Analysis of linear relationships in block ciphers

This thesis is devoted to the study of linear relationships in symmetric block ciphers. A block cipher is designed so that the ciphertext is produced as a nonlinear function of the plaintext and secret master key. However, linear relationships within the cipher can still exist if the texts and components of the cipher are manipulated in a number of ways, as shown in this thesis. There are four main contributions of this thesis. The first contribution is the extension of the applicability of integral attacks from word-based to bitbased block ciphers. Integral attacks exploit the linear relationship between texts at intermediate stages of encryption. This relationship can be used to recover subkey bits in a key recovery attack. In principle, integral attacks can be applied to bit-based block ciphers. However, specific tools to define the attack on these ciphers are not available. This problem is addressed in this thesis by introducing a refined set of notations to describe the attack. The bit patternbased integral attack is successfully demonstrated on reduced-round variants of the block ciphers Noekeon, Present and Serpent. The second contribution is the discovery of a very small system of equations that describe the LEX-AES stream cipher. LEX-AES is based heavily on the 128-bit-key (16-byte) Advanced Encryption Standard (AES) block cipher. In one instance, the system contains 21 equations and 17 unknown bytes. This is very close to the upper limit for an exhaustive key search, which is 16 bytes. One only needs to acquire 36 bytes of keystream to generate the equations. Therefore, the security of this cipher depends on the difficulty of solving this small system of equations. The third contribution is the proposal of an alternative method to measure diffusion in the linear transformation of Substitution-Permutation-Network (SPN) block ciphers. Currently, the branch number is widely used for this purpose. It is useful for estimating the possible success of differential and linear attacks on a particular SPN cipher. However, the measure does not give information on the number of input bits that are left unchanged by the transformation when producing the output bits. The new measure introduced in this thesis is intended to complement the current branch number technique. The measure is based on fixed points and simple linear relationships between the input and output words of the linear transformation. The measure represents the average fraction of input words to a linear diffusion transformation that are not effectively changed by the transformation. This measure is applied to the block ciphers AES, ARIA, Serpent and Present. It is shown that except for Serpent, the linear transformations used in the block ciphers examined do not behave as expected for a random linear transformation. The fourth contribution is the identification of linear paths in the nonlinear round function of the SMS4 block cipher. The SMS4 block cipher is used as a standard in the Chinese Wireless LAN Wired Authentication and Privacy Infrastructure (WAPI) and hence, the round function should exhibit a high level of nonlinearity. However, the findings in this thesis on the existence of linear relationships show that this is not the case. It is shown that in some exceptional cases, the first four rounds of SMS4 are effectively linear. In these cases, the effective number of rounds for SMS4 is reduced by four, from 32 to 28. The findings raise questions about the security provided by SMS4, and might provide clues on the existence of a flaw in the design of the cipher.

Curvilinear relationships between the job demands-resources (JD-R) model, and work engagement : a police service case study

The current study aims to investigate the non-linear relationship between the JD-R model and work engagement. Previous research has identified linear relationships between these constructs; however there are strong theoretical arguments for testing curvilinear relationships (e.g., Warr, 1987). Data were collected via a self-report online survey from officers of one Australian police service (N = 2,626). Results demonstrated a curvilinear relationship between job demands and job resources and engagement. Gender (as a control variable) was also found to be a significant predictor of work engagement. The results indicated that male police officers experienced significantly higher job demands and colleague support than female officers. However, female police officers reported significantly higher levels of work engagement than male officers. This study emphasises the need to test curvilinear relationships, as well as simple linear associations, when measuring psychological health.

Non-linear principal components analysis : an alternative method for finding patterns in environmental data

The main purpose of this article is to gain an insight into the relationships between variables describing the environmental conditions of the Far Northern section of the Great Barrier Reef, Australia. Several of the variables describing these conditions had different measurement levels and often they had non-linear relationships. Using non-linear principal component analysis, it was possible to acquire an insight into these relationships. Furthermore, three geographical areas with unique environmental characteristics could be identified.

