Foundations of quantitative information flow: Channels, cascades, and the information order

Secrecy is fundamental to computer security, but real systems often cannot avoid leaking some secret information. For this reason, the past decade has seen growing interest in quantitative theories of information flow that allow us to quantify the information being leaked. Within these theories, the system is modeled as an information-theoretic channel that specifies the probability of each output, given each input. Given a prior distribution on those inputs, entropy-like measures quantify the amount of information leakage caused by the channel. ^ This thesis presents new results in the theory of min-entropy leakage. First, we study the perspective of secrecy as a resource that is gradually consumed by a system. We explore this intuition through various models of min-entropy consumption. Next, we consider several composition operators that allow smaller systems to be combined into larger systems, and explore the extent to which the leakage of a combined system is constrained by the leakage of its constituents. Most significantly, we prove upper bounds on the leakage of a cascade of two channels, where the output of the first channel is used as input to the second. In addition, we show how to decompose a channel into a cascade of channels. ^ We also establish fundamental new results about the recently-proposed g-leakage family of measures. These results further highlight the significance of channel cascading. We prove that whenever channel A is composition refined by channel B, that is, whenever A is the cascade of B and R for some channel R, the leakage of A never exceeds that of B, regardless of the prior distribution or leakage measure (Shannon leakage, guessing entropy leakage, min-entropy leakage, or g-leakage). Moreover, we show that composition refinement is a partial order if we quotient away channel structure that is redundant with respect to leakage alone. These results are strengthened by the proof that composition refinement is the only way for one channel to never leak more than another with respect to g-leakage. Therefore, composition refinement robustly answers the question of when a channel is always at least as secure as another from a leakage point of view.^

Lattice Boltzmann method for flow and heat transfer in microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Spatial variability in Florida Bay particulate organic matter composition: combining flow cytometry with stable isotope analyses

Long-term management plans for restoration of natural flow conditions through the Everglades increase the importance of understanding potential nutrient impacts of increased freshwater delivery on Florida Bay biogeochemistry. Planktonic communities respond quickly to changes in water quality, thus spatial variability in community composition and relationships to nutrient parameters must be understood in order to evaluate future downstream impacts of modifications to Everglades hydrology. Here we present initial results combining flow cytometry analyses of phytoplankton and bacterial populations (0.1–50 μm size fraction) with measurements of δ13C and δ15N composition and dissolved inorganic nutrient concentrations to explore proxies for planktonic species assemblage compositions and nutrient cycling. Particulate organic material in the 0.1–50 μm size fraction was collected from five stations in Northeastern and Western Florida Bay to characterize spatial variability in species assemblage and stable isotopic composition. A dense bloom of the picocyanobacterium, Synechococcus elongatus, was observed at Western Florida Bay sites. Smaller Synechococcus sp. were present at Northeast sites in much lower abundance. Bacteria and detrital particles were also more abundant at Western Florida Bay stations than in the northeast region. The highest abundance of detritus occurred at Trout Creek, which receives freshwater discharge from the Everglades through Taylor Slough. In terms of nutrient availability and stable isotopic values, the S. elongatus population in the Western bay corresponded to low DIN (0.5 μM NH 4 + ; 0.2 μM NO 3 − ) concentrations and depleted δ15N signatures ranging from +0.3 to +0.8‰, suggesting that the bloom supported high productivity levels through N2-fixation. δ15N values from the Northeast bay were more enriched (+2.0 to +3.0‰), characteristic of N-recycling. δ13C values were similar for all marine Florida Bay stations, ranging from −17.6 to −14.4‰, however were more depleted at the mangrove ecotone station (−25.5 to −22.3‰). The difference in the isotopic values reflects differences in carbon sources. These findings imply that variations in resource availability and nutrient sources exert significant control over planktonic community composition, which is reflected by stable isotopic signatures.

Lattice boltzmann modeling of fluid flow to determine the permeability of a karst specimen

A limestone sample was scanned using computed tomography (CT) and the hydraulic conductivity of the 3D reconstructed sample was determined using Lattice- Boltzmann methods (LBM) at varying scales. Due to the shape and size of the original sample, it was challenging to obtain a consistent rectilinear test sample. Through visual inspection however, 91 mm and 76 mm samples were digitally cut from the original. The samples had porosities of 58% and 64% and produced hydraulic conductivity values of K= 13.5 m/s and K=34.5 m/s, respectively. Both of these samples were re-sampled to 1/8 and 1/64 of their original size to produce new virtual samples at lower resolutions of 0.542 mm/lu and 1.084 mm/lu, while still representing the same physical dimensions. The hydraulic conductivity tended to increase slightly as the resolution became coarser. In order to determine an REV, the 91 mm sample was also sub-sampled into blocks that were 1/8 and 1/64 the size of the original. The results were consistent with analytical expectations such as those produced by the Kozeny-Carman equation. A definitive REV size was not reached, however, indicating the need for a larger sample. The methods described here demonstrate the ability of LBM to test rock structures and sizes not normally attainable.

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Modeling the Effect of Land Use and Climate Change Scenarios on the Water Flux of the Upper Mara River Flow, Kenya

Increasingly erratic flow in the upper reaches of the Mara River, has directed attention to land use change as the major cause of this problem. The semi-distributed hydrological model SWAT and Landsat imagery were utilized in order to 1) map existing land use practices, 2) determine the impacts of land use change on water flux; and 3) determine the impacts of climate change scenarios on the water flux of the upper Mara River. This study found that land use change scenarios resulted in more erratic discharge while climate change scenarios had a more predictable impact on the discharge and water balance components. The model results showed the flow was more sensitive to the rainfall changes than land use changes but land use changes reduce dry season flows which is a major problem in the basin. Deforestation increased the peak flows which translated to increased sediment loading in the Mara River.