Ultimate shear strength of LiteSteel beams

This paper presents the details of an investigation on the shear behaviour of a recently developed, cold-formed steel beam known as LiteSteel Beam (LSB).The LSB section has a unique shape of a channel beam with two rectangular hollow flanges and is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. In the present investigation, a series of numerical analyses based on three-dimensional finite element modeling and an experimental study were carried out to investigate the shear behaviour of 10 different LSB sections. It was found that the current design rules in cold-formed steel structures design codes are very conservative for the shear design of LiteSteel beams. Significant improvements to web shear buckling occurred due to the presence of rectangular hollow flanges while considerable post-buckling strength was also observed. Therefore the design rules were further modified to include the available post-buckling strength. Suitable design rules were also developed under the direct strength method format. This paper presents the details of this investigation and the results including the final design rules for the shear capacity of LSBs. It also presents new shear strength formulae for lipped channel beams based on the current design equations for shear strength given in AISI (2007) using the same approach used for LSBs.

Selective growth of carbon nanotubes on bare silicon : MWNT sinthesys on patterned substrates without predeposition of metal catalyst

Carbon nanotubes (CNTs) are expected to become the ideal constituent of many technologes, in particular for future generation electronics. This considerable interest is due to their unique electrical and mechanical properties. They show indeed super-high current-carrying capacity, ballistic electron transport and good field-emission properties. Then, these superior features make CNTs the most promising building blocks for electronic devices, as organic solar cells and organic light emitting devices (OLED). By using Focused Ion Beam (FIB) patterning it is possible to a obtain a high control on position, relative distances and diameter of CNTs. The present work shows how to grow three-dimensional architecture made of vertical-aligned CNTs directly on silicon. Thanks to the higher activity of a pre-patterned surface the synthesis process results very quick, cheap and simple. Such large area growths of CNTs could be used in preliminary test for application as electrodes for organic solar cells.

An ESR study of irradiated poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether) (PFA)

Poly(tetrafluoroethylene-co-perfluoropropyl vinyl ether) (PFA) with 2 mol% perfluoropropyl vinyl ether (PPVE) was exposed to γ-irradiation in vacuum at both 77 K and room temperature and the ESR spectra recorded. Both the main chain, CF2–C.F–CF2, and end chain, CF2C.F2 radicals were identified at both temperatures and their thermal stabilities measured. No radicals unique to the radiolytic cleavage at the PPVE units were observed at room temperature, either due to the low concentration of the comonomer or β-scission to form a chain end radical and a non-radical species. G-values for radical formation at room temperature and 77 K were found to be 0.93 and 0.16, respectively.

Electro-spinning of pure collagen nano-fibres – just an expensive way to make gelatin?

Scaffolds manufactured from biological materials promise better clinical functionality, providing that characteristic features are preserved. Collagen, a prominent biopolymer, is used extensively for tissue engineering applications, because its signature biological and physico-chemical properties are retained in vitro preparations. We show here for the first time that the very properties that have established collagen as the leading natural biomaterial are lost when it is electro-spun into nano-fibres out of fluoroalcohols such as 1,1,1,3,3,3-hexafluoro-2-propanol or 2,2,2-trifluoroethanol. We further identify the use of fluoroalcohols as the major culprit in the process. The resultant nano-scaffolds lack the unique ultra-structural axial periodicity that confirms quarter-staggered supramolecular assemblies and the capacity to generate second harmonic signals, representing the typical crystalline triple-helical structure. They were also characterised by low denaturation temperatures, similar to those obtained from gelatin preparations ( p > 0.05). Likewise, circular dichroism spectra revealed extensive denaturation of the electro-spun collagen. Using pepsin digestion in combination with quantitative SDS-PAGE, we corroborate great losses of up to 99% of triple-helical collagen. In conclusion, electro-spinning of collagen out of fluoroalcohols effectively denatures this biopolymer, and thus appears to defeat its purpose, namely to create biomimetic scaffolds emulating the collagen structure and function of the extracellular matrix.

