6 research outputs found
Privacy amplification theorem for noisy main channel
Secret key agreement protocol between legal parties based on reconciliation and privacy amplification procedure has been considered in [2]. The so called privacy amplification theorem is used to estimate the amount of Shannonâs information leaking to an illegal party (passive eavesdropper) about the final key.We consider a particular case where one of the legal parties (Alice) sends to another legal party (Bob) a random binary string x through a binary symmetric channel (BSC) with bit error probability Δm while an eavesdropper (Eve) receives this string through an independent BSC with bit error probability Δw. We assume that Δm < Δw and hence the main channel is superior to the wire-tap channel. To reconcile the strings between legal parties Alice sends to Bob through noiseless channel the check string y based on some good error correcting code. Since this transmission is completely public Eve can eavesdrop it and therefore this extra information has to be taken into account in an estimation of the information leaking to Eve about the final key. In [3] an inequality has been proved to upper bound the information of Eve in such scenario. The main contribution of the running paper is to improve this inequality and hence to enhance the privacy amplification theorem. We present also bounds for the probability of false reconciliation when the check symbols of the linear code are transmitted through noiseless channel. The presented results can be very useful when considering the non-asymptotic case
Correlation of the late eoceneâearly Oligocene IzĂșcar de matamoros evaporites (Cuayuca Formation) in Mexico based on parsimony analysis of endemicity
Physicomechanical Characteristics of Composite Based on Polyimide Matrix Filled with Tungsten Oxide
Extreme events in population dynamics with functional carrying capacity
A class of models is introduced describing the evolution of population
species whose carrying capacities are functionals of these populations. The
functional dependence of the carrying capacities reflects the fact that the
correlations between populations can be realized not merely through direct
interactions, as in the usual predator-prey Lotka-Volterra model, but also
through the influence of species on the carrying capacities of each other. This
includes the self-influence of each kind of species on its own carrying
capacity with delays. Several examples of such evolution equations with
functional carrying capacities are analyzed. The emphasis is given on the
conditions under which the solutions to the equations display extreme events,
such as finite-time death and finite-time singularity. Any destructive action
of populations, whether on their own carrying capacity or on the carrying
capacities of co-existing species, can lead to the instability of the whole
population that is revealed in the form of the appearance of extreme events,
finite-time extinctions or booms followed by crashes.Comment: Latex file, 60 pages, 24 figure