An important advantage of Elliptic Curve Cryptosystem (ECC) is the shorter key length in public key cryptographic systems. It can provide adequate security when the bit length over than 160 bits. Therefore, it has become a popular system in recent years. Scalar multiplication also called point multiplication is the core operation in ECC. In this thesis, we propose the ECC architectures of two different irreducible polynomial versions that are trinomial in GF(2167) and pentanomial in GF(2163). These architectures are based on Montgomery point multiplication with projective coordinate. We use polynomial basis representation for finite field arithmetic. All adopted multiplication, square and add operations over binary field can be completed within one clock cycle, and the critical path lies on multiplication. In addition, we use Itoh-Tsujii algorithm combined with addition chain, to execute binary inversion through using iterative binary square and multiplication. Because the double and add operations in point multiplication need to run many iterations, the execution time in overall design will be decreased if we can improve this partition. We propose two ways to improve the performance of point multiplication. The first way is Minus Cycle Version. In this version, we reschedule the double and add operations according to point multiplication algorithm. When the clock cycle time (i.e., critical path) of multiplication is longer than that of add and square, this method will be useful in improving performance. The second way is Pipeline Version. It speeds up the multiplication operations by executing them in pipeline, leading to shorter clock cycle time. For the hardware implementation, TSMC 0.13um library is employed and all modules are organized in a hierarchy structure. The implementation result shows that the proposed 167-bit Minus Cycle Version requires 156.4K gates, and the execution time of point multiplication is 2.34us and the maximum speed is 591.7Mhz. Moreover, we compare the Area x Time (AT) value of proposed architectures with other relative work. The results exhibit that proposed 167-bit Minus Cycle Version is the best one and it can save up to 38% A T value than traditional one.

In asymmetric cryptosystems, an important advantage of Elliptic Curve Cryptosystem (ECC) is the shorter key lengths than other cryptosystems. It can provide a level of security when the bit length over than 160 bits. So it has become a popular public key cryptographic system in recent year. Multiplier needs to run many times in scalar multiplication and it plays an essential role in ECC. Since the registers in multiplier are shifted every iteration, it will consume a lot of power in the computing process. So in this thesis, we propose five methods to save multiplication¡¦s energy consumption based on a scalable serial-parallel algorithm[1]. The first method is to design a low-power shift-register by modifying shift-register B to reduce the frequency of registers shifted. The second method is to use a frequency divider circuit. It can make registers to access a value every two clock cycles by modifying RA units. The third method is to introduce the gated clock circuit, and the clock signal of register will be disabled if its value is the same. The fourth method is to skip redundant operations and it can decrease the number of clock cycles for completing a multiplication operation. The last method raises multiplier¡¦s throughput by modifying RA units. The former three methods focus on low-power design, and the latter two methods emphasize on improving performance. Reducing power consumption and improving performance will save multiplication¡¦s energy consumption. Finally, we propose a Half Cycles schedule to raise scalar multiplication¡¦s performance. It is based on Montgomery scalar multiplication algorithm with projective coordinate[22][26]. For the hardware implementation, TSMC 0.13um library is employed and all modules are organized in a hierarchy structure. The implementation results show that the proposed multipliers have less energy consumption than traditional multiplier. It can get 5% ~ 24% energy saving. For Montgomery scalar multiplication, it can also reduce 12% ~ 47% energy consumption and is suitable for portable electronic products because its low area complexity and low energy.

This dissertation presents a series of laboratory experiments to study flow and mixing properties of multiphase plumes. The particle image velocimetry (PIV) and laserinduced fluorescence (LIF) techniques are developed to measure two-dimensional velocity and concentration fields of multiphase plumes. The developed measurement techniques are applied to bubble plumes in different ambient conditions. The problems and errors in the two-phase PIV application to a bubble plume case are addressed through a comparative study between the optical separation method using fluorescent particles and a new phase separation method using vector postprocessing. The study shows that the new algorithm predicts well the instantaneous and time-averaged velocity profiles and has errors comparable to those for image masking techniques. The phase separation method developed in the previous section is applied to study the mean flow characteristics of a bubble plume in quiescent and unstratified condition. The entrainment coefficients representing the mixing properties of a bubble plume are calculated to lie between 0.08 near the plume source and 0.05 in the upper region, and to depend on the non-dimensional quantity us/(B/z)1/3, where us is the bubble slip velocity, B is the initial buoyancy flux, and z is the height from the diffuser. Further, the LIF technique is investigated to measure the scalar concentration field around a bubble plume in quiescent, unstratified condition. This new application to bubble plumes accounts for light scattering by bubbles using an attenuation coef- ficient that is proportional to the local void fraction. Measured scalar concentration fields show similar trend in concentration fluctuation to turbulent plume cases. Finally, the velocity and concentration field measurements using the developed two-phase PIV and LIF methods are applied for a bubble plume in a density-stratified ambient. The turbulent flow characteristics induced by a bubble plume in a stratified ambient water are studied. The plume fluctuation frequency is measured as about 0.1 Hz and compares well to plume wandering frequency measured in unstratified plume cases.