Relationships between major ions in coal seam gas groundwaters: Examples from the Surat and Clarence-Moreton basins

Using a combination of multivariate statistical techniques and the graphical assessment of major ion ratios, the influences on hydrochemical variability of coal seam gas (or coal bed methane) groundwaters from several sites in the Surat and Clarence-Moreton basins in Queensland, Australia, were investigated. Several characteristic relationships between major ions were observed: 1) strong positive linear correlation between the Na/Cl and alkalinity/Cl ratios; 2) an exponentially decaying trend between the Na/Cl and Na/alkalinity ratios; 3) inverse linear relationships between increasing chloride concentrations and decreasing pH for high salinity groundwaters, and; 4) high residual alkalinity for lower salinity waters, and an inverse relationship between decreasing residual alkalinity and increasing chloride concentrations for more saline waters. The interpretation of the hydrochemical data provides invaluable insights into the hydrochemical evolution of coal seam gas (CSG) groundwaters that considers both the source of major ions in coals and the influence of microbial activity. Elevated chloride and sodium concentrations in more saline groundwaters appear to be influenced by organic-bound chlorine held in the coal matrix; a sodium and chloride ion source that has largely been neglected in previous CSG groundwater studies. However, contrastingly high concentrations of bicarbonate in low salinity waters could not be explained, and are possibly associated with a number of different factors such as coal degradation, methanogenic processes, the evolution of high-bicarbonate NaHCO3 water types earlier on in the evolutionary pathway, and variability in gas reservoir characteristics. Using recently published data for CSG groundwaters in different basins, the characteristic major ion relationships identified for new data presented in this study were also observed in other CSG groundwaters from Australia, as well as for those in the Illinois Basin in the USA. This observation suggests that where coal maceral content and the dominant methanogenic pathway are similar, and where organic-bound chlorine is relatively abundant, distinct hydrochemical responses may be observed. Comparisons with published data of other NaHCO3 water types in non-CSG environments suggest that these characteristic major ion relationships described here can: i) serve as an indicator of potential CSG groundwaters in certain coal-bearing aquifers that contain methane; and ii) help in the development of strategic sampling programmes for CSG exploration and to monitor potential impacts of CSG activities on groundwater resources.

Multicomponent kinetic spectrophotometric determination of pefloxacin and norfloxacin in pharmaceutical preparations and human plasma samples with the aid of chemometrics

A spectrophotometric method for the simultaneous determination of the important pharmaceuticals, pefloxacin and its structurally similar metabolite, norfloxacin, is described for the first time. The analysis is based on the monitoring of a kinetic spectrophotometric reaction of the two analytes with potassium permanganate as the oxidant. The measurement of the reaction process followed the absorbance decrease of potassium permanganate at 526 nm, and the accompanying increase of the product, potassium manganate, at 608 nm. It was essential to use multivariate calibrations to overcome severe spectral overlaps and similarities in reaction kinetics. Calibration curves for the individual analytes showed linear relationships over the concentration ranges of 1.0–11.5 mg L−1 at 526 and 608 nm for pefloxacin, and 0.15–1.8 mg L−1 at 526 and 608 nm for norfloxacin. Various multivariate calibration models were applied, at the two analytical wavelengths, for the simultaneous prediction of the two analytes including classical least squares (CLS), principal component regression (PCR), partial least squares (PLS), radial basis function-artificial neural network (RBF-ANN) and principal component-radial basis function-artificial neural network (PC-RBF-ANN). PLS and PC-RBF-ANN calibrations with the data collected at 526 nm, were the preferred methods—%RPET not, vert, similar 5, and LODs for pefloxacin and norfloxacin of 0.36 and 0.06 mg L−1, respectively. Then, the proposed method was applied successfully for the simultaneous determination of pefloxacin and norfloxacin present in pharmaceutical and human plasma samples. The results compared well with those from the alternative analysis by HPLC.

Linearity within the SMS4 Block Cipher

We present several new observations on the SMS4 block cipher, and discuss their cryptographic significance. The crucial observation is the existence of fixed points and also of simple linear relationships between the bits of the input and output words for each component of the round functions for some input words. This implies that the non-linear function T of SMS4 does not appear random and that the linear transformation provides poor diffusion. Furthermore, the branch number of the linear transformation in the key scheduling algorithm is shown to be less than optimal. The main security implication of these observations is that the round function is not always non-linear. Due to this linearity, it is possible to reduce the number of effective rounds of SMS4 by four. We also investigate the susceptibility of SMS4 to further cryptanalysis. Finally, we demonstrate a successful differential attack on a slightly modified variant of SMS4. These findings raise serious questions on the security provided by SMS4.

