Elliptic curves, group law, and efficient computation

This thesis is about the derivation of the addition law on an arbitrary elliptic curve and efficiently adding points on this elliptic curve using the derived addition law. The outcomes of this research guarantee practical speedups in higher level operations which depend on point additions. In particular, the contributions immediately find applications in cryptology. Mastered by the 19th century mathematicians, the study of the theory of elliptic curves has been active for decades. Elliptic curves over finite fields made their way into public key cryptography in late 1980’s with independent proposals by Miller [Mil86] and Koblitz [Kob87]. Elliptic Curve Cryptography (ECC), following Miller’s and Koblitz’s proposals, employs the group of rational points on an elliptic curve in building discrete logarithm based public key cryptosystems. Starting from late 1990’s, the emergence of the ECC market has boosted the research in computational aspects of elliptic curves. This thesis falls into this same area of research where the main aim is to speed up the additions of rational points on an arbitrary elliptic curve (over a field of large characteristic). The outcomes of this work can be used to speed up applications which are based on elliptic curves, including cryptographic applications in ECC. The aforementioned goals of this thesis are achieved in five main steps. As the first step, this thesis brings together several algebraic tools in order to derive the unique group law of an elliptic curve. This step also includes an investigation of recent computer algebra packages relating to their capabilities. Although the group law is unique, its evaluation can be performed using abundant (in fact infinitely many) formulae. As the second step, this thesis progresses the finding of the best formulae for efficient addition of points. In the third step, the group law is stated explicitly by handling all possible summands. The fourth step presents the algorithms to be used for efficient point additions. In the fifth and final step, optimized software implementations of the proposed algorithms are presented in order to show that theoretical speedups of step four can be practically obtained. In each of the five steps, this thesis focuses on five forms of elliptic curves over finite fields of large characteristic. A list of these forms and their defining equations are given as follows: (a) Short Weierstrass form, y2 = x3 + ax + b, (b) Extended Jacobi quartic form, y2 = dx4 + 2ax2 + 1, (c) Twisted Hessian form, ax3 + y3 + 1 = dxy, (d) Twisted Edwards form, ax2 + y2 = 1 + dx2y2, (e) Twisted Jacobi intersection form, bs2 + c2 = 1, as2 + d2 = 1, These forms are the most promising candidates for efficient computations and thus considered in this work. Nevertheless, the methods employed in this thesis are capable of handling arbitrary elliptic curves. From a high level point of view, the following outcomes are achieved in this thesis. - Related literature results are brought together and further revisited. For most of the cases several missed formulae, algorithms, and efficient point representations are discovered. - Analogies are made among all studied forms. For instance, it is shown that two sets of affine addition formulae are sufficient to cover all possible affine inputs as long as the output is also an affine point in any of these forms. In the literature, many special cases, especially interactions with points at infinity were omitted from discussion. This thesis handles all of the possibilities. - Several new point doubling/addition formulae and algorithms are introduced, which are more efficient than the existing alternatives in the literature. Most notably, the speed of extended Jacobi quartic, twisted Edwards, and Jacobi intersection forms are improved. New unified addition formulae are proposed for short Weierstrass form. New coordinate systems are studied for the first time. - An optimized implementation is developed using a combination of generic x86-64 assembly instructions and the plain C language. The practical advantages of the proposed algorithms are supported by computer experiments. - All formulae, presented in the body of this thesis, are checked for correctness using computer algebra scripts together with details on register allocations.

Influence of iodine value on combustion and NOx emission characteristics of a DI diesel engine

Biodiesel is a renewable fuel that has been shown to reduce many exhaust emissions, except oxides of nitrogen (NOx), in diesel engine cars. This is of special concern in inner urban areas that are subject to strict environmental regulations, such as EURO norms. Also, the use of pure biodiesel (B100) is inhibited because of its higher NOx emissions compared to petroleum diesel fuel. The aim of this present work is to investigate the effect of the iodine value and cetane number of various biodiesel fuels obtained from different feed stocks on the combustion and NOx emission characteristics of a direct injection (DI) diesel engine. The biodiesel fuels were chosen from various feed stocks such as coconut, palm kernel, mahua (Madhuca indica), pongamia pinnata, jatropha curcas, rice bran, and sesame seed oils. The experimental results show an approximately linear relationship between iodine value and NOx emissions. The biodiesels obtained from coconut and palm kernel showed lower NOx levels than diesel, but other biodiesels showed an increase in NOx. It was observed that the nature of the fatty acids of the biodiesel fuels had a significant influence on the NOx emissions. Also, the cetane numbers of the biodiesel fuels are affected both premixed combustion and the combustion rate, which further affected the amount of NOx formation. It was concluded that NOx emissions are influenced by many parameters of biodiesel fuels, particularly the iodine value and cetane number.