Raman spectroscopy of gallium based hydrotalcites of formula Mg6Ga2(CO3)(OH)16•4H2O

Insight into the unique structure of hydrotalcites has been obtained using Raman spectroscopy. Gallium containing hydrotalcites of formula Mg4Ga2(CO3)(OH)12•4H2O (2:1 Ga-HT) to Mg8Ga2(CO3)(OH)20•4H2O (4:1 Ga-HT) have been successfully synthesised and characterized by X-ray diffraction and Raman spectroscopy. The d(003) spacing varied from 7.83 Å for the 2:1 hydrotalcite to 8.15 Å for the 3:1 gallium containing hydrotalcite. Raman spectroscopy complemented with selected infrared data has been used to characterise the synthesised gallium containing hydrotalcites of formula Mg6Ga2(CO3)(OH)16•4H2O. Raman bands observed at around 1046, 1048 and 1058 cm-1 were attributed to the symmetric stretching modes of the (CO32-) units. Multiple ν3 CO32- antisymmetric stretching modes are found at around 1346, 1378, 1446, 1464 and 1494 cm-1. The splitting of this mode indicates the carbonate anion is in a perturbed state. Raman bands observed at 710 and 717 cm-1 assigned to the ν4 (CO32-) modes support the concept of multiple carbonate species in the interlayer.

Osteoarthritis Index delivered by mobile phone (m-WOMAC) is valid, reliable, and responsive

Objectives: To evaluate the validity, reliability and responsiveness of EDC using the WOMAC® NRS 3.1 Index on Motorola V3 mobile phones. ---------- Methods: Patients with osteoarthritis (OA) undergoing primary unilateral hip or knee joint replacement surgery were assessed pre-operatively and 3-4 months post-operatively. Patients completed the WOMAC® Index in paper (p-WOMAC®) and electronic (m-WOMAC®) format in random order. ---------- Results: 24 men and 38 women with hip and knee OA participated and successfully completed the m-WOMAC® questionnaire. Pearson correlations between the summated total index scores for the p-WOMAC® and m-WOMAC® pre- and post-surgery were 0.98 and 0.99 (p<0.0001). There was no clinically important or statistically significant between-method difference in the adjusted total summated scores, pre- and post-surgery (adjusted mean difference = 4.44, p = 0.474 and 1.73, p = 0.781). Internal consistency estimates of m-WOMAC® reliability were 0.87 – 0.98. The m-WOMAC® detected clinically important, statistically significant (p<0.0001) improvements in pain, stiffness, function and total index score. ---------- Conclusions: Sixty-two patients with hip and knee OA successfully completed EDC by Motorola V3 mobile phone using the m-WOMAC® NRS3.1 Index; completion times averaging only 1-1.5 minutes longer than the p-WOMAC® Index. Data were successfully and securely transmitted from patients in Australia to a server in the USA. There was close agreement and no significant differences between m-WOMAC® and p-WOMAC® scores. This study confirms the validity, reliability and responsiveness of the Exco InTouch engineered, Java-based m-WOMAC® Index application. EDC with the m-WOMAC® Index provides unique opportunities for using quantitative measurement in clinical research and practice.

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.

Wireless sensor devices for animal tracking and control

This paper describes some new wireless sensor hardware developed for pastoral and environmental applications. From our early experiments with Mote hardware we were inspired to develop our devices with improved radio range, solar power capability, mechanical and electrical robustness, and with unique combinations of sensors. Here we describe the design and evolution of a small family of devices: radio/processor board, a soil moisture sensor interface, and a single board multi-sensor unit for animal tracking experiments.

Vibration isolation for autonomous helicopter flight

The mechanisms of helicopter flight create a unique, high-vibration environment which can play havoc with the accurate operation of on-board sensors. Vibration isolation of electronic sensors from structural borne oscillations is paramount to their reliable and accurate use. Effective isolation is achieved by realising a trade-off between the properties of the suspended instrument package, and the isolation mechanism. This is made more difficult as the weight and size of the sensors and computing hardware decreases with advances in technology. This paper presents a history of the design, challenges, constraints and construction of an integrated isolated vision and sensor platform and landing gear for the CSIRO autonomous X-Cell helicopter. The results of isolation performance and in-flight tests of the platform in autonomous flight are presented.