Temperature dependent electrical resistivity in expoxy : multiwall carbon nanotube nanocomposites

Thin films of expoxy nanocomposites modified by multiwall carbon nanotubes (MWCNTs) were prepared by shear mixing and spin casting. The electrical behaviour and its dependence with temperature between 243 and 353 degrees Kelvin were characterized by measuring the direct current (DC) conductivity. Depending on the fabrication process, both linear and non-linear relationships between conductivity and temperature were observed. In addition, the thermal history also played a role in dictating the conductivity. The implications of these observations for potential application of these files as strain sensors are discussed.

The 3D kinematics of the single leg flat and decline squat

Background: Pre-participation screening is commonly used to measure and assess potential intrinsic injury risk. The single leg squat is one such clinical screening measure used to assess lumbopelvic stability and associated intrinsic injury risk. With the addition of a decline board, the single leg decline squat (SLDS) has been shown to reduce ankle dorsiflexion restrictions and allowed greater sagittal plane movement of the hip and knee. On this basis, the SLDS has been employed in the Cricket Australia physiotherapy screening protocols as a measure of lumbopelvic control in the place of the more traditional single leg flat squat (SLFS). Previous research has failed to demonstrate which squatting technique allows for a more comprehensive assessment of lumbopelvic stability. Tenuous links are drawn between kinematics and hip strength measures within the literature for the SLS. Formal evaluation of subjective screening methods has also been suggested within the literature. Purpose: This study had several focal points namely 1) to compare the kinematic differences between the two single leg squatting conditions, primarily the five key kinematic variables fundamental to subjectively assess lumbopelvic stability; 2) determine the effect of ankle dorsiflexion range of motion has on squat kinematics in the two squat techniques; 3) examine the association between key kinematics and subjective physiotherapists’ assessment; and finally 4) explore the association between key kinematics and hip strength. Methods: Nineteen (n=19) subjects performed five SLDS and five SLFS on each leg while being filmed by an 8 camera motion analysis system. Four hip strength measures (internal/external rotation and abd/adduction) and ankle dorsiflexion range of motion were measured using a hand held dynamometer and a goniometer respectively on 16 of these subjects. The same 16 participants were subjectively assessed by an experienced physiotherapist for lumbopelvic stability. Paired samples t-tests were performed on the five predetermined kinematic variables to assess the differences between squat conditions. A Bonferroni correction for multiple comparisons was used which adjusted the significance value to p = 0.005 for the paired t-tests. Linear regressions were used to assess the relationship between kinematics, ankle range of motion and hip strength measures. Bivariate correlations between hip strength measures and kinematics and pelvic obliquity were employed to investigate any possible relationships. Results: 1) Significant kinematic differences between squats were observed in dominant (D) and non-dominant (ND) end of range hip external rotation (ND p = <0.001; D p = 0.004) and hip adduction kinematics (ND p = <0.001; D p = <0.001). With the mean angle, only the non-dominant leg observed significant differences in hip adduction (p = 0.001) and hip external rotation (p = <0.001); 2) Significant linear relationships were observed between clinical measures of ankle dorsiflexion and sagittal plane kinematic namely SLFS dominant ankle (p = 0.006; R2 = .429), SLFS non-dominant knee (p = 0.015; R2 = .352) and SLFS non-dominant ankle (p = 0.027; R2 = .305) kinematics. Only the dominant ankle (p = 0.020; R2 = .331) was found to have a relationship with the decline squat. 3) Strength measures had tenuous associations with the subjective assessments of lumbopelvic stability with no significant relationships being observed. 4) For the non-dominant leg, external rotation strength and abduction strength were found to be significantly correlated with hip rotation kinematics (Newtons r = 0.458 p = 0.049; Normalised for bodyweight: r = 0.469; p = 0.043) and pelvic obliquity (normalised for bodyweight: r = 0.498 p = 0.030) respectively for the SLFS only. No significant relationships were observed in the dominant leg for either squat condition. Some elements of the hip strength screening protocols had linear relationships with kinematics of the lower limb, particularly the sagittal plane movements of the knee and ankle. Strength measures had tenuous associations with the subjective assessments of lumbopelvic stability with no significant relationships being observed; Discussion: The key finding of this study illustrated that kinematic differences can occur at the hip without significant kinematic differences at the knee as a result of the introduction of a decline board. Further observations reinforce the role of limited ankle dorsiflexion range of motion on sagittal plane movement of the hip and knee and in turn multiplanar kinematics of the lower limb. The kinematic differences between conditions have clinical implications for screening protocols that employ frontal plane movement of the knee as a guide for femoral adduction and rotation. Subjects who returned stronger hip strength measurements also appeared to squat deeper as characterised by differences in sagittal plane kinematics of the knee and ankle. Despite the aforementioned findings, the relationship between hip strength and lower limb kinematics remains largely tenuous in the assessment of the lumbopelvic stability using the SLS. The association between kinematics and the subjective measures of lumbopelvic stability also remain tenuous between and within SLS screening protocols. More functional measures of hip strength are needed to further investigate these relationships. Conclusion: The type of SLS (flat or decline) should be taken into account when screening for lumbopelvic stability. Changes to lower limb kinematics, especially around the hip and pelvis, were observed with the introduction of a decline board despite no difference in frontal plane knee movements. Differences in passive ankle dorsiflexion range of motion yielded variations in knee and ankle kinematics during a self-selected single leg squatting task. Clinical implications of removing posterior ankle restraints and using the knee as a guide to illustrate changes at the hip may result in inaccurate screening of lumbopelvic stability. The relationship between sagittal plane lower limb kinematics and hip strength may illustrate that self-selected squat depth may presumably be a useful predictor of the lumbopelvic stability. Further research in this area is required.

