Code-based cryptography is an area of classical cryptography in which cryptographic primitives rely on hard problems and trapdoor functions related to linear error-correcting codes. Since its inception in 1978, the area has produced the McEliece and the Niederreiter cryptosystems, multiple digital signature schemes, identification schemes and code-based hash functions. All of these are believed to be resistant to attacks by quantum computers. Hence, code-based cryptography represents a post-quantum alternative to the widespread number-theoretic systems. This thesis summarizes recent developments in the field of code-based cryptography, with a particular emphasis on code-based signature schemes. After a brief introduction and analysis of the McEliece and the Niederreiter cryptosystems, we discuss the currently unresolved issue of constructing a practical, yet provably secure signature scheme. A detailed analysis is provided for the Courtois, Finiasz and Sendrier signature scheme, along with the mCFS and parallel CFS variations. Finally, we discuss a recent proposal by Preetha et al. that attempts to solve the issue of provable security, currently failing in the CFS scheme case, by randomizing the public key construct. We conclude that, while the proposal is not yet practical, it represents an important advancement in the search for an ideal code-based signature scheme.

Hypersonic vehicles generate shocks that can heat the air sufficiently to partially ionize the air and create an electrically conducting plasma that can be studied using the equations of single fluid magnetohydrodynamics (MHD). Introducing strong applied magnetic and electric fields into the flow could have beneficial effects such as reducing heat damage, providing a sort of MHD parachute, and generating electric power or thrust in the vehicle. The Low Diffusion E-CUSP (LDE) scheme with a fifth order WENO scheme has recently been developed by Zha et al. [1, 2]. The purpose of this work is to incorporate the low magnetic Reynolds number MHD model and the thermodynamics of high temperature air to the above CFD algorithm so that it can be used to simulate hypersonic flows with MHD effects. In this work we compare results treating air as chemically frozen, neglecting all high temperature real gas effects with results obtained treating the air as a real gas in thermodynamic equilibrium, whose thermodynamic properties are changed by the high temperature. The hypersonic flows at high altitudes considered in this study have low Reynolds numbers. The Reynolds numbers range from about 2000 to 5000 for Mach 6 flows and reach up to 1200000 for Mach 15 flows. Thus, the flows are treated as laminar for the former cases and as turbulent for the latter using the Baldwin-Lomax turbulence model.

Thesis (M. Hous. M.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 102-106).

Thesis (M.Hous.M.)--University of Hong Kong, 1999. / Includes bibliographical references (leaves 102-106). Also available in print.

This thesis considers the application of the type II third order WENO finite volume reconstruction for unstructured tetrahedral meshes proposed by Zhang and Shu in (CCP, 2009) and the third order multirate Runge-Kutta time-stepping to the solution of Maxwell's equations. The dependance of accuracy of the third order WENO scheme on the small parameter in the definition of non-linear weights is studied in detail for one-dimensional uniform meshes and numerical results confirming the theoretical analysis are presented for the linear advection equation. This analysis is found to be crucial in the design of the efficient three-dimensional WENO scheme, full details of which are presented. Several multirate Runge-Kutta (MRK) schemes which advance the solution with local time-steps assigned to different multirate groups are studied. Analysis of accuracy of three different MRK approaches for linear problems based on classic order-conditions is presented. The most flexible and efficient multirate schemes based on works by Tang and Warnecke (JCM, 2006) and Liu, Li and Hu (JCP, 2010) are implemented in three-dimensional finite volume time-domain (FVTD) method. The main characteristics of chosen MRK schemes are flexibility in defining the time-step ratios between multirate groups and consistency of the scheme. Various approaches to partition the three-dimensional computational domain into multirate groups to maximize the achievable speedup are discussed. Numerical experiments with three-dimensional electromagnetic problems are presented to validate the performance of the proposed FVTD method. Three-dimensional results agree with theoretical and numerical accuracy analysis performed for the one-dimensional case. The proposed implementation of multirate schemes demonstrates greater speedup than previously reported in literature. / February 2016

京都大学 / 0048 / 新制・課程博士 / 博士(情報学) / 甲第18416号 / 情博第531号 / 新制||情||94(附属図書館) / 31274 / 京都大学大学院情報学研究科複雑系科学専攻 / (主査)教授 磯 祐介, 教授 西村 直志, 教授 木上 淳, 講師 吉川 仁 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DFAM