A secure architecture for Australia’s index based e-health environment

This paper proposes a security architecture for the basic cross indexing systems emerging as foundational structures in current health information systems. In these systems unique identifiers are issued to healthcare providers and consumers. In most cases, such numbering schemes are national in scope and must therefore necessarily be used via an indexing system to identify records contained in pre-existing local, regional or national health information systems. Most large scale electronic health record systems envisage that such correlation between national healthcare identifiers and pre-existing identifiers will be performed by some centrally administered cross referencing, or index system. This paper is concerned with the security architecture for such indexing servers and the manner in which they interface with pre-existing health systems (including both workstations and servers). The paper proposes two required structures to achieve the goal of a national scale, and secure exchange of electronic health information, including: (a) the employment of high trust computer systems to perform an indexing function, and (b) the development and deployment of an appropriate high trust interface module, a Healthcare Interface Processor (HIP), to be integrated into the connected workstations or servers of healthcare service providers. This proposed architecture is specifically oriented toward requirements identified in the Connectivity Architecture for Australia’s e-health scheme as outlined by NEHTA and the national e-health strategy released by the Australian Health Ministers.

Elastic shear buckling characteristics of LiteSteel Beams

LiteSteel beam (LSB) is a new cold-formed steel hollow flange channel beam. The unique LSB section is produced by a patented manufacturing process involving simultaneous cold-forming and dual electric resistance welding. To date, limited research has been undertaken on the shear buckling behaviour of LSBs with torsionally rigid, rectangular hollow flanges. For the shear design of LSB web panels, their elastic shear buckling strength must be determined accurately including the potential post-buckling strength. Currently the elastic shear buckling coefficients of web panels are determined by assuming conservatively that the web panels are simply supported at the junction between the flange and web elements. Therefore finite element analyses were carried out to investigate the elastic shear buckling behaviour of LSB sections including the effect of true support conditions at the junction between their flange and web elements. An improved equation for the higher elastic shear buckling coefficient of LSBs was developed and included in the shear capacity equations of Australian cold-formed steel codes. Predicted ultimate shear capacity results were compared with available experimental results, both of which showed considerable improvement to the shear capacities of LSBs. A study on the shear flow distribution of LSBs was also undertaken prior to the elastic buckling analysis study. This paper presents the details of this investigation and the results including the shear flow distribution of LSBs. Keywords: LiteSteel beam, Elastic shear buckling, Shear flow, Cold-formed steel structures, Slender web, Hollow flanges.

Port of Brisbane stormwater quality : stage 1 rainfall simulation to evaluate pollutant build-up and wash-off from selected land uses

