Some Notes on Code-Based Cryptography

This thesis presents new cryptanalytic results in several areas of coding-based cryptography. In addition, we also investigate the possibility of using convolutional codes in code-based public-key cryptography. The first algorithm that we present is an information-set decoding algorithm, aiming towards the problem of decoding random linear codes. We apply the generalized birthday technique to information-set decoding, improving the computational complexity over previous approaches. Next, we present a new version of the McEliece public-key cryptosystem based on convolutional codes. The original construction uses Goppa codes, which is an algebraic code family admitting a well-defined code structure. In the two constructions proposed, large parts of randomly generated parity checks are used. By increasing the entropy of the generator matrix, this presumably makes structured attacks more difficult. Following this, we analyze a McEliece variant based on quasi-cylic MDPC codes. We show that when the underlying code construction has an even dimension, the system is susceptible to, what we call, a squaring attack. Our results show that the new squaring attack allows for great complexity improvements over previous attacks on this particular McEliece construction. Then, we introduce two new techniques for finding low-weight polynomial multiples. Firstly, we propose a general technique based on a reduction to the minimum-distance problem in coding, which increases the multiplicity of the low-weight codeword by extending the code. We use this algorithm to break some of the instances used by the TCHo cryptosystem. Secondly, we propose an algorithm for finding weight-4 polynomials. By using the generalized birthday technique in conjunction with increasing the multiplicity of the low-weight polynomial multiple, we obtain a much better complexity than previously known algorithms. Lastly, two new algorithms for the learning parities with noise (LPN) problem are proposed. The first one is a general algorithm, applicable to any instance of LPN. The algorithm performs favorably compared to previously known algorithms, breaking the 80-bit security of the widely used (512,1/8) instance. The second one focuses on LPN instances over a polynomial ring, when the generator polynomial is reducible. Using the algorithm, we break an 80-bit security instance of the Lapin cryptosystem

Bringing Theory Closer to Practice in Post-quantum and Leakage-resilient Cryptography

Modern cryptography pushed forward the need of having provable security. Whereas ancient cryptography was only relying on heuristic assumptions and the secrecy of the designs, nowadays researchers try to make the security of schemes to rely on mathematical problems which are believed hard to solve. When doing these proofs, the capabilities of potential adversaries are modeled formally. For instance, the black-box model assumes that an adversary does not learn anything from the inner-state of a construction. While this assumption makes sense in some practical scenarios, it was shown that one can sometimes learn some information by other means, e.g., by timing how long the computation take. In this thesis, we focus on two different areas of cryptography. In both parts, we take first a theoretical point of view to obtain a result. We try then to adapt our results so that they are easily usable for implementers and for researchers working in practical cryptography. In the first part of this thesis, we take a look at post-quantum cryptography, i.e., at cryptographic primitives that are believed secure even in the case (reasonably big) quantum computers are built. We introduce HELEN, a new public-key cryptosystem based on the hardness of the learning from parity with noise problem (LPN). To make our results more concrete, we suggest some practical instances which make the system easily implementable. As stated above, the design of cryptographic primitives usually relies on some well-studied hard problems. However, to suggest concrete parameters for these primitives, one needs to know the precise complexity of algorithms solving the underlying hard problem. In this thesis, we focus on two recent hard-problems that became very popular in post-quantum cryptography: the learning with error (LWE) and the learning with rounding problem (LWR). We introduce a new algorithm that solves both problems and provide a careful complexity analysis so that these problems can be used to construct practical cryptographic primitives. In the second part, we look at leakage-resilient cryptography which studies adversaries able to get some side-channel information from a cryptographic primitive. In the past, two main disjoint models were considered. The first one, the threshold probing model, assumes that the adversary can put a limited number of probes in a circuit. He then learns all the values going through these probes. This model was used mostly by theoreticians as it allows very elegant and convenient proofs. The second model, the noisy-leakage model, assumes that every component of the circuit leaks but that the observed signal is noisy. Typically, some Gaussian noise is added to it. According to experiments, this model depicts closely the real behaviour of circuits. Hence, this model is cherished by the practical cryptographic community. In this thesis, we show that making a proof in the first model implies a proof in the second model which unifies the two models and reconciles both communities. We then look at this result with a more practical point-of-view. We show how it can help in the process of evaluating the security of a chip based solely on the more standard mutual information metric

Mechanisms of spinal cord degeneration and repair in multiple sclerosis: A 3T MRI study of the spinal cord