CT and radiographic analysis of sagittal profile changes after thoracoscopic anterior scoliosis surgery

Background. Previous studies report an increase in thoracic kyphosis after anterior approaches and a flattening of sagittal contours following posterior approaches. Difficulties with measuring sagittal parameters on radiographs are avoided with reformatted sagittal CT reconstructions due to the superior endplate clarity afforded by this imaging modality. Methods. A prospective study of 30 Lenke 1 adolescent idiopathic scoliosis (AIS) patients receiving selective thoracoscopic anterior spinal fusion (TASF) was performed. Participants had ethically approved low dose CT scans at minimum 24 months after surgery in addition to their standard care following surgery. The change in sagittal contours on supine CT was compared to standing radiographic measurements of the same patients and with previous studies. Inter-observer variability was assessed as well as whether hypokyphotic and normokyphotic patient groups responded differently to the thoracoscopic anterior approach. Results. Mean T5-12 kyphosis Cobb angle increased by 11.8 degrees and lumbar lordosis increased by 5.9 degrees on standing radiographs two years after surgery. By comparison, CT measurements of kyphosis and lordosis increased by 12.3 degrees and 7.0 degrees respectively. 95% confidence intervals for inter-observer variability of sagittal contour measurements on supine CT ranged between 5-8 degrees. TASF had a slightly greater corrective effect on patients who were hypokyphotic before surgery compared with those who were normokyphotic. Conclusions. Restoration of sagittal profile is an important goal of scoliosis surgery, but reliable measurement with radiographs suffers from poor endplate clarity. TASF significantly improves thoracic kyphosis and lumbar lordosis while preserving proximal and distal junctional alignment in thoracic AIS patients. Supine CT allows greater endplate clarity for sagittal Cobb measurements and linear relationships were found between supine CT and standing radiographic measurements. In this study, improvements in sagittal kyphosis and lordosis following surgery were in agreement with prior anterior surgery studies, and add to the current evidence suggesting that anterior correction is more capable than posterior approaches of addressing the sagittal component of both the instrumented and adjacent non instrumented segments following surgical correction of progressive Lenke 1 idiopathic scoliosis.

A hybrid approach to combining CART and logistic regression for stock ranking

The benefits of applying tree-based methods to the purpose of modelling financial assets as opposed to linear factor analysis are increasingly being understood by market practitioners. Tree-based models such as CART (classification and regression trees) are particularly well suited to analysing stock market data which is noisy and often contains non-linear relationships and high-order interactions. CART was originally developed in the 1980s by medical researchers disheartened by the stringent assumptions applied by traditional regression analysis (Brieman et al. [1984]). In the intervening years, CART has been successfully applied to many areas of finance such as the classification of financial distress of firms (see Frydman, Altman and Kao [1985]), asset allocation (see Sorensen, Mezrich and Miller [1996]), equity style timing (see Kao and Shumaker [1999]) and stock selection (see Sorensen, Miller and Ooi [2000])...