Radiative Decays of the phi-meson to the scalar mesons f0(980) and a0(980) are investigated within the framework of charged kaon loop model for both point-like scalar mesons and for scalar mesons with extended structure. Then, the radiative phi-meson decay into neutral K-meson is studied via a two step mechanism in which the scalar mesons couple the final state to the phi-meson through the charged kaon loop. The branching ratio of this decay is calculated and it is shown that this reaction will not provide a significant background to the measurements of phi-meson into neutral K-meson states decay for testing CP violation.

Elliptic curve cryptography has gained much popularity in the past decade and has been challenging the dominant RSA/DSA systems today. This is mainly due to elliptic curves offer cryptographic systems with higher speed, less memory and smaller key sizes than older ones. Among the various arithmetic operations required in implementing public key cryptographic algorithms based on elliptic curves, the elliptic curve scalar multiplication has probably received the maximum attention from the research community in the past a few years. Many methods for efficient and secure implementation of scalar multiplication have been proposed by many researchers. In this thesis, many scalar multiplication methods are studied in terms of their mathematical, computational and implementational points.

We explore the capability of lattice Boltzmann equation (LBE) method for complex fluid flows involving turbulence, mixing, and reaction. In the first study, LBE schemes for binary scalar mixing and multi-component reacting flow with reactions are developed. Simulations of initially non-premixed mixtures yield scalar probability distribution functions that are in good agreement with numerical data obtained from Navier-Stokes (NS) equation based computation. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally determined value. The second study involves direct numerical simulation (DNS) and large-eddy simulation (LES) of decaying homogenous isotropic turbulence (HIT) with and without frame rotation. Three categories of simulations are performed: (i) LBE-DNS in both inertial and rotating frames; (ii) LBE-LES in inertial frame; (iii) Comparison of the LBE-LES vs. NS-LES. The LBE-DNS results of the decay exponents for kinetic energy k and dissipation rate ε, and the low wave-number scaling of the energy spectrum agree well with established classical results. The LBE-DNS also captures rotating turbulence physics. The LBE-LES accurately captures low-wave number scaling, energy decay and large scale structures. The comparisons indicate that the LBE-LES simulations preserve flow structures somewhat more accurately than the NS-LES counterpart. In the third study, we numerically investigate the near-field mixing features in low aspect-ratio (AR) rectangular turbulent jets (RTJ) using the LBE method. We use D3Q19 multiple-relaxation-time (MRT) LBE incorporating a subgrid Smagorinsky model for LES. Simulations of four jets which characterized by AR, exit velocity, and Reynolds number are performed. The investigated near-field behaviors include: (1) Decay of mean streamwise velocity (MSV) and inverse MSV; (2) Spanwise and lateral profiles of MSV; (3) Half-velocity width development and MSV contours; and (4) Streamwise turbulence intensity distribution and spanwise profiles of streamwise turbulence intensity. The computations are compared against experimental data and the agreement is good. We capture both unique features of RTJ: the saddle-back spanwise profile of MSV and axis-switching of long axis from spanwise to lateral direction. Overall, this work serves to establish the feasibility of the LBE method as a viable tool for computing mixing, combustion, and turbulence.

Consider a linear regression model with a two-dimensional control vector (x_1, x_2) and an m-dimensional response vector y = (y_1, . . . , y_m). The components of y are correlated with a known covariance matrix. Based on the assumed regression model, there are two problems of interest. The first one is to estimate unknown control vector x_c corresponding to an observed y, where xc will be estimated by the classical estimator. The second one is to obtain a suitable estimation of the control vector x_T corresponding to a given target T = (T_1, . . . , T_m) on the expected responses. Consideration in this work includes the deviation of the expected response E(y_i) from its corresponding target value T_i for each component and defines the optimal control vector x, say x_T , to be the one which minimizes the weighted sum of squares of standardized deviations within the range of x. The objective of this study is to find c-optimal designs for estimating x_c and x_T , which minimize the mean squared error of the estimator of xc and x_T respectively. The comparison of the difference between the optimal calibration design and the optimal design for estimating x_T is provided. The efficiencies of the optimal calibration design relative to the uniform design are also presented, and so are the efficiencies of the optimal design for given target vector relative to the uniform design.

