Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the algebraic attack approach of Berbain et al. to Trivium-like ciphers and perform new analyses on them. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques to recover Bivium-A's initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analyses. We also answer an open question posed by Berbain et al. on the feasibility of applying their technique on Trivium-like ciphers. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail. Analysis of Bivium-B and Trivium-N are omitted from this manuscript. The full paper is available on the IACR ePrint Archive.

Primary stability of two uncemented acetabular components of different geometry : hemispherical or peripherally enhanced?

Objective This study compared the primary stability of two commercially available acetabular components from the same manufacturer, which differ only in geometry; a hemispherical and a peripherally enhanced design (peripheral self-locking (PSL)). The objective was to determine whether altered geometry resulted in better primary stability. Methods Acetabular components were seated with 0.8 mm to 2 mm interference fits in reamed polyethylene bone substrate of two different densities (0.22 g/cm3 and 0.45 g/cm3). The primary stability of each component design was investigated by measuring the peak failure load during uniaxial pull-out and tangential lever-out tests. Results There was no statistically significant difference in seating force (p = 0.104) or primary stability (pull-out p = 0.171, lever-out p = 0.087) of the two components in the low-density substrate. Similarly, in the high-density substrate, there was no statistically significant difference in the peak pull-out force (p = 0.154) or lever-out moment (p = 0.574) between the designs. However, the PSL component required a significantly higher seating force thanthe hemispherical cup in the high-density bone analogue (p = 0.006). Conclusions Higher seating forces associated with the PSL design may result in inadequate seating and increased risk of component malpositioning or acetabular fracture in the intra-operative setting in high-density bone stock. Our results, if translated clinically, suggest that a purely hemispherical geometry may have an advantage over a peripherally enhanced geometry in high density bone stock.

Evaluation of two-view geometry methods with automatic ground-truth generation

A large number of methods have been published that aim to evaluate various components of multi-view geometry systems. Most of these have focused on the feature extraction, description and matching stages (the visual front end), since geometry computation can be evaluated through simulation. Many data sets are constrained to small scale scenes or planar scenes that are not challenging to new algorithms, or require special equipment. This paper presents a method for automatically generating geometry ground truth and challenging test cases from high spatio-temporal resolution video. The objective of the system is to enable data collection at any physical scale, in any location and in various parts of the electromagnetic spectrum. The data generation process consists of collecting high resolution video, computing accurate sparse 3D reconstruction, video frame culling and down sampling, and test case selection. The evaluation process consists of applying a test 2-view geometry method to every test case and comparing the results to the ground truth. This system facilitates the evaluation of the whole geometry computation process or any part thereof against data compatible with a realistic application. A collection of example data sets and evaluations is included to demonstrate the range of applications of the proposed system.

Analysis of terrain geometry representations for traversability of a Mars rover

For a planetary rover to successfully traverse across unstructured terrain autonomously, one of the major challenges is to assess its local traversability such that it can plan a trajectory to achieve its mission goals efficiently while minimising risk to the vehicle itself. This paper aims to provide a comparative study on different approaches for representing the geometry of Martian terrain for the purpose of evaluating terrain traversability. An accurate representation of the geometric properties of the terrain is essential as it can directly affect the determination of traversability for a ground vehicle. We explore current state-of-the-art techniques for terrain estimation, in particular Gaussian Processes (GP) in various forms, and discuss the suitability of each technique in the context of an unstructured Martian terrain. Furthermore, we present the limitations of regression techniques in terms of spatial correlation and continuity assumptions, and the impact on traversability analysis of a planetary rover across unstructured terrain. The analysis was performed on datasets of the Mars Yard at the Powerhouse Museum in Sydney, obtained using the onboard RGB-D camera.

