17,761 research outputs found
Results on Rotation Symmetric Bent Functions
In this paper we analyze the combinatorial properties related to the Walsh spectra of rotation symmetric Boolean functions on even number of variables. These results are then applied in studying rotation symmetric bent functions
Rotation symmetric Boolean functions---count and cryptographic properties
The article of record as published may be located at http://dx.doi.org/10.1.1.137.6388Rotation symmetric (RotS) Boolean functions have been used as components of different cryptosystems. This class of Boolean functions are invariant under circular translation of indices. Using Burnsideï¾’s lemma it can be seen that the number of n-variable rotation symmetric Boolean functions is 2gn, where gn = 1 nPt|n (t) 2n t , and (.) is the Euler phi-function. In this paper, we find the number of short and long cycles of elements in Fn2 having fixed weight, under the RotS action. As a consequence we obtain the number of homogeneous RotS functions having algebraic degree w. Our results make the search space of RotS functions much reduced and we successfully analyzed important cryptographic properties of such functions by executing computer programs. We study RotS bent functions up to 10 variables and observe (experimentally) that there is no homogeneous rotation symmetric bent function having degree > 2. Further, we studied the RotS functions on 5, 6, 7 variables by computer search for correlation immunity and propagation characteristics and found some functions with very good cryptographic properties which were not known earlier
On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees
In the literature, few constructions of -variable rotation symmetric bent
functions have been presented, which either have restriction on or have
algebraic degree no more than . In this paper, for any even integer
, a first systemic construction of -variable rotation symmetric
bent functions, with any possible algebraic degrees ranging from to , is
proposed
A simple approach to the correlation of rotovibrational states in four-atomic molecules
The problem of correlation between quantum states of four-atomic molecules in
different geometrical configurations is reviewed in detail. A general, still
simple rule is obtained which allows one to correlate states of a linear
four-atomic molecule with those of any kind of non-linear four-atomic molecule.Comment: 16 pages (+8 figures), Postscript (ready to print!
Bose-Einstein condensates with a bent vortex in rotating traps
We consider a 3D dilute Bose-Einstein condensate at thermal equilibrium in a
rotating harmonic trap. The condensate wavefunction is a local minimum of the
Gross-Pitaevskii energy functional and we determine it numerically with the
very efficient conjugate gradient method. For single vortex configurations in a
cigar-shaped harmonic trap we find that the vortex line is bent, in agreement
with the numerical prediction of Garcia-Ripoll and Perez-Garcia, Phys.Rev.A 63,
041603 (2001). We derive a simple energy functional for the vortex line in a
cigar-shaped condensate which allows to understand physically why the vortex
line bends and to predict analytically the minimal rotation frequency required
to stabilize the bent vortex line. This analytical prediction is in excellent
agreement with the numerical results. It also allows to find in a simple way a
saddle point of the energy, where the vortex line is in a stationary
configuration in the rotating frame but not a local minimum of energy. Finally
we investigate numerically the effect of thermal fluctuations on the vortex
line for a condensate with a straight vortex: we can predict what happens in a
single realization of the experiment by a Monte Carlo sampling of an atomic
field quasi-distribution function of the density operator of the gas at thermal
equilibrium in the Bogoliubov approximation.Comment: 25 pages, 20 figures, version including discussion of energy saddle
poin
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