Le infrastrutture viarie dismesse o declassate ed il progetto di paesaggio

Paesaggio ed infrastrutture viarie sono un binomio molto forte: il primo ha insito il concetto di accessibilità, in quanto non può esistere senza la presenza di un osservatore; la strada, invece, trova i fattori che la connotano nel suo rapporto con la morfologia su cui insiste. Le infrastrutture viarie sono elemento strutturale e strutturante non solo di un territorio, ma anche di un paesaggio. Le attuali esigenze di mobilità portano oggi a ripensare ed adeguare molte infrastrutture viarie: laddove è possibile si potenziano le strutture esistenti, in diversi casi si ricorre a nuovi tracciati o a varianti di percorso. Porsi il problema di conservare itinerari testimoni della cultura materiale ed economica di una società implica considerazioni articolate, che travalicano i limiti del sedime: una via è un organismo più complesso della semplice linea di trasporto in quanto implica tutta una serie di manufatti a supporto della mobilità e soprattutto il corridoio infrastrutturale che genera e caratterizza, ovvero una porzione variabile di territorio definita sia dal tracciato che dalla morfologia del contesto. L’evoluzione dei modelli produttivi ed economici, che oggi porta quote sempre maggiori di popolazione a passare un tempo sempre minore all’interno del proprio alloggio, rende la riflessione sulle infrastrutture viarie dismesse o declassate occasione per la progettazione di spazi per l’abitare collettivo inseriti in contesti paesaggistici, tanto urbani che rurali, tramite reti di percorsi pensate per assorbire tagli di mobilità specifici e peculiari. Partendo da queste riflessioni la Tesi si articola in: Individuazioni del contesto teorico e pratico: Lo studio mette in evidenza come la questione delle infrastrutture viarie e del loro rapporto con il paesaggio implichi riflessioni incrociate a diversi livelli e tramite diverse discipline. La definizione dello spazio fisico della strada passa infatti per la costruzione di un itinerario, un viaggio che si appoggia tanto ad elementi fisici quanto simbolici. La via è un organismo complesso che travalica il proprio sedime per coinvolgere una porzione ampia di territorio, un corridoio variabile ed articolato in funzione del paesaggio attraversato. Lo studio propone diverse chiavi di lettura, mettendo in luce le possibili declinazioni del tema, in funzione del taglio modale, del rapporto con il contesto, del regime giuridico, delle implicazioni urbanistiche e sociali. La mobilità dolce viene individuata quale possibile modalità di riuso, tutela e recupero, del patrimonio diffuso costituito dalle diversi reti di viabilità. Antologia di casi studio: Il corpo principale dello studio si basa sulla raccolta, analisi e studio dello stato dell’arte nel settore; gli esempi raccolti sono presentati in due sezioni: la prima dedicata alle esperienze più significative ed articolate, che affrontano il recupero delle infrastrutture viarie a più livelli ed in modo avanzato non concentrandosi solo sulla conversione del sedime, ma proponendo un progetto che coinvolga tutto il corridoio attraversato dall’infrastruttura; la seconda parte illustra la pratica corrente nelle diverse realtà nazionali, ponendo in evidenza similitudini e differenze tra i vari approcci.

Assetti proprietari e meccanismi di governance nelle imprese familiari [Finacial reporting in small family firms : searching for a new framework]

SOMMARIO: 1. La “governance” nelle aziende familiari: rilevanza, aspetti distintivi e criticità. 2. Il ruolo della compagine proprietaria nella definizione dei meccanismi di governo. 3. Composizione e funzioni del consiglio d’amministrazione. 4. I patti di famiglia come strumento di disciplina dei rapporti impresa-famiglia. 5. Considerazioni conclusive: prospettive di analisi e scenari futuri negli studi sulla governance delle imprese familiari.

L'informativa di bilancio nelle imprese familiari di piccole dimensioni : caratteri distintivi e aspetti evolutivi

SOMMARIO: 1. I fattori che incidono sulla funzione informativa del bilancio nelle imprese familiari. 2. Funzione, obiettivi e attese informative nella comunicazione esterna delle imprese familiari. 3. I caratteri del “familismo” nei prospetti di bilancio. 4. Verso un nuovo modello di bilancio per le imprese familiari: riflessioni critiche e spunti per la ricerca.

An infrared study of adsorption of paranitrophenol on mono, di and trialkyl surfactant intercalated organoclays

Infrared spectroscopy has been used to study the adsorption of paranitrophenol on mono, di and tri alkyl surfactant intercalated montmorillonite. Organoclays were obtained by the cationic exchange of mono, di and tri alkyl chain surfactants for sodium ions [hexadecyltrimethylammonium bromide (HDTMAB), dimethyldioctadecylammonium bromide (DDOAB), methyltrioctadecylammonium bromide (MTOAB)] in an aqueous solution with Na-montmorillonite. Upon formation of the organoclay, the properties change from strongly hydrophilic to strongly hydrophobic. This change in surface properties is observed by a decrease in intensity of the OH stretching vibrations assigned to water in the cation hydration sphere of the montmorillonite. As the cation is replaced by the surfactant molecules the paranitrophenol replaces the surfactant molecules in the clay interlayer. Bands attributed to CH stretching and bending vibrations change for the surfactant intercalated montmorillonite. Strong changes occur in the HCH deformation modes of the methyl groups of the surfactant. These changes are attributed to the methyl groups locking into the siloxane surface of the montmorillonite. Such a concept is supported by changes in the SiO stretching bands of the montmorillonite siloxane surface. This study demonstrates that paranitrophenol will penetrate into the untreated clay interlayer and replace the intercalated surfactant in surfactant modified clay, resulting in the change of the arrangement of the intercalated surfactant.