An algebraic approach for determination of DG parameters to support voltage profiles in radial distribution networks

Rapidly increasing electricity demands and capacity shortage of transmission and distribution facilities are the main driving forces for the growth of Distributed Generation (DG) integration in power grids. One of the reasons for choosing a DG is its ability to support voltage in a distribution system. Selection of effective DG characteristics and DG parameters is a significant concern of distribution system planners to obtain maximum potential benefits from the DG unit. This paper addresses the issue of improving the network voltage profile in distribution systems by installing a DG of the most suitable size, at a suitable location. An analytical approach is developed based on algebraic equations for uniformly distributed loads to determine the optimal operation, size and location of the DG in order to achieve required levels of network voltage. The developed method is simple to use for conceptual design and analysis of distribution system expansion with a DG and suitable for a quick estimation of DG parameters (such as optimal operating angle, size and location of a DG system) in a radial network. A practical network is used to verify the proposed technique and test results are presented.

An algebraic analysis of trivium ciphers based on the boolean satisfiability problem

Trivium is a stream cipher candidate of the eStream project. It has successfully moved into phase three of the selection process under the hardware category. No attacks faster than the exhaustive search have so far been reported on Trivium. Bivium-A and Bivium-B are simplified versions of Trivium that are built on the same design principles but with two registers. The simplified design is useful in investigating Trivium type ciphers with a reduced complexity and provides insight into effective attacks which could be extended to Trivium. This paper focuses on an algebraic analysis which uses the boolean satisfiability problem in propositional logic. For reduced variants of the cipher, this analysis recovers the internal state with a minimal amount of keystream observations.

Are in vitro estimates of cell diffusivity and cell proliferation rate sensitive to assay geometry?

Cells respond to various biochemical and physical cues during wound–healing and tumour progression. In vitro assays used to study these processes are typically conducted in one particular geometry and it is unclear how the assay geometry affects the capacity of cell populations to spread, or whether the relevant mechanisms, such as cell motility and cell proliferation, are somehow sensitive to the geometry of the assay. In this work we use a circular barrier assay to characterise the spreading of cell populations in two different geometries. Assay 1 describes a tumour–like geometry where a cell population spreads outwards into an open space. Assay 2 describes a wound–like geometry where a cell population spreads inwards to close a void. We use a combination of discrete and continuum mathematical models and automated image processing methods to obtain independent estimates of the effective cell diffusivity, D, and the effective cell proliferation rate, λ. Using our parameterised mathematical model we confirm that our estimates of D and λ accurately predict the time–evolution of the location of the leading edge and the cell density profiles for both assay 1 and assay 2. Our work suggests that the effective cell diffusivity is up to 50% lower for assay 2 compared to assay 1, whereas the effective cell proliferation rate is up to 30% lower for assay 2 compared to assay 1.

Energy-based positioning control of underactuated vehicles using manifold regulation

In this paper, we consider the problem of position regulation of a class of underactuated rigid-body vehicles that operate within a gravitational field and have fully-actuated attitude. The control objective is to regulate the vehicle position to a manifold of dimension equal to the underactuation degree. We address the problem using Port-Hamiltonian theory, and reduce the associated matching PDEs to a set of algebraic equations using a kinematic identity. The resulting method for control design is constructive. The point within the manifold to which the position is regulated is determined by the action of the potential field and the geometry of the manifold. We illustrate the performance of the controller for an unmanned aerial vehicle with underactuation degree two-a quadrotor helicopter.

Object tracking via non-Euclidean geometry : a Grassmann approach

A robust visual tracking system requires an object appearance model that is able to handle occlusion, pose, and illumination variations in the video stream. This can be difficult to accomplish when the model is trained using only a single image. In this paper, we first propose a tracking approach based on affine subspaces (constructed from several images) which are able to accommodate the abovementioned variations. We use affine subspaces not only to represent the object, but also the candidate areas that the object may occupy. We furthermore propose a novel approach to measure affine subspace-to-subspace distance via the use of non-Euclidean geometry of Grassmann manifolds. The tracking problem is then considered as an inference task in a Markov Chain Monte Carlo framework via particle filtering. Quantitative evaluation on challenging video sequences indicates that the proposed approach obtains considerably better performance than several recent state-of-the-art methods such as Tracking-Learning-Detection and MILtrack.

Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

Algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering

This paper presents algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering. For unstuttered SOBER-t32, two different attacks are implemented. In the first attack, we obtain multivariate equations of degree 10. Then, an algebraic attack is developed using a collection of output bits whose relation to the initial state of the LFSR can be described by low-degree equations. The resulting system of equations contains 2^69 equations and monomials, which can be solved using the Gaussian elimination with the complexity of 2^196.5. For the second attack, we build a multivariate equation of degree 14. We focus on the property of the equation that the monomials which are combined with output bit are linear. By applying the Berlekamp-Massey algorithm, we can obtain a system of linear equations and the initial states of the LFSR can be recovered. The complexity of attack is around O(2^100) with 2^92 keystream observations. The second algebraic attack is applicable to SOBER-t16 without stuttering. The attack takes around O(2^85) CPU clocks with 2^78 keystream observations.

Surface magnetoplasma waves at the interface between a plasma-like medium and a metal in the Voigt geometry

Theoretical and experimental results associated with the studies of different properties of surface-type waves (SW) in plasma-like medium-metal structures are reviewed. The propagation of surface waves in the Voigt geometry (the SW propagate across the external magnetic field, which is parallel to the interface) is considered. Various problems dealing with the linear properties of the SW (dispersion characteristics, electromagnetic fields topography, influence of the inhomogeneity of the medium, etc.); excitation mechanisms of the plasma-metal waveguide structures (parametric, drift, diffraction, etc. mechanisms); nonlinear effects associated with SW propagation (higher harmonics generation, self-interaction, nonlinear damping, nonlinear interactions, etc.) are presented. In many cases the results are valid for both gaseous and solid-state plasmas. © 1999 Elsevier Science B.V. All rights reserved.

On algebraic immunity and annihilators

Algebraic immunity AI(f) defined for a boolean function f measures the resistance of the function against algebraic attacks. Currently known algorithms for computing the optimal annihilator of f and AI(f) are inefficient. This work consists of two parts. In the first part, we extend the concept of algebraic immunity. In particular, we argue that a function f may be replaced by another boolean function f^c called the algebraic complement of f. This motivates us to examine AI(f ^c ). We define the extended algebraic immunity of f as AI *(f)= min {AI(f), AI(f^c )}. We prove that 0≤AI(f)–AI *(f)≤1. Since AI(f)–AI *(f)= 1 holds for a large number of cases, the difference between AI(f) and AI *(f) cannot be ignored in algebraic attacks. In the second part, we link boolean functions to hypergraphs so that we can apply known results in hypergraph theory to boolean functions. This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI *(f).

Three-dimensional geological modelling of the Galilee and central Eromanga basins, Australia: New insights into aquifer/aquitard geometry and potential influence of faults on inter-connectivity

Study region The Galilee and Eromanga basins are located in central Queensland, Australia. Both basins are components of the Great Artesian Basin which host some of the most significant groundwater resources in Australia. Study focus This study evaluates the influence of regional faults on groundwater flow in an aquifer/aquitard interbedded succession that form one of the largest Artesian Basins in the world. In order to assess the significance of regional faults as potential barriers or conduits to groundwater flow, vertical displacements of the major aquifers and aquitards were studied at each major fault and the general hydraulic relationship of units that are juxtaposed by the faults were considered. A three-dimensional (3D) geological model of the Galilee and Eromanga basins was developed based on integration of well log data, seismic surfaces, surface geology and elevation data. Geological structures were mapped in detail and major faults were characterised. New hydrological insights for the region Major faults that have been described in previous studies have been confirmed within the 3D geological model domain and a preliminary assessment of their hydraulic significance has been conducted. Previously unknown faults such as the Thomson River Fault (herein named) have also been identified in this study.