Background: The quality of stormwater runoff from ports is significant as it can be an important source of pollution to the marine environment. This is also a significant issue for the Port of Brisbane as it is located in an area of high environmental values. Therefore, it is imperative to develop an in-depth understanding of stormwater runoff quality to ensure that appropriate strategies are in place for quality improvement. ---------------- The Port currently has a network of stormwater sample collection points where event based samples together with grab samples are tested for a range of water quality parameters. Whilst this information provides a ‘snapshot’ of the pollutants being washed from the catchment/s, it does not allow for a quantifiable assessment of total contaminant loads being discharged to the waters of Moreton Bay. It also does not represent pollutant build-up and wash-off from the different land uses across a broader range of rainfall events which might be expected. As such, it is difficult to relate stormwater quality to different pollutant sources within the Port environment. ----------------- Consequently, this would make the source tracking of pollutants to receiving waters extremely difficult and in turn the ability to implement appropriate mitigation measures. Also, without this detailed understanding, the efficacy of the various stormwater quality mitigation measures implemented cannot be determined with certainty. --------------- Current knowledge on port stormwater runoff quality Currently, little knowledge exists with regards to the pollutant generation capacity specific to port land uses as these do not necessarily compare well with conventional urban industrial or commercial land use due to the specific nature of port activities such as inter-modal operations and cargo management. Furthermore, traffic characteristics in a port area are different to a conventional urban area. Consequently, as data inputs based on an industrial and commercial land uses for modelling purposes is questionable. ------------------ A comprehensive review of published research failed to locate any investigations undertaken with regards to pollutant build-up and wash-off for port specific land uses. Furthermore, there is very limited information made available by various ports worldwide about the pollution generation potential of their facilities. Published work in this area has essentially focussed on the water quality or environmental values in the receiving waters such as the downstream bay or estuary. ----------------- The Project: The research project is an outcome of the collaborative Partnership between the Port of Brisbane Corporation (POBC) and Queensland University of Technology (QUT). A key feature of this Partnership is the undertaking of ‘cutting edge’ research to strengthen the environmental custodianship of the Port area. This project aims to develop a port specific stormwater quality model to allow informed decision making in relation to stormwater quality improvement in the context of the increased growth of the Port. --------------- Stage 1 of the research project focussed on the assessment of pollutant build-up and wash-off using rainfall simulation from the current Port of Brisbane facilities with the longer-term objective of contributing to the development of ecological risk mitigation strategies for future expansion scenarios. Investigation of complex processes such as pollutant wash-off using naturally occurring rainfall events has inherent difficulties. These can be overcome using simulated rainfall for the investigations. ----------------- The deliverables for Stage 1 included the following: * Pollutant build-up and wash-off profiles for six primary land uses within the Port of Brisbane to be used for water quality model development. * Recommendations with regards to future stormwater quality monitoring and pollution mitigation measures. The outcomes are expected to deliver the following benefits to the Port of Brisbane: * The availability of Port specific pollutant build-up and wash-off data will enable the implementation of customised stormwater pollution mitigation strategies. * The water quality data collected would form the baseline data for a Port specific water quality model for mitigation and predictive purposes. * To be at the cutting-edge in terms of water quality management and environmental best practice in the context of port infrastructure. ---------------- Conclusions: The important conclusions from the study are: * It confirmed that the Port environment is unique in terms of pollutant characteristics and is not comparable to typical urban land uses. * For most pollutant types, the Port land uses exhibited lower pollutant concentrations when compared to typical urban land uses. * The pollutant characteristics varied across the different land uses and were not consistent in terms of the land use. Hence, the implementation of stereotypical structural water quality improvement devices could be of limited value. * The <150m particle size range was predominant in suspended solids for pollutant build-up as well as wash-off. Therefore, if suspended solids are targeted as the surrogate parameter for water quality improvement, this specific particle size range needs to be removed. ------------------- Recommendations: Based on the study results the following preliminary recommendations are made: * Due to the appreciable variation in pollutant characteristics for different port land uses, any water quality monitoring stations should preferably be located such that source areas can be easily identified. * The study results having identified significant pollutants for the different land uses should enable the development of a more customised water quality monitoring and testing regime targeting the critical pollutants. * A ‘one size fits all’ approach may not be appropriate for the different port land uses due to the varying pollutant characteristics. As such, pollution mitigation will need to be specifically tailored to suit the specific land use. * Any structural measures implemented for pollution mitigation to be effective should have the capability to remove suspended solids of size <150m. * Based on the results presented and the particularly the fact that the Port land uses cannot be compared to conventional urban land uses in relation to pollutant generation, consideration should be given to the development of a port specific water quality model.

Port of Brisbane stormwater quality : stage 2 development of a port specific water quality model