<p>Despite its importance in various industrial applications there is still a lack of experimental studies on the dynamic and thermal field of swirling jets in the near-field region. The present study is an attempt to close this lack and provide new insights on the effect of rotation on the turbulent mixing of a <i>passive scalar</i>, on turbulence (joint) statistics as well as the turbulence structure.</p><p>Swirl is known to increase the spreading of free turbulent jets and hence to entrain more ambient fluid. Contrary to previous experiments, which leave traces of the swirl generating method especially in the near-field, the swirl was imparted by discharging a slightly heated air flow from an axially rotating and thermally insulated pipe (6 m long, diameter 60 mm). This gives well-defined axisymmetric streamwise and azimuthal velocity distributions as well as a well-defined temperature profile at the jet outlet. The experiments were performed at a <i>Reynolds</i> number of 24000 and a swirl number (ratio between the angular velocity of the pipe wall and the bulk velocity in the pipe) of 0.5.</p><p>By means of a specially designed combined X-wire and cold-wire probe it was possible to simultaneously acquire the instantaneous axial and azimuthal velocity components as well as the temperature and compensate the former against temperature variations. The comparison of the swirling and non-swirling cases clearly indicates a modification of the turbulence structure to that effect that the swirling jet spreads and mixes faster than its non-swirling counterpart. It is also shown that the streamwise velocity and temperature fluctuations are highly correlated and that the addition of swirl drastically increases the streamwise<i> passive scalar</i> flux in the near field.</p>

Le mélange d'un scalaire passif par un écoulement turbulent est étudié. D'abord, la simulation numérique directe (DNS), la simulation des grandes échelles (LES) et des arguments dimensionnels sont employés pour étudier le spectre du flux de scalaire dans une turbulence isotrope avec un gradient moyen uniforme de scalaire. Une loi d'échelle est dérivée. Cette loi conduit à des pentes du spectre variant entre -5/3 et -7/3 en zone inertielle. De premiers résultats de LES plaident en faveur d'un comportement en K^-2. Ensuite, en utilisant une fermeture en deux points (EDQNM), nous montrons qu'aux nombres de Reynolds très élevés, le spectre de flux de scalaire dans la zone intertielle se comporte en K^-7/3. Ce résultat est en accord avec l'analyse dimensionnelle classique de Lumley (1967). Aux nombres de Reynolds correspondant aux expériences de laboratoire, la fermeture conduit à des spectres plus près de K^-2. Nous montrons ensuite que le comportement en K^-2 trouvé en LES est induit par le forçage à grande échelle. La fermeture est alors appliquée au cas des écoulements homogènes cisaillés et les spectres du flux de scalaire longitudinal et transverse sont étudiés. Le spectre du flux longitudinal est trouvé proportionnelle à K^-23/9. Ce résultat est en accord avec l'expérience mais est en désaccord avec l'analyse dimensionnelle classique. Finalement, nous montrons que le lien entre la dispersion de particules et le mélange d'un scalaire permet de formuler une fermeture en deux points et un temps qui ne nécessite l'introduction d'aucune constante dans le modèle.

In the recent past, LES methodology has emerged as a viable tool for modeling turbulent combustion. LES computes the large scale mixing process accurately, thereby providing a better starting point for small-scale models that describe the combustion process. Significant effort has been made over past decades to improve accuracy and applicability of the LES approach to a wide range of flows, though the current conventions often lack consistency to the problems at hand. To this end, the two main objectives of this dissertation are to develop a dynamic transport equation-based combustion model for large- eddy simulation (LES) of turbulent spray combustion and to investigate grid- independent LES modeling for scalar mixing. Long-standing combustion modeling approaches have shown to be suc- cessful for a wide range of gas-phase flames, however, the assumptions required to derive these formulations are invalidated in the presence of liquid fuels and non-negligible evaporation rates. In the first part of this work, a novel ap- proach is developed to account for these evaporation effects and the resulting multi-regime combustion process. First, the mathematical formulation is de- rived and the numerical implementation in a low-Mach number computational solver is verified against one-dimensional and lab scale, both non-reacting and reacting spray-laden flows. In order to clarify the modeling requirements in LES for spray combustion applications, results from a suite of fully-resolved direct numerical simulations (DNS) of a spray laden planar jet flame are fil- tered at a range of length scales. LES results are then validated against two sets of experimental jet flames, one having a pilot and allowing for reduced chemistry modeling and the second requiring the use of detail chemistry with in situ tabulation to reduce the computational cost of the direct integration of a chemical mechanism. The conventional LES governing equations are derived from a low-pass filtering of the Navier-Stokes equations. In practice, the filter used to derive the LES governing equations is not formally defined and instead, it is assumed that the discretization of LES equations will implicitly act as a low-pass filter. The second part of this study investigates an alternative derivation of the LES governing equations that requires the formal definition of the filtering operator, known as explicitly filtered LES. It has been shown that decoupling the filter- ing operation from the underlying grid allows for the isolation of subfilter-scale modeling errors from numerical discretization errors. Specific to combustion modeling are the aggregate errors associated with modeling sub-filter distribu- tions of scalars that are transported by numerical impacted turbulent fields. Quantities of interest to commonly-used combustion models, including sub- filter scalar variance and filtered scalar dissipation rate, are investigated for both homogeneous and shear-driven turbulent mixing. / text