38,725 research outputs found