Ubiquitous Weak-key Classes of BRW-polynomial Function

BRW-polynomial function is suggested as a preferred alternative of polynomial function, owing to its high efficiency and seemingly non-existent weak keys. In this paper we investigate the weak-key issue of BRW-polynomial function as well as BRW-instantiated cryptographic schemes. Though, in BRW-polynomial evaluation, the relationship between coefficients and input blocks is indistinct, we give out a recursive algorithm to compute another $(2^{v+1}-1)$-block message, for any given $(2^{v+1}-1)$-block message, such that their output-differential through BRW-polynomial evaluation, equals any given $s$-degree polynomial, where $v\ge\lfloor\log_2(s+1)\rfloor$. With such algorithm, we illustrate that any non-empty key subset is a weak-key class in BRW-polynomial function. Moreover any key subset of BRW-polynomial function, consisting of at least $2$ keys, is a weak-key class in BRW-instantiated cryptographic schemes like the Wegman-Carter scheme, the UHF-then-PRF scheme, DCT, etc. Especially in the AE scheme DCT, its confidentiality, as well as its integrity, collapses totally, when using weak keys of BRW-polynomial function, which are ubiquitous

A Uniform Class of Weak Keys for Universal Hash Functions

In this paper we investigate weak keys of universal hash functions (UHFs) from their combinatorial properties. We find that any UHF has a general class of keys, which makes the combinatorial properties totally disappear, and even compromises the security of the UHF-based schemes, such as the Wegman-Carter scheme, the UHF-then-PRF scheme, etc. By this class of keys, we actually get a general method to search weak-key classes of UHFs, which is able to derive all previous weak-key classes of UHFs found by intuition or experience. Moreover we give a weak-key class of the BRW polynomial function which was once believed to have no weak-key issue, and exploit such weak keys to implement a distinguish attack and a forgery attack against DTC - a BRW-based authentication encryption scheme. Furthermore in Grain-128a, with the linear structure revealed by weak-key classes of its UHF, we can recover any first $(32+b)$ bits of the UHF key, spending no more than $1$ encryption and $(2^{32} + b)$ decryption queries

Field theoretic formulation and empirical tracking of spatial processes

Spatial processes are attacked on two fronts. On the one hand, tools from theoretical and statistical physics can be used to understand behaviour in complex, spatially-extended multi-body systems. On the other hand, computer vision and statistical analysis can be used to study 4D microscopy data to observe and understand real spatial processes in vivo. On the rst of these fronts, analytical models are developed for abstract processes, which can be simulated on graphs and lattices before considering real-world applications in elds such as biology, epidemiology or ecology. In the eld theoretic formulation of spatial processes, techniques originating in quantum eld theory such as canonical quantisation and the renormalization group are applied to reaction-di usion processes by analogy. These techniques are combined in the study of critical phenomena or critical dynamics. At this level, one is often interested in the scaling behaviour; how the correlation functions scale for di erent dimensions in geometric space. This can lead to a better understanding of how macroscopic patterns relate to microscopic interactions. In this vein, the trace of a branching random walk on various graphs is studied. In the thesis, a distinctly abstract approach is emphasised in order to support an algorithmic approach to parts of the formalism. A model of self-organised criticality, the Abelian sandpile model, is also considered. By exploiting a bijection between recurrent con gurations and spanning trees, an e cient Monte Carlo algorithm is developed to simulate sandpile processes on large lattices. On the second front, two case studies are considered; migratory patterns of leukaemia cells and mitotic events in Arabidopsis roots. In the rst case, tools from statistical physics are used to study the spatial dynamics of di erent leukaemia cell lineages before and after a treatment. One key result is that we can discriminate between migratory patterns in response to treatment, classifying cell motility in terms of sup/super/di usive regimes. For the second case study, a novel algorithm is developed to processes a 4D light-sheet microscopy dataset. The combination of transient uorescent markers and a poorly localised specimen in the eld of view leads to a challenging tracking problem. A fuzzy registration-tracking algorithm is developed to track mitotic events so as to understand their spatiotemporal dynamics under normal conditions and after tissue damage.Open Acces

