GPS measurements are linearly combined to eliminate effects of ionosphere delays in various positioning and analysis. This typical treatment method has imitations in processing signals at three or more frequencies from more than one system and can be hardly adapted itself to cope with the booming of various receivers with a broad variety of singles. In this contribution, a generalized-positioning model that the navigation system independent and the carrier number unrelated is promoted, which is suitable for both single- and multi-sites data processing. For the synchronization of different signals, uncalibrated signal delays (USD) are more generally defined to compensate the signal specific offsets in code and phase signals respectively. In addition, the ionospheric delays are included in the parameterization with an elaborate consideration. Based on the analysis of the algebraic structures, this generalized-positioning model is further refined with a set of proper constrains to regularize the datum deficiency of the observation equation system. With this new model, uncalibrated signal delays (USD) and ionospheric delays are derived for both GPS and BeiDou with a large dada set. Numerical results demonstrate that, with a limited number of stations, the uncalibrated code delays (UCD) are determinate to a precision of about 0.1 ns for GPS and 0.4 ns for BeiDou signals, while the uncalibrated phase delays (UPD) for L1 and L2 are generated with 37 stations evenly distributed in China for GPS with a consistency of about 0.3 cycle. Extra experiments concerning the performance of this novel model in point positioning with mixed-frequencies of mixed-constellations is analyzed, in which the USD parameters are fixed with our generated values. The results are evaluated in terms of both positioning accuracy and convergence time.

A family of Alltop functions that are EA-inequivalent to the cubic function

Sequences with optimal correlation properties are much sought after for applications in communication systems. In 1980, Alltop (\emph{IEEE Trans. Inf. Theory} 26(3):350-354, 1980) described a set of sequences based on a cubic function and showed that these sequences were optimal with respect to the known bounds on auto and crosscorrelation. Subsequently these sequences were used to construct mutually unbiased bases (MUBs), a structure of importance in quantum information theory. The key feature of this cubic function is that its difference function is a planar function. Functions with planar difference functions have been called \emph{Alltop functions}. This paper provides a new family of Alltop functions and establishes the use of Alltop functions for construction of sequence sets and MUBs.

Analysis of nonlinear sequences and streamciphers

Streamciphers are common cryptographic algorithms used to protect the confidentiality of frame-based communications like mobile phone conversations and Internet traffic. Streamciphers are ideal cryptographic algorithms to encrypt these types of traffic as they have the potential to encrypt them quickly and securely, and have low error propagation. The main objective of this thesis is to determine whether structural features of keystream generators affect the security provided by stream ciphers.These structural features pertain to the state-update and output functions used in keystream generators. Using linear sequences as keystream to encrypt messages is known to be insecure. Modern keystream generators use nonlinear sequences as keystream.The nonlinearity can be introduced through a keystream generator's state-update function, output function, or both. The first contribution of this thesis relates to nonlinear sequences produced by the well-known Trivium stream cipher. Trivium is one of the stream ciphers selected in a final portfolio resulting from a multi-year project in Europe called the ecrypt project. Trivium's structural simplicity makes it a popular cipher to cryptanalyse, but to date, there are no attacks in the public literature which are faster than exhaustive keysearch. Algebraic analyses are performed on the Trivium stream cipher, which uses a nonlinear state-update and linear output function to produce keystream. Two algebraic investigations are performed: an examination of the sliding property in the initialisation process and algebraic analyses of Trivium-like streamciphers using a combination of the algebraic techniques previously applied separately by Berbain et al. and Raddum. For certain iterations of Trivium's state-update function, we examine the sets of slid pairs, looking particularly to form chains of slid pairs. No chains exist for a small number of iterations.This has implications for the period of keystreams produced by Trivium. Secondly, using our combination of the methods of Berbain et al. and Raddum, we analysed Trivium-like ciphers and improved on previous on previous analysis with regards to forming systems of equations on these ciphers. Using these new systems of equations, we were able to successfully recover the initial state of Bivium-A.The attack complexity for Bivium-B and Trivium were, however, worse than exhaustive keysearch. We also show that the selection of stages which are used as input to the output function and the size of registers which are used in the construction of the system of equations affect the success of the attack. The second contribution of this thesis is the examination of state convergence. State convergence is an undesirable characteristic in keystream generators for stream ciphers, as it implies that the effective session key size of the stream cipher is smaller than the designers intended. We identify methods which can be used to detect state convergence. As a case study, theMixer streamcipher, which uses nonlinear state-update and output functions to produce keystream, is analysed. Mixer is found to suffer from state convergence as the state-update function used in its initialisation process is not one-to-one. A discussion of several other streamciphers which are known to suffer from state convergence is given. From our analysis of these stream ciphers, three mechanisms which can cause state convergence are identified.The effect state convergence can have on stream cipher cryptanalysis is examined. We show that state convergence can have a positive effect if the goal of the attacker is to recover the initial state of the keystream generator. The third contribution of this thesis is the examination of the distributions of bit patterns in the sequences produced by nonlinear filter generators (NLFGs) and linearly filtered nonlinear feedback shift registers. We show that the selection of stages used as input to a keystream generator's output function can affect the distribution of bit patterns in sequences produced by these keystreamgenerators, and that the effect differs for nonlinear filter generators and linearly filtered nonlinear feedback shift registers. In the case of NLFGs, the keystream sequences produced when the output functions take inputs from consecutive register stages are less uniform than sequences produced by NLFGs whose output functions take inputs from unevenly spaced register stages. The opposite is true for keystream sequences produced by linearly filtered nonlinear feedback shift registers.