The spinal cord is a clinically eloquent structure, commonly affected in multiple sclerosis (MS) and spinal neuroaxonal loss is an important cause of non-remitting, disability progression. Neuroaxonal loss in MS is likely to be multifactorial and caused by several disease pathways. In contrast, repair and adaptive mechanisms can ameliorate disability following clinical relapses. This thesis has explored some of these clinically relevant disease mechanisms by combining single-voxel proton spectroscopy (MRS) and Q-space imaging (QSI), two advanced MRI techniques, which have increased pathological specificity for neurodegeneration and myelin, and allow quantification of metabolites that reflect biological mechanisms, to study spinal neurodegeneration and repair in MS. In persons with early primary progressive MS (PPMS), spinal MRS and QSI exhibited increased sensitivity for detection of early disease changes than more conventional measures such as spinal cord atrophy and correlated with clinical disability measures suggesting these measures are functionally relevant. Region of interest analysis of the relationship between QSI indices in spinal white matter tracts and clinical scores which reflect the motor or sensory functions conveyed within those tracts, suggests a strong structure-function relationship exists between axonal integrity and disability. In persons with relapsing remitting MS (RRMS), with recent (within 4 weeks) symptoms suggestive of spinal cord relapse, serial imaging with spinal MRS and QSI over 6 months reflected clinical changes over that time. Specifically, rising spinal concentrations of total N-acetyl-aspartate (tNAA) and restriction of QSI-derived perpendicular diffusivity, which I hypothesise reflect, restoration of mitochondrial function and remyelination, respectively, underlie clinical recovery. Within the RRMS cohort, MRS and QSI measures at baseline were predictive of clinical outcomes at 6 months; elevated baseline spinal glutamate-glutamine (Glx), myo-inositol (Ins) and total creatine (tCr) concentrations and increased QSI-derived perpendicular diffusivity predicted poor outcomes and may reflect important mechanisms of disability progression such as; demyelination, neurodegeneration, astrogliosis and altered neuronal metabolism. Taken together the results suggest that mechanisms of disability following spinal cord relapse are complex and glutamate excitotoxicity, gliosis and axonal metabolic dysfunction may be important determinants of residual disability following relapses. This work suggests that newer, quantitative MRI techniques when applied to the spinal cord are sensitive markers of disease activity and progression and could be useful in monitoring therapies that aim to prevent neurodegeneration and enhance remyelination in MS

Neurocognitive predictors of post-stroke cognitive trajectory

The current thesis examined cognitive trajectories following stroke, and tested potential predictors of cognitive outcome, and trajectories. It used data from two existing databases: the Birmingham Cognitive Screen Study (BUCS) collected in the UK, and the C-BCoS collected in China, and newly collected data as part of the HiPPS-CI study (The role of Hippocampus Pathology in Post-Stroke-Cognitive Impairment). Chapter two aimed to answer the question; does the proportional recovery rule exist in cognition, as it does with motor recovery? We found that 80% of patients showed 40- 50% proportional recovery of cognition at nine months post-stroke. This was evident across and within cognitive domains. Recovery was not limited to the first three months following stroke. We further identified two other recovery trajectories, where around 10% of patients showed an accelerated recovery, while around 10% showed decelerated recovery and even decline. We then investigated the predictive value of years of education on post-stroke cognitive outcomes, and recovery rate (Chapter three). We found that education improved cognitive outcomes following stroke, and accelerated recovery in the first year following stroke beyond age. Finally, we explored the predictive value of hippocampal pathology, and the impact of hippocampal pathology on post-stroke cognition. We found that beyond stroke and age, hippocampal pathology predicted cognition within three months post-stroke. This was evident in grey matter volume, mean diffusivity, creatine, choline and N-acetylaspartate. Hippocampus pathology (specifically grey matter volume) interacted with education, age, vascular risk, cortical atrophy and small vessel disease. These factors also predicted cognition. It is concluded that post-stroke cognitive outcomes are affected by pre-stroke clinical, and socio-demographic factors, where education ameliorates the impact of stroke on cognition potentially by preserving the hippocampus, while neurovascular health potentially aggravates the cognitive impairments

