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The Vernam cipher is robust to small deviations from randomness
running-key cipher Vernam cipher Shannon entropy unconditional secrecy
2013/4/18
The Vernam cipher (or one-time pad) has played an important rule in cryptography because it is a perfect secrecy system. For example, if an English text (presented in binary system) $X_1 X_2 ... $ is ...
On Small deviations of Gaussian processes using majorizing measures
small deviations Gaussian processes entropy numbers
2011/2/21
We give two examples of periodic Gaussian processes, having en-tropy numbers of exactly same order but radically different small deviations.Our construction is based on classical Knopp’s result yieldi...
Small deviations for a family of smooth Gaussian processes
Small deviations family of smooth Gaussian processes
2010/12/14
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling properties as standard Brownian motion...
Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes
Degenerate self-similar measures spectral asymptotics small deviations of Gaussian processes
2010/12/1
The problem of small ball behavior for the norms of Gaussian processes is intensively studied
in recent years. The simplest and most explored case is that of L2-norm. Let us consider a
Gaussian proc...