The 4C spectrum of fundamental behavioral relations for concurrent systems

The design of concurrent software systems, in particular process-aware information systems, involves behavioral modeling at various stages. Recently, approaches to behavioral analysis of such systems have been based on declarative abstractions defined as sets of behavioral relations. However, these relations are typically defined in an ad-hoc manner. In this paper, we address the lack of a systematic exploration of the fundamental relations that can be used to capture the behavior of concurrent systems, i.e., co-occurrence, conflict, causality, and concurrency. Besides the definition of the spectrum of behavioral relations, which we refer to as the 4C spectrum, we also show that our relations give rise to implication lattices. We further provide operationalizations of the proposed relations, starting by proposing techniques for computing relations in unlabeled systems, which are then lifted to become applicable in the context of labeled systems, i.e., systems in which state transitions have semantic annotations. Finally, we report on experimental results on efficiency of the proposed computations.

Microstructure of an artificial grain boundary weak link in an YBa2Cu3O(7-δ) thin film grown on a (100)(110), [001]-tilt Y-ZrO2 bicrystal

The microstructure of an artificial grain boundary in an YBa2Cu3O7-δ (YBCO) thin film grown on a (100)(110), [001]-tilt yttria-stabilized-zirconia (YSZ) bicrystal substrate has been studied using transmission electron microscopy (TEM). The orientation relationship between the YBCO film and the YSZ substrate was [001]YBCO∥[001]YSZ and [110]YBCO∥[100]YSZ for each half of the bicrystal film. However, the exact boundary geometry of the bicrystal substrate was not transferred to the film. The substrate boundary was straight while the film boundary was wavy. In several cases there was bending of the lattice confined within a distance of a few basal-plane lattice spacings from the boundary plane and microfaceting. No intergranular secondary phase was observed but about 25% of the boundary was covered by c-axis-tilted YBCO grains and a-axis-oriented grains, both of which were typically adjacent to CuO grains or surrounded by a thin Cu-rich amorphous layer.

Microstructure and properties of artificial grain boundaries in epitaxial YBA2Cu3O7-δ thin films grown on [001] tilt YZrO2 bicrystals

The microstructure of artificial grain boundaries in YBa2Cu3O7-δ (YBCO) thin films grown on [001] tilt YZrO2 (YSZ) bicrystal substrates has been characterized using transmission electron microscopy and atomic force microscopy. Despite a relatively straight morphology of the substrate boundaries, the film boundaries were wavy. The waviness was a result of the combined effects of grooving at the substrate boundaries prior to the film deposition and an island-growth mechanism for YBCO on YSZ substrates. The dihedral angle of the groove walls varied with the misorientation angle and depended on the symmetry of the substrate boundary. The amplitudes of the film boundary waviness compared well with the widths of the grooves. In addition, the grooves induced local bending of the YBCO lattice planes and additional tilt components perpendicular to the c-axis close to the film boundaries. © 1995.

Adapting Lyubashevsky's signature schemes to the ring signature setting

Basing signature schemes on strong lattice problems has been a long standing open issue. Today, two families of lattice-based signature schemes are known: the ones based on the hash-and-sign construction of Gentry et al.; and Lyubashevsky’s schemes, which are based on the Fiat-Shamir framework. In this paper we show for the first time how to adapt the schemes of Lyubashevsky to the ring signature setting. In particular we transform the scheme of ASIACRYPT 2009 into a ring signature scheme that provides strong properties of security under the random oracle model. Anonymity is ensured in the sense that signatures of different users are within negligible statistical distance even under full key exposure. In fact, the scheme satisfies a notion which is stronger than the classical full key exposure setting as even if the keypair of the signing user is adversarially chosen, the statistical distance between signatures of different users remains negligible. Considering unforgeability, the best lattice-based ring signature schemes provide either unforgeability against arbitrary chosen subring attacks or insider corruption in log-sized rings. In this paper we present two variants of our scheme. In the basic one, unforgeability is ensured in those two settings. Increasing signature and key sizes by a factor k (typically 80 − 100), we provide a variant in which unforgeability is ensured against insider corruption attacks for arbitrary rings. The technique used is pretty general and can be adapted to other existing schemes.

