4,729 research outputs found
On the Simulatability Condition in Key Generation Over a Non-authenticated Public Channel
Simulatability condition is a fundamental concept in studying key generation
over a non-authenticated public channel, in which Eve is active and can
intercept, modify and falsify messages exchanged over the non-authenticated
public channel. Using this condition, Maurer and Wolf showed a remarkable "all
or nothing" result: if the simulatability condition does not hold, the key
capacity over the non-authenticated public channel will be the same as that of
the case with a passive Eve, while the key capacity over the non-authenticated
channel will be zero if the simulatability condition holds. However, two
questions remain open so far: 1) For a given joint probability mass function
(PMF), are there efficient algorithms (polynomial complexity algorithms) for
checking whether the simulatability condition holds or not?; and 2) If the
simulatability condition holds, are there efficient algorithms for finding the
corresponding attack strategy? In this paper, we answer these two open
questions affirmatively. In particular, for a given joint PMF, we construct a
linear programming (LP) problem and show that the simulatability condition
holds \textit{if and only if} the optimal value obtained from the constructed
LP is zero. Furthermore, we construct another LP and show that the minimizer of
the newly constructed LP is a valid attack strategy. Both LPs can be solved
with a polynomial complexity
Hybrid Functional Study Rationalizes the Simple Cubic Phase of Calcium at High Pressures
Simple cubic (SC) phase has been long experimentally determined as the
high-pressure phase III of elemental calcium (Ca) since 1984. However, recent
density functional calculations within semi-local approximation showed that
this SC phase is structurally unstable by exhibiting severely imaginary
phonons, and is energetically unstable with respect to a theoretical
body-centered tetragonal I41/amd structure over the pressure range of phase
III. These calculations generated extensive debates on the validity of SC
phase. Here we have re-examined the SC structure by performing more precise
density functional calculations within hybrid functionals of
Heyd-Scuseria-Erhzerhof (HSE) and PBE0. Our calculations were able to
rationalize fundamentally the phase stability of SC structure over all other
known phases by evidence of its actual energetic stability above 33 GPa and its
intrinsically dynamical stability without showing any imaginary phonons in the
entire pressure range studied. We further established that the long-thought
theoretical I41/amd structure remains stable in a narrow pressure range before
entering SC phase and is actually the structure of experimental Ca-III'
synthesized recently at low temperature 14 K as supported by the excellent
agreement between our simulated X-ray diffraction patterns and the experimental
data. Our results shed strong light on the crucial role played by the precise
electron exchange energy in a proper description of the potential energy of Ca.Comment: submitted to Physical Review
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