Responses of boreal vegetation to recent climate change

The high northern latitudes have warmed faster than anywhere else in the globe during the past few decades. Boreal ecosystems are responding to this rapid climatic change in complex ways and some times contrary to expectations, with large implications for the global climate system. This thesis investigates how boreal vegetation has responded to recent climate change, particularly to the lengthening of the growing season and changes in drought severity with warming. The links between the timing of the growing season and the seasonal cycle of atmospheric CO2 are evaluated in detail to infer large-scale ecosystem responses to changing seasonality and extended period of plant growth. The influence of warming on summer drought severity is estimated at a regional scale for the first time using improved data. The results show that ecosystem responses to warming and lengthening of the growing season in autumn are opposite to those in spring. Earlier springs are associated with earlier onset of photosynthetic uptake of atmospheric CO2 by northern vegetation, whereas a delayed autumn, rather than being associated with prolonged photosynthetic uptake, is associated with earlier ecosystem carbon release to the atmosphere. Moreover, the photosynthetic growing season has closely tracked the pace of warming and extension of the potential growing season in spring, but not in autumn. Rapid warming since the late 1980s has increased evapotranspiration demand and consequently summer and autumn drought severity, offsetting the effect of increasing cold-season precipitation. This is consistent with ongoing amplification of the hydrological cycle and with model projections of summer drying at northern latitudes in response to anthropogenic warming. However, changes in snow dynamics (accumulation and melting) appear to be more important than increased evaporative demand in controlling changes in summer soil moisture availability and vegetation photosynthesis across extensive regions of the boreal zone, where vegetation growth is often assumed to be dominantly temperature-limited. Snow-mediated moisture controls of vegetation growth are particularly significant in northwestern North America. In this region, a non-linear growth response of white spruce growth to recent warming at high elevations was observed. Taken together, these results indicate that net observed responses of northern ecosystems to warming involve significant seasonal contrasts, can be non-linear and are mediated by moisture availability in about a third of the boreal zone

Doctor of Philosophy

dissertationThis research was undertaken to investigate the impacts of finer rock fragmentation (arising from higher energy blasting) on the unit costs of a hard-rock surface mine. The investigation was carried out at a copper operation in southern Utah, which exploits its deposits by conventional methods, including drilling, blasting, loading, and truck haulage. The run of mine is processed in a three-stage crushing circuit and a two-stage grinding circuit, which feed a flotation plant that produces a copper concentrate. The research was carried out using modeling and simulation techniques. Fifty-five blast designs in total were developed for ore and waste units, with energy inputs ranging from 100 kcal/st to 400 kcal/st. For each design, fragmentation was predicted using the Kuz-Ram method. Crushing of the predicted ore fragment size distributions was simulated using MODSIMTM. Data from pit face imaging and timed motion studies were collected and analyzed for the influence of fragmentation on shovel and truck productivity. Analyses indicated that fragment size distribution alone does not significantly impact this productivity. From simulation of the crushing circuit, it was found that the impact of differences in the blast-generated fragment distribution on the crusher energy is limited to the primary crusher, where a vast range of feed size distributions are introduced. No such relationships were evident at the secondary and tertiary crushers. Energy savings from increasing blasting intensity proved negligible and would not justify the costs of higher energy blasting. There was no evidence from this work that any beneficial influences of blast-generated fragment size distribution reach the grinding mill. Costs were estimated for drilling, blasting, and crushing, which were the principal unit operations inferred to be affected in some meaningful way by the varying intensities of blast energy input. The research shows that, principally as a result of jaw crusher gape restrictions and the significant unit costs of secondary reduction for both ore and waste, the net of all breakage (primary blast, secondary reduction, and crushing) does reduce to a transient minimum before they begin to ramp up again, thus fitting a classical mine-to-mill curve