Background: The quality of stormwater runoff from ports is significant as it can be an important source of pollution to the marine environment. This is also a significant issue for the Port of Brisbane as it is located in an area of high environmental values. Therefore, it is imperative to develop an in-depth understanding of stormwater runoff quality to ensure that appropriate strategies are in place for quality improvement, where necessary. To this end, the Port of Brisbane Corporation aimed to develop a port specific stormwater model for the Fisherman Islands facility. The need has to be considered in the context of the proposed future developments of the Port area. ----------------- The Project: The research project is an outcome of the collaborative Partnership between the Port of Brisbane Corporation (POBC) and Queensland University of Technology (QUT). A key feature of this Partnership is that it seeks to undertake research to assist the Port in strengthening the environmental custodianship of the Port area through ‘cutting edge’ research and its translation into practical application. ------------------ The project was separated into two stages. The first stage developed a quantitative understanding of the generation potential of pollutant loads in the existing land uses. This knowledge was then used as input for the stormwater quality model developed in the subsequent stage. The aim is to expand this model across the yet to be developed port expansion area. This is in order to predict pollutant loads associated with stormwater flows from this area with the longer term objective of contributing to the development of ecological risk mitigation strategies for future expansion scenarios. ----------------- Study approach: Stage 1 of the overall study confirmed that Port land uses are unique in terms of the anthropogenic activities occurring on them. This uniqueness in land use results in distinctive stormwater quality characteristics different to other conventional urban land uses. Therefore, it was not scientifically valid to consider the Port as belonging to a single land use category or to consider as being similar to any typical urban land use. The approach adopted in this study was very different to conventional modelling studies where modelling parameters are developed using calibration. The field investigations undertaken in Stage 1 of the overall study helped to create fundamental knowledge on pollutant build-up and wash-off in different Port land uses. This knowledge was then used in computer modelling so that the specific characteristics of pollutant build-up and wash-off can be replicated. This meant that no calibration processes were involved due to the use of measured parameters for build-up and wash-off. ---------------- Conclusions: Stage 2 of the study was primarily undertaken using the SWMM stormwater quality model. It is a physically based model which replicates natural processes as closely as possible. The time step used and catchment variability considered was adequate to accommodate the temporal and spatial variability of input parameters and the parameters used in the modelling reflect the true nature of rainfall-runoff and pollutant processes to the best of currently available knowledge. In this study, the initial loss values adopted for the impervious surfaces are relatively high compared to values noted in research literature. However, given the scientifically valid approach used for the field investigations, it is appropriate to adopt the initial losses derived from this study for future modelling of Port land uses. The relatively high initial losses will reduce the runoff volume generated as well as the frequency of runoff events significantly. Apart from initial losses, most of the other parameters used in SWMM modelling are generic to most modelling studies. Development of parameters for MUSIC model source nodes was one of the primary objectives of this study. MUSIC, uses the mean and standard deviation of pollutant parameters based on a normal distribution. However, based on the values generated in this study, the variation of Event Mean Concentrations (EMCs) for Port land uses within the given investigation period does not fit a normal distribution. This is possibly due to the fact that only one specific location was considered, namely the Port of Brisbane unlike in the case of the MUSIC model where a range of areas with different geographic and climatic conditions were investigated. Consequently, the assumptions used in MUSIC are not totally applicable for the analysis of water quality in Port land uses. Therefore, in using the parameters included in this report for MUSIC modelling, it is important to note that it may result in under or over estimations of annual pollutant loads. It is recommended that the annual pollutant load values given in the report should be used as a guide to assess the accuracy of the modelling outcomes. A step by step guide for using the knowledge generated from this study for MUSIC modelling is given in Table 4.6. ------------------ Recommendations: The following recommendations are provided to further strengthen the cutting edge nature of the work undertaken: * It is important to further validate the approach recommended for stormwater quality modelling at the Port. Validation will require data collection in relation to rainfall, runoff and water quality from the selected Port land uses. Additionally, the recommended modelling approach could be applied to a soon-to-be-developed area to assess ‘before’ and ‘after’ scenarios. * In the modelling study, TSS was adopted as the surrogate parameter for other pollutants. This approach was based on other urban water quality research undertaken at QUT. The validity of this approach should be further assessed for Port land uses. * The adoption of TSS as a surrogate parameter for other pollutants and the confirmation that the <150 m particle size range was predominant in suspended solids for pollutant wash-off gives rise to a number of important considerations. The ability of the existing structural stormwater mitigation measures to remove the <150 m particle size range need to be assessed. The feasibility of introducing source control measures as opposed to end-of-pipe measures for stormwater quality improvement may also need to be considered.

Synthesis and thermal analysis of Indium based hydrotalcites of formula Mg6In2(CO3)(OH)16•4H2O

Insight into the unique structure of layered double hydroxides has been obtained using a combination of X-ray diffraction and thermal analysis. Indium containing hydrotalcites of formula Mg4In2(CO3)(OH)12•4H2O (2:1 In-LDH) through to Mg8In2(CO3)(OH)18•4H2O (4:1 In-LDH) with variation in the Mg:In ratio have been successfully synthesised. The d(003) spacing varied from 7.83 Å for the 2:1 LDH to 8.15 Å for the 3:1 indium containing layered double hydroxide. Distinct mass loss steps attributed to dehydration, dehydroxylation and decarbonation are observed for the indium containing hydrotalcite. Dehydration occurs over the temperature range ambient to 205 °C. Dehydroxylation takes place in a series of steps over the 238 to 277 °C temperature range. Decarbonation occurs between 763 and 795 °C. The dehydroxylation and decarbonation steps depend upon the Mg:In ratio. The formation of indium containing hydrotalcites and their thermal activation provides a method for the synthesis of indium oxide based catalysts.

An analysis of the RC4 family of stream ciphers against algebraic attacks

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.