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.^

Seasonal and spatial variation in the stable isotopic composition (δ18O and δD) of precipitation in south Florida

Precipitation data collected from five sites in south Florida indicate a strong seasonal and spatial variation in δ18O and δD, despite the relatively limited geographic coverage and low-lying elevation of each of the collection sites. Based upon the weighted-mean stable isotope values, the sites were classified as coastal Atlantic, inland, and lower Florida Keys. The coastal Atlantic sites had weighted-mean values of δ18O and δD of −2.86‰ and −12.8‰, respectively, and exhibited a seasonal variation with lower δ18O and δD values in the summer wet-season precipitation (δ18O = −3.38‰, δD = −16.5‰) as compared to the winter-time precipitation (δ18O = −1.66‰, δD = −3.2‰). The inland site was characterized as having the highest d-excess value (+13.3‰), signifying a contribution of evaporated Everglades surface water to the local atmospheric moisture. In spite of its lower latitude, the lower Keys site located at Long Key had the lowest weighted-mean stable isotope values (δ18O = −3.64‰, δD = −20.2‰) as well as the lowest d-excess value of (+8.8‰). The lower δD and δ18O values observed at the Long Key site reflect the combined effects of oceanic vapor source, fractionation due to local precipitation, and slower equilibration of the larger raindrops nucleated by a maritime aerosol. Very low δ18O and δD values (δ18O < −6‰, δD < −40‰) were observed just prior to the passage of hurricanes from the Gulf of Mexico as well as during cold fronts from the north-west. These results suggest that an oceanic vapor source region to the west, may be responsible for the extremely low δD and δ18O values observed during some tropical storms and cold fronts.