The objective of this paper is to give a comprehensive introduction to applied cryptography with an engineer or computer scientist in mind. The emphasis is on the knowledge needed to create practical systems which supports integrity, confidentiality, or authenticity. Topics covered includes an introduction to the concepts in cryptography, attacks against cryptographic systems, key use and handling, random bit generation, encryption modes, and message authentication codes. Recommendations on algorithms and further reading is given in the end of the paper. This paper should make the reader able to build, understand and evaluate system descriptions and designs based on the cryptographic components described in the paper.

[서평]「Applied Cryptography」

International Journal of Computer and Applications

. A transport equation that uses fractional-order dispersion derivatives hasfundamental solutions that are Le´vy’s a-stable densities. These densities represent plumesthat spread proportional to time 1/a , have heavy tails, and incorporate any degree ofskewness. The equation is parsimonious since the dispersion parameter is not a functionof time or distance. The scaling behavior of plumes that undergo Le´vy motion isaccounted for by the fractional derivative. A laboratory tracer test is described by adispersion term of order 1.55, while the Cape Cod bromide plume is modeled by anequation of order 1.65 to 1.8. 1. Introduction Anomalous, or non-Fickian, dispersion has been an activearea of research in the physics community since the introduc-tion of continuous time random walks (CTRW) by Montrolland Weiss [1965]. These random walks extended the predictivecapability of models built on the stochastic process of Brown-ian motion, which is the basis for the classical advection-dispersion equation (ADE). The CTRW assign a joint space-time distribution, called the transition density, to individualparticle motions. When the tails are heavy enough (i.e., powerlaw), non-Fickian dispersion results for all time scales andspace scales.

/pdf/application-of-a-fractional-advection-dispersion-equation-4ax1zvo1uu.pdf

Application of a fractional advection-dispersion equation

A governing equation of stable random walks is developed in one dimension. This Fokker-Planck equation is similar to, and contains as a subset, the second-order advection dispersion equation (ADE) except that the order (a) of the highest derivative is fractional (e.g., the 1.65th derivative). Fundamental solutions are Levy's a-stable densities that resemble the Gaussian except that they spread proportional to time 1/a , have heavier tails, and incorporate any degree of skewness. The measured variance of a plume undergoing Levy motion would grow faster than Fickian plume, at a rate of time 2/a , where 0 , a # 2. The equation is parsimonious since the parameters are not functions of time or distance. The scaling behavior of plumes that undergo Levy motion is accounted for by the fractional derivatives, which are appropriate measures of fractal functions. In real space the fractional derivatives are integrodifferential operators, so the fractional ADE describes a spatially nonlocal process that is ergodic and has analytic solutions for all time and space.

/pdf/the-fractional-order-governing-equation-of-levy-motion-1vw7ien6a9.pdf

The fractional‐order governing equation of Lévy Motion

Mixing, spreading and reaction in heterogeneous media: a brief review.

This paper describes the Elliptic Curve Cryptography algorithm and its suitability for smart cards.

https://dl.acm.org/doi/pdf/10.1145/1386853.1378356

Elliptic curve cryptography

The concentration variance, i.e., mean squared concentration fluctuations, undergoes mean advection, a local dispersive flux, and a macrodispersive flux due to a correlation between squared concentration perturbations and velocity perturbations. The products of the macrodispersion coefficient and the squared gradient of the mean concentration field determine the rate of production of concentration variance. The rate of dissipation of concentration variance is determined by the product of the local dispersion coefficient and the mean squared gradient of the concentration perturbation field. Variance dissipation is represented as a first-order decay with the decay coefficient equal to twice the sum of the local dispersion coefficient divided by the squared concentration microscale. The concentration microscale, estimated for an advection-dominated log hydraulic conductivity microscale, is an increasing function of the log conductivity microscale. Thus the larger the log conductivity microscale is, the slower is the rate of dissipation of concentration fluctuations by local dispersion and vice versa. The wave number squared dependence of fluctuation dissipation requires intensive sampling to realistically model the log conductivity spectrum and its microscale, which determines the rate of dissipation of concentration fluctuations by the action of local dispersion. There is no mechanism of destroying concentration fluctuations without the action of local dispersion.

