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This paper describes and compares a variety of algorithms for secure transmission of information via open communication channels based on the discrete logarithm problem that do not require search for a generator (primitive element). Modifications that simplify the cryptosystem are proposed, and, as a result, accelerate its performance. It is shown that hiding information via exponentiation is more efficient than other seemingly simpler protocols. Some of these protocols also provide digital signature/sender identification. Numeric illustrations are provided.
The monomer fraction density based analysis of precise
thermophysical data for pure fluids is developed to study the molecular
structures in supercritical fluids in general and in CO2 in particular. The series expansion by
powers of the monomer fraction density of the potential energy density is used
to discover the cluster structure in supercritical fluids and the clusters’
bond energies in CO2. The method of clusters separation between
classes of loose and dense clusters in the CO2 supercritical fluid
is developed. The method of the energetically averaged number of dense clusters
is developed to study the mechanism of the soft structural transition
between the gas-like and liquid-like fluids in the supercritical
This paper describes an algorithm for secure transmission of information via open communication channels based on the discrete logarithm problem. The proposed algorithm also provides sender identification (digital signature). It is twice as fast as the RSA algorithm and requires fifty per cent fewer exponentiations than the ElGamal cryptosystems. In addition, the algorithm requires twice less bandwidth than the ElGamal algorithm. Numerical examples illustrate all steps of the proposed algorithm: system design (selection of private and public keys), encryption, transmission of information, decryption and information recovery.
The thermal analysis of precise thermophysical data for pure fluids
from electronic databases is developed to investigate the molecular interaction
mechanisms and parameters and the structural features of heterogeneities in
fluids. The method is based on the series expansion of thermophysical values by
powers of the monomer fraction density. Unlike the virial expansion by powers
of the total density, the series expansion terms in this method directly
reflect properties of the corresponding cluster fractions. The internal energy
had been selected among thermophysical properties as the most informative for
this method. The thermal analysis of its series expansion coefficients permits
to estimate the temperature dependence of the pair bond parameters, the
clusters’ bond energies and equilibrium constants, the structural transitions
between dominating isomers of clusters. The application of method to different
pure fluids, including noble and molecular gases with van der Waals and polar
molecular interactions, brings unknown clusters’ characteristics for the
fluids under investigation. The thermal analysis of the ordinary and heavy
Water vapors points on no trivial isotopic effects. The unpredictable growth of
the pair bond energy with temperature in Alkanes points on existence in hydrocarbons
of some unknown molecular interaction forces in addition to dispersion forces.
To discover particular features of pure supercritical fluids, important for the supercritical fluid extraction and cleaning technologies, the preprocessed and generalized experimental data from the US National Institute of Standards and Technology (NIST) online database have been analyzed. The soft transition between gas-like and liquid-like structures in pure supercritical fluids has been considered in comparison with the abrupt vapor-liquid phase transition. A rough, diffused and boiling boundary between these structures in conditions of extra high gravity is opposed to a flat vapor-liquid boundary at a moderate gravity. The model for molecular diffusivity in carbon dioxide at temperatures near the critical temperature discovers its proportionality to the monomer fraction density. The cluster fraction based model for small molecular weight solids’ solubility in supercritical fluids has been suggested and successfully compared with the well-known experimental results for the solubility of silica in water.The model shows that at growing pressure the dissolution process has already startedin a real gas and discovers the cluster fractions’ role in the solubility process.