Yes / The redesign of defined benefit pension schemes usually results in a substantial redistribution of wealth between age cohorts of members, pensioners, and the sponsor. This is the first study to quantify the redistributive effects of a rule change by a real world scheme (the Universities Superannuation Scheme, USS) where the sponsor underwrites the pension promise. In October 2011 USS closed its final salary scheme to new members, opened a career average revalued earnings (CARE) section, and moved to ‘cap and share’ contribution rates. We find that the pre-October 2011 scheme was not viable in the long run, while the post-October 2011 scheme is probably viable in the long run, but faces medium term problems. In October 2011 future members of USS lost 65% of their pension wealth (or roughly £100,000 per head), equivalent to a reduction of roughly 11% in their total compensation, while those aged over 57 years lost almost nothing. The riskiness of the pension wealth of future members increased by a third, while the riskiness of the present value of the sponsor’s future contributions reduced by 10%. Finally, the sponsor’s wealth increased by about £32.5 billion, equivalent to a reduction of 26% in their pension costs. / The full text will be available at the end of the publisher's embargo; Oct 16 2017

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25097号 / 理博第5004号 / 新制||理||1714(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 望月 新一, 教授 大木谷 耕司, 准教授 星 裕一郎 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DGAM

Nous élaborons et analysons mathématiquement des approximations numériques par des méthodes de type volumes finis de solutions faibles de systèmes hyperboliques pour des écoulements géophysiques. Dans une première partie nous approchons les solutions du système de la magnétohydrodynamique en faible épaisseur avec un fond plat. Nous développons un schéma de type Godunov utilisant un solveur de Riemann approché défini via une méthode de relaxation. Des expressions explicites sont établies pour les vitesses de relaxation, qui permettent d'obtenir un schéma satisfaisant un ensemble de bonnes propriétés de consistance et de stabilité. Il conserve la masse, préserve la positivité de la hauteur de fluide, vérifie une inégalité d'entropie discrète, résout les discontinuités de contact même résonantes, donne des vitesses de propagations contrôlées par les données initiales. Des tests numériques sont effectués, validant les résultats théoriques énoncés. Dans une seconde partie nous approchons les solutions du système de la magnétohydrodynamique en faible épaisseur avec fond variable. Nous développons un schéma équilibre pour certains états stationnaires au repos. Nous utilisons la méthode de reconstruction hydrostatique, avec des états reconstruits pour la hauteur d'eau et les composantes du champ magnétique. Nous trouvons des termes correctifs pour les flux numériques par rapport au cadre habituel, et nous prouvons que le schéma obtenu préserve la positivité de la hauteur d'eau, vérifie une inégalité d'entropie semi-discrète et est consistant. Des tests numériques sont effectués, validant les résultats théoriques. Dans une troisième partie nous établissons la convergence d'un schéma cinétique avec reconstruction hydrostatique pour le système de Saint-Venant avec topographie. De nouvelles estimations sur le gradient des solutions approchées sont obtenues par l'analyse de la dissipation d'énergie. La convergence est obtenue par la méthode de compacité par compensation, sous des hypothèses sur les données initiales et la régularité du fond / We build and analyze mathematically numerical approximations by finite volume methods of weak solutions to hyperbolic systems for geophysical flows. In a first part we approximate the solutions of the shallow water magneto hydrodynamics system with flat bottom. We develop a Godunov scheme using an approximate Riemann solver defined via a relaxation method. Explicit formulas are established for the relaxation speeds, that lead to a scheme satisfying good properties of consistency and stability. It preserves mass, positivity of the fluid height, satisfies a discrete entropy inequality, resolves contact discontinuities, and involves propagation speeds controlled by the initial data. Several numerical tests are performed, endorsing the theoretical results. In a second part we approximate the solutions of the shallow water magneto hydrodynamics system with non-flat bottom. We develop a well-balanced scheme for several steady states at rest. We use the hydrostatic reconstruction method, with reconstructed states for the fluid height and the magnetic field. We get some new corrective terms for the numerical fluxes with respect to the classical framework, and we prove that the obtained scheme preserves the positivity of height, satisfies a semi-discrete entropy inequality, and is consistent. Several numerical tests are presented, endorsing the theoretical results. In a third part we prove the convergence of a kinetic scheme with hydrostatic reconstruction for the Saint-Venant system with topography. Some new estimates on the gradient of approximate solutions are established, by the analysis of energy dissipation. The convergence is obtained by the compensated compactness method, under some hypotheses concerning the initial data and the regularity of the topography

This thesis investigated Stochastic Runge–Kutta Lawson (SRKL) schemes and their application to the Heston model. Two distinct SRKL discretization methods were used to simulate a single asset’s dynamics under the Heston model, notably the Euler–Maruyama and Midpoint schemes. Additionally, standard Monte Carlo and variance reduction techniques were implemented. European and Asian option prices were estimated and compared with a benchmark value regarding accuracy, effectiveness, and computational complexity. Findings showed that the SRKL Euler–Maruyama schemes exhibited promise in enhancing the price for simple and path-dependent options. Consequently, integrating SRKL numerical methods into option valuation provides notable advantages by addressing challenges posed by the Heston model’s SDEs. Given the limited scope of this research topic, it is imperative to conduct further studies to understand the use of SRKL schemes within other models.