Poly[di-mu-aqua-bis(mu-2-amino-4-nitrobenzoato)dicaesium]

In the structure of title compound [Cs2(C7H5N2O4)2(H2O)2]n the asymmetric unit comprises two independent and different Cs centres, one nine-coordinate, the other seven coordinate, with both having irregular stereochemistry. The CsO9 coordination comprises oxygen donors from three bridging water molecules, one of which is doubly bridging, three from carboxylate groups, and three from nitro groups, of which two are bidentate chelate bridging. The CsO6N coordination comprises the two bridging water molecules, one amine N donor, one carboxyl O donor and four O donors from nitro groups (two from the chelate bridges). The extension of the dimeric unit gives a two-dimensional polymeric structure which is stabilized by both intra- and intermolecular amine N-H...O and water O-H...O hydrogen bonds to carboxyl O acceptors, as well as inter-ring pi-pi interactions [minimum ring centroid separation, 3.4172(15)A].

[P,P-Di-tert-butyl-N-trimethylsilyl- P-(trimethylsilylamino)phosphineimidato-N,N]bis(pyridine-N)- lithium(I)

In the title compound, [Li(C14H36N2PSi2)(C5H5N)2], the bulky chelating monoanionic P,P-di-tert-butyl-N-trimethylsilyl-P-(trimethylsilylamino)phosphine imidate ligand and two pyridine ligands bind to Li in a pseudo-tetrahedral arrangement with twofold symmetry. The Li-N [phosphine]distance is 2.048 (5) Å, while the LiP distance is 2.520 (6) Å

Bayesian models for the determination of resonant frequencies in a DI diesel engine

A time series method for the determination of combustion chamber resonant frequencies is outlined. This technique employs the use of Markov-chain Monte Carlo (MCMC) to infer parameters in a chosen model of the data. The development of the model is included and the resonant frequency is characterised as a function of time. Potential applications for cycle-by-cycle analysis are discussed and the bulk temperature of the gas and the trapped mass in the combustion chamber are evaluated as a function of time from resonant frequency information.

Methyl ester preparation from peanut oil and its effect on DI diesel engine combustion

This study investigated the preparation of methyl ester (Biodiesel) from peanut oil by transesterification method and its effect on DI diesel engine. Two parameters were measured during the engine operation: one is engine performance (brake thermal efficiency and brake specific fuel consumption), and the other is the exhaust emissions (NOx and CO). The result showed that, when compared with neat diesel fuel, the brake thermal efficiency of biodiesel blend was almost similar or a slight lower. However, brake specific fuel consumption (bsfc) was a little higher than neat diesel. CO was lower and NOx was little higher with biodiesel blend than that of diesel. The engine performance for B10 and B20 was very similar. At medium and high load conditions the engine emissions for B10 and B20 has no significant variation. Hence, B20 can safely be used in diesel engine without any significant penalty in engine performance and emissions.

Thyroxine and reserpine-induced changes in metabolic profiles of rat urine and the therapeutic effect of Liu Wei Di Huang Wan detected by UPLC-HDMS

The promise of metabonomics, a new "omics" technique, to validate Chinese medicines and the compatibility of Chinese formulas has been appreciated. The present study was undertaken to explore the excretion pattern of low molecular mass metabolites in the male Wistar-derived rat model of kidney yin deficiency induced with thyroxine and reserpine as well as the therapeutic effect of Liu Wei Di Huang Wan (LW) and its separated prescriptions, a classic traditional Chinese medicine formula for treating kidney yin deficiency in China. The study utilized ultra-performance liquid chromatography/electrospray ionization synapt high definition mass spectrometry (UPLC/ESI-SYNAPT-HDMS) in both negative and positive electrospray ionization (ESI). At the same time, blood biochemistry was examined to identify specific changes in the kidney yin deficiency. Distinct changes in the pattern of metabolites, as a result of daily administration of thyroxine and reserpine, were observed by UPLC-HDMS combined with a principal component analysis (PCA). The changes in metabolic profiling were restored to their baseline values after treatment with LW according to the PCA score plots. Altogether, the current metabonomic approach based on UPLC-HDMS and orthogonal projection to latent structures discriminate analysis (OPLS-DA) indicated 20 ions (14 in the negative mode, 8 in the positive mode, and 2 in both) as "differentiating metabolites".