Transport in three-dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations

The concentration of solute undergoing advection and local dispersion in a random hydraulic conductivity field is analyzed to quantify its variability and dilution. Detailed numerical evaluations of the concentration variance sc are compared to an approximate analytical description, which is based on a characteristic variance residence time (VRT), over which local dispersion destroys concentration fluctuations, and effective dispersion coefficients that quantify solute spreading rates. Key features of the analytical description for a finite size impulse input of solute are (1) initially, the concentration fields become more irregular with time, i.e., coefficient of variation, CV 5 sc/^c&, increases with time (^c& being the mean concentration); (2) owing to the action of local dispersion, at large times (t . VRT), s c is a linear combination of ^c& 2 and (›^c&/› xi) 2 , and the CV decreases with time (at the center, CV > (N) 1/2 VRT/t, N being the macroscopic dimensionality of the plume); (3) at early time, dilution and spreading can be severely disconnected; however, at large time the volume occupied by solute approaches that apparent from its spatial second moments; and (4) in contrast to the advection-local dispersion case, under advection alone, the CV grows unboundedly with time (at the center, CV } t N/4 ), and spatial second moment is increasingly disconnected from dilution, as time progresses. The predicted large time evolution of dilution and concentration fluctuation measures is observed in the numerical simulations.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/97WR03608

Concentration fluctuations and dilution in aquifers

The representation of multispecies chemical transformations into models for porous media flow and transport is investigated. Since the rate of transformation is dependent on the actual concentrations of the reactants inside the pore-spaces (rather than the averaged concentration that is amenable to a porous continuum model) such models may show a lesser or greater rate of transformation than is actually occurring, depending on the pore-scale correlation of the reactant concentrations. To examine this experimentally, a bimolecular reaction (A + B → Product) in a saturated porous media flow in a column was studied using a spectrophotometer. The second-order rate constant of the reaction was independently determined in well-mixed batch tests. In the reactive transport experiments, the porous medium column was initially saturated with one reactant, the other reactant was injected at one longitudinal end of the column, and the effluent concentrations were measured. It is documented that a reactive transport mo...

Experimental study of bimolecular reaction kinetics in porous media.

For a multidimensional finite-size impulse input, analytical solutions to the conservation equation for concentration variance σc2 are presented. Due to the dissipating action of local dispersion, at large times, σc is a decreasing fraction of the mean concentration. The Cape Cod bromide tracer exhibits this decrease. The larger the log conductivity microscale is, the slower is the action of local dispersion, and the slower is the predicted rate of decrease of the ratio of σc and the mean concentration (i.e., the coefficient of variation) with time, at large times, and vice versa. The coefficient of variation increases with distance from the center. A balance between the rates of production and dissipation of σc2 relates it linearly to the squared gradients of the mean concentration field, away from the center of mass. For the zero local dispersion case, σc is an unboundedly growing multiple with time of the mean concentration. The longitudinal spatial second moment and macrodispersivities are insensitive to the inclusion/exclusion of local dispersion and therefore do not differentiate between the concentration fields for the two different cases. In contrast, the spatial-temporal evolution of σc2 is singularly determined by the dissipating action of local dispersion. Measurements of local dispersivities need to be made along with a characterization of hydraulic conductivity variations to assess contaminant concentrations in aquifers.

Vivek Kapoor

Papers

Elliptic curve cryptography

Transport in three-dimensionally heterogeneous aquifers: 1. Dynamics of concentration fluctuations

Concentration fluctuations and dilution in aquifers

Experimental study of bimolecular reaction kinetics in porous media.

Transport in three-dimensionally heterogeneous aquifers: 2. Predictions and observations of concentration fluctuations