Assessing the impacts of lifetime sun exposure on skin damage and skin aging using a non-invasive method

Background: Ultraviolet radiation exposure during an individuals' lifetime is a known risk factor for the development of skin cancer. However, less evidence is available on assessing the relationship between lifetime sun exposure and skin damage and skin aging. Objectives: This study aims to assess the relationship between lifetime sun exposure and skin damage and skin aging using a non-invasive measure of exposure. Methods: We recruited 180 participants (73 males, 107 females) aged 18-83 years. Digital imaging of skin hyper-pigmentation (skin damage) and skin wrinkling (skin aging) on the facial region was measured. Lifetime sun exposure (presented as hours) was calculated from the participants' age multiplied by the estimated annual time outdoors for each year of life. We analyzed the effects of lifetime sun exposure on skin damage and skin aging. We adjust for the influence of age, sex, occupation, history of skin cancer, eye color, hair color, and skin color. Results: There were non-linear relationships between lifetime sun exposure and skin damage and skin aging. Younger participant's skin is much more sensitive to sun exposure than those who were over 50 years of age. As such, there were negative interactions between lifetime sun exposure and age. Age had linear effects on skin damage and skin aging. Conclusion: The data presented showed that self reported lifetime sun exposure was positively associated with skin damage and skin aging, in particular, the younger people. Future health promotion for sun exposure needs to pay attention to this group for skin cancer prevention messaging. (C) 2012 Elsevier B.V. All rights reserved.

The slumbarumba jumbuck problem

The potential for simple linear relationships arising from a computer game to build student modelling and "world problem" skills is explored. The fundamental capability of the spreadsheet to tabulate and graph possible solutions is used to lay bare the problem structure for the students.

Teaching basic finance with Excel, and without pain

The five quantities of interest in elementary finance problems are present value, future value, amount of periodic payment, number of periods and the rate of compound interest per period. A recursive approach to computing each of these five quantities in a modern version of Excel, for the case of ordinary annuities, is described. The aim is to increase student understanding and build confidence in the answer obtained, and this may be achieved with only linear relationships and in cases where student knowledge of algebra is essentially zero. Annuity problems may be solved without use of logarithms and black-box intrinsic functions; these being used only as check mechanisms. The author has had success with the method at Bond University and surrounding high schools in Queensland, Australia.

A Model to Estimate the Population Contributing to the Wastewater Using Samples Collected on Census Day

An important uncertainty when estimating per capita consumption of, for example, illicit drugs by means of wastewater analysis (sometimes referred to as “sewage epidemiology”) relates to the size and variability of the de facto population in the catchment of interest. In the absence of a day-specific direct population count any indirect surrogate model to estimate population size lacks a standard to assess associated uncertainties. Therefore, the objective of this study was to collect wastewater samples at a unique opportunity, that is, on a census day, as a basis for a model to estimate the number of people contributing to a given wastewater sample. Mass loads for a wide range of pharmaceuticals and personal care products were quantified in influents of ten sewage treatment plants (STP) serving populations ranging from approximately 3500 to 500 000 people. Separate linear models for population size were estimated with the mass loads of the different chemical as the explanatory variable: 14 chemicals showed good, linear relationships, with highest correlations for acesulfame and gabapentin. De facto population was then estimated through Bayesian inference, by updating the population size provided by STP staff (prior knowledge) with measured chemical mass loads. Cross validation showed that large populations can be estimated fairly accurately with a few chemical mass loads quantified from 24-h composite samples. In contrast, the prior knowledge for small population sizes cannot be improved substantially despite the information of multiple chemical mass loads. In the future, observations other than chemical mass loads may improve this deficit, since Bayesian inference allows including any kind of information relating to population size.

Shaping and re-shaping social capital in buyer-supplier relationships

Social capital plays an important role in explaining how value is created from firms' network relationships, but little is understood about how social capital is shaped over time and how it is re-shaped when firms consolidate their network ties. In response, this study explores the evolution of social capital in buyer–supplier relationships through a case study of a company undertaking radical product innovation, and examines the corresponding changes in the firm's network of buyer–supplier relationships. The analysis shows that social capital is built in a decidedly non-linear and non-uniform manner. The study also reveals considerable interaction among the dimensions of social capital throughout the evolution of the firm's network, and emphasizes the importance of the cognitive dimension—a feature receiving little attention thus far. The evidence shows, too, that efforts to strengthen social capital need to increase when network ties are sacrificed to prevent unintended consequences for firms' longer-term value creation.