An evaluation of the Australian ‘reconceptualising early mathematics learning’ project : key findings and implications

The Pattern and Structure Mathematics Awareness Project (PASMAP) has investigated the development of patterning and early algebraic reasoning among 4 to 8 year olds over a series of related studies. We assert that an awareness of mathematical pattern and structure (AMPS) enables mathematical thinking and simple forms of generalization from an early age. This paper provides an overview of key findings of the Reconceptualizing Early Mathematics Learning empirical evaluation study involving 316 Kindergarten students from 4 schools. The study found highly significant differences on PASA scores for PASMAP students. Analysis of structural development showed increased levels for the PASMAP students; those categorised as low ability developed improved structural responses over a short period of time.

Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

Efficient lattice (H)IBE in the standard model

We construct an efficient identity based encryption system based on the standard learning with errors (LWE) problem. Our security proof holds in the standard model. The key step in the construction is a family of lattices for which there are two distinct trapdoors for finding short vectors. One trapdoor enables the real system to generate short vectors in all lattices in the family. The other trapdoor enables the simulator to generate short vectors for all lattices in the family except for one. We extend this basic technique to an adaptively-secure IBE and a Hierarchical IBE.

Lattice mixing and vanishing trapdoors : a framework for fully secure short signatures and more

We propose a framework for adaptive security from hard random lattices in the standard model. Our approach borrows from the recent Agrawal-Boneh-Boyen families of lattices, which can admit reliable and punctured trapdoors, respectively used in reality and in simulation. We extend this idea to make the simulation trapdoors cancel not for a specific forgery but on a non-negligible subset of the possible challenges. Conceptually, we build a compactly representable, large family of input-dependent “mixture” lattices, set up with trapdoors that “vanish” for a secret subset which we hope the forger will target. Technically, we tweak the lattice structure to achieve “naturally nice” distributions for arbitrary choices of subset size. The framework is very general. Here we obtain fully secure signatures, and also IBE, that are compact, simple, and elegant.

The uber-assumption family

We offer an exposition of Boneh, Boyen, and Goh’s “uber-assumption” family for analyzing the validity and strength of pairing assumptions in the generic-group model, and augment the original BBG framework with a few simple but useful extensions.

Lattice-based completely non-malleable public-key encryption in the standard model

An encryption scheme is non-malleable if giving an encryption of a message to an adversary does not increase its chances of producing an encryption of a related message (under a given public key). Fischlin introduced a stronger notion, known as complete non-malleability, which requires attackers to have negligible advantage, even if they are allowed to transform the public key under which the related message is encrypted. Ventre and Visconti later proposed a comparison-based definition of this security notion, which is more in line with the well-studied definitions proposed by Bellare et al. The authors also provide additional feasibility results by proposing two constructions of completely non-malleable schemes, one in the common reference string model using non-interactive zero-knowledge proofs, and another using interactive encryption schemes. Therefore, the only previously known completely non-malleable (and non-interactive) scheme in the standard model, is quite inefficient as it relies on generic NIZK approach. They left the existence of efficient schemes in the common reference string model as an open problem. Recently, two efficient public-key encryption schemes have been proposed by Libert and Yung, and Barbosa and Farshim, both of them are based on pairing identity-based encryption. At ACISP 2011, Sepahi et al. proposed a method to achieve completely non-malleable encryption in the public-key setting using lattices but there is no security proof for the proposed scheme. In this paper we review the mentioned scheme and provide its security proof in the standard model. Our study shows that Sepahi’s scheme will remain secure even for post-quantum world since there are currently no known quantum algorithms for solving lattice problems that perform significantly better than the best known classical (i.e., non-quantum) algorithms.

Cryptanalysis of WG-7 : a lightweight stream cipher

WG-7 is a stream cipher based on WG stream cipher and has been designed by Luo et al. (2010). This cipher is designed for low cost and lightweight applications (RFID tags and mobile phones, for instance). This paper addresses cryptographic weaknesses of WG-7 stream cipher. We show that the key stream generated by WG-7 can be distinguished from a random sequence after knowing 213.5 keystream bits and with a negligible error probability. Also, we investigate the security of WG-7 against algebraic attacks. An algebraic key recovery attack on this cipher is proposed. The attack allows to recover both the internal state and the secret key with the time complexity about 2/27.