Developing new imaging biomarkers in multiple sclerosis

To date, there have been significant advances in the use of magnetic resonance imaging (MRI) in the initial diagnostic work-up of patients suspected of having MS and also in the monitoring of disease activity during active treatment. However, there is often a discrepancy between the clinical and conventional MRI findings which arises due to the complex heterogeneous features of MS pathology. The development of imaging biomarkers, which are directly linked to the pathological processes underlying progressive and relapsing forms of MS, are vital to developing a better understanding of the pathological mechanisms driving the disease. In order to address this, I performed clinical studies in both progressive and relapsing forms of MS with both innovative imaging techniques and with other more established imaging measures. After the introduction (where I review the main characteristics of MS (Chapter I) and of conventional and advanced MRI techniques employed in the studies presented in this thesis (Chapter II)), I present the following studies: (A)Pilot studies with innovative imaging techniques – this included a gammaaminobutyric acid (GABA) magnetic resonance spectroscopy study in patients with secondary progressive multiple sclerosis (SPMS) (Chapter III) and a novel diffusion study (neurite orientation dispersion and density imaging, NODDI) in the brain of patients with relapsing remitting multiple sclerosis (RRMS) (Chapter IV). The main results of these investigations are that GABA may be a marker of neurodegeneration and NODDI may better characterise microstructural changes in the brain than standard diffusion tensor imaging. (B) Clinical studies with more established imaging measures including an MRI follow-up spinal cord study in primary progressive multiple sclerosis (PPMS) (Chapter V) using 1H-Magnetic resonance spectroscopy (1HMRS), Q-space imaging (QSI) and spinal cord area. Another study looked at the development of spinal cord atrophy in a progressive MS cohort of patients over 1 year to determine the sample sizes required to demonstrate a reduction in spinal cord cross-sectional area as a primary outcome measure in clinical trials (Chapter VI). Both of these studies demonstrated spinal cord atrophy occurred over 1 year and it may be a useful outcome measure in phase II neuroprotective trials in early PPMS. In the final chapter (Chapter VII), I will summarise the results of the studies presented in the thesis and propose future directions for the research

Fucoidan degradation by marine bacteria

The oceans are an important carbon sink that have sequestered about half of all anthropogenic CO2 emissions. Marine carbon cycling is driven by the deposition of photosynthetic micro- and macroalgae in ocean sediments, where carbon is stored over thousands of years. The algal polysaccharide fucoidan is considered to be recalcitrant to microbial degradation and may therefore facilitate long-term carbon storage. Yet, factors that render fucoidan recalcitrant against microbial degradation remain unidentified, hampering our understanding of fucoidans in the carbon cycle. Fucoidans originating from the cell wall of brown algae are often co-extracted with other cell wall components. In Chapter I, I develop a simple step-wise protocol to purify fucoidans from different brown algae. Using mass spectrometry and nuclear magnetic resonance analyses, I describe the highly diverse and branched structures of different fucoidans. In Chapter II, I examine how marine bacteria degrade those complex branched fucoidans. Using genomics, proteomics and biochemistry, I characterize the newly isolated Verrucomicrobium a Lentimonasa sp. CC4 and show that fucoidan degradation requires highly dedicated pathways of over 100 enzymes covering 20% of the a Lentimonasa sp. CC4 proteome. The complexity of these pathways implies that only highly specialized bacteria can effectively degrade fucoidans and gives a clue why it may be recalcitrant. The proteomic analysis of a Lentimonasa sp. CC4 in chapter II suggested that two protein families, S1 15 and GH29, are key in fucoidan degradation. In Chapter III, I biochemically and structurally characterize one S1 15 sulfatase and one GH29 fucosidase, revealing their exo-enzyme activity and a novel catalytic pair of two aspartate residues. This provides insights into the molecular mechanism of exo-enzymatic fucoidan degradation. In Chapter IV, I trace the dynamics of different polysaccharides during a diatom spring bloom in Helgoland. I found that the dominant bloom-forming diatom Chaetoceros socialis secretes fucoidan in dissolved form, which aggregates and accumulates in particles at the end of the bloom. Known enzymes to degrade this polysaccharide are not expressed in the microbial community which indicates that fucoidans are not microbially degraded and act as vector for organic carbon drawdown. To summarize, fucoidans are diverse, highly branched polysaccharides whose degradation requires a large set of enzymes found in very few specialized marine bacteria. Their stability-enhancing properties lead to increased brown algal deposition in coastal sediments and in the open ocean they may acts as aggregation nuclei that enhance aggregation and settling of phytoplankton aggregates. Their abundance, recalcitrant nature and stickiness make fucoidans a likely key players in oceanic carbon sequestration

The imprecatory Psalms in the light of the evangelical message

https://place.asburyseminary.edu/ecommonsatsdissertations/2012/thumbnail.jp

1965-02-04 Morehead News

Morehead News published on February 4, 1965