On the effectiveness of isogeny walks for extending cover attacks on elliptic curves

Cryptographic systems based on the elliptic curve discrete logarithm problem (ECDLP) are widely deployed in the world today. In order for such a system to guarantee a particular security level, the elliptic curve selected must be such that it avoids a number of well-known attacks. Beyond this, one also needs to be wary of attacks whose reach can be extended via the use of isogenies. It is an open problem as to whether there exists a field for which the isogeny walk strategy can render all elliptic curves unsuitable for cryptographic use. This thesis provides a survey of the theory of elliptic curves from a cryptographic perspective and overviews a few of the well-known algorithms for computing elliptic curve discrete logarithms. We perform some experimental verification for the assumptions used in the analysis of the isogeny walk strategy for extending Weil descent-type cover attacks, and explore its applicability to elliptic curves of cryptographic size. In particular, we demonstrate for the first time that the field F_2^{150} is partially weak for elliptic curve cryptography

Recent progress on the elliptic curve discrete logarithm problem

International audienceWe survey recent work on the elliptic curve discrete logarithm problem. In particular we review index calculus algorithms using summation polynomials, and claims about their complexity

Prym varieties and their moduli

We discuss the geometry of the moduli space of Prym varieties. The article is based on series of lectures given in Bedlewo and Luminy. The first section of the paper contains a detailed historical account of the lives of Friedrich Prym and Friedrich Schottky.Comment: 35 pages, minor corrections and additions. To appear in "Contributions to algebraic geometry" edited by P. Pragacz and published by the EM

Discrete logarithms in curves over finite fields

A survey on algorithms for computing discrete logarithms in Jacobians of curves over finite fields

En studie av humane kitinaser med hensyn på overflate-eksponerte aromatiske residuer og karbohydrat-bindende moduler ved nedbrytning av substrat og rolle i inflammasjon

Chitin is an insoluble, linear polymer consisting of β-1, 4-linked N-acetyl-glucosamine units tightly packed in a crystalline structure. It is the second most abundant polysaccharide in nature, after cellulose, with an estimated annual production of about 1011 tons. Chitin is an essential structural component in the exoskeleton of crustaceans, arthropods, and insects, and is also found in the cell walls of certain fungi, algae, and parasitic nematodes. Enzymatic degradation of recalcitrant polysaccharides in biomass is of great biological importance. In nature, the degradation of chitin is catalyzed by chitinases, which are assigned to the glycoside hydrolase (GH) family 18 in the CAZY database (www.cazy.org). Humans have two active chitinases that are considered elements of the immune system because they degrade chitin-containing pathogens as a part of the host defense mechanism. The aim of the work presented in this thesis was to study the enzymatic mechanisms of one of the human chitinases, namely the human chitotriosidase (HCHT), to gain mechanistic insight into substrate degradation. A second goal was to study the expression of mammalian chitinases and chitinase-like proteins (CLP) in response to specific inflammatory stimuli to increase knowledge about the enzymes’ roles in the immune system.Kitin er en uløselig, lineær polymer bestående av β-1, 4-linket N-acetyl-glykosamin enheter tett pakket i en krystalinsk struktur. Etter cellulose er kitin det polysakkaridet i naturen det er størst forekomst av. Kitin er en viktig strukturell komponent i skalldyr, insekter og sopp, og er også tilstede i celleveggen til enkelte sopper, alger og parasitter. Til tross for de enorme mengdene kitin som produseres årlig akkumulerer ikke kitin i naturen. Dette skyldes en mengde proteiner som effektivt er med på enzymatisk nedbrytning av kitin, kjent som kitinaser. Humane kitinaser er også involvert i immunsystemet og i nedbrytning av kitin-holdige patogener. Formålet med dette prosjektet har vært å studere de enzymatiske mekanismene til en av de humane kitinasene, human kitotriosidase (HCHT). Dette for å tilegne kunnskap om mekanismene bak nedbrytning av polysakkarider. I tillegg ble rollen til mammalske kitinaser studert i en spesifikk inflammasjon for å øke kunnskapen om disse enzymene i immunsystemet

Final Report: Investigation into the Loss of the H.L. Hunley

The H.L. Hunley carried out the first successful submarine attack in history. However after a successful attack, the submarine disappeared with little evidence has to how it happened. This report documents work on two ONR grants exploring the naval architecture of the submarine. This work was conducted to support high-fidelity underwater explosion modeling of the attack at NSWCCD (not discussed here), but also sheds new light on the final mission and circumstances of the vessel’s loss. The vessel’s hullform, weights, stability are all discussed, along with model test for the vessel’s resistance and potential flooding rates. While the investigation did not reach a firm conclusion the cause of the loss, the results further illuminate the operation of vessel and avenues for further technical study.Office of Naval Research, Code 331https://deepblue.lib.umich.edu/bitstream/2027.42/142864/1/2017-001_final_complete.pdfDescription of 2017-001_final_complete.pdf : Repor

UNDERSTANDING GLYCOSIDE HYDROLASE PROCESSIVITY FOR IMPROVED BIOMASS CONVERSION

In nature, organisms secrete synergistic enzyme cocktails to deconstruct crystalline polysaccharides, such as cellulose and chitin, to soluble sugars. The cocktails consist of multiple classes of processive and non-processive glycoside hydrolases (GH) that aid in substrate accessibility and reduce product inhibition. Processive GHs attach to chain ends and hydrolyze many glycosidic linkages in sequence to produce disaccharide units before dissociation, and as such, are responsible for the majority of hydrolytic bond cleavages. Accordingly, processive GHs are targets for activity improvements towards efficient and economical biomass conversion. However, the mechanism and factors responsible for processivity are still not understood completely at the molecular level. Specifically, the relationship between processive GH function and the enzyme active site topology and chemical composition has yet to be elucidated. Using molecular simulation and free energy calculations, this work presents a molecular-level understanding of the protein-carbohydrate interactions governing processive GHs, which will facilitate rational design of GHs for enhanced biomass conversion. We hypothesize that processive GHs, having long tunnels or deep active site clefts, will allow more amino acids to interact with the ligand and exhibit strong ligand binding and low substrate dissociation rate constants; whereas non-processive enzymes, having more open tunnels or clefts, will exhibit comparatively weak binding and high dissociation rate constants. Moreover, the ligand binding free energy of a processive enzyme must also be more thermodynamically favorable than the work required to decrystallize a polymer from the substrate matrix. We selected the Serratia marcescens Family 18 chitinase model system, including processive chitinases, ChiA and ChiB, and a non-processive chitinase, ChiC, to test our hypotheses. We find that processive ChiA and ChiB exhibit ligand binding free energies that are more thermodynamically favorable than the work to decrystallize a chito-oligosaccharide from the crystalline chitin surface, which is essential for forward processive movement. The non-processive ChiC binds chito-oligosaccharides with a free energy that is significantly less favorable than the work of decrystallization. In general, our findings suggest that processive GH function necessitates tight binding within the enzyme active site. We also observed that aromatic and polar residues close to the catalytic center of ChiA and ChiB have a greater effect on ligand binding and processivity than the residues at the entrance or exit of the cleft. Mutation of active site aromatic and polar residues generally resulted in reduction in processivity and substantial reduction in substrate binding. Overall, our work demonstrates the existence of a fundamental relationship between ligand binding free energy and processive GH active site characteristics

Interactions between Algebraic Geometry and Noncommutative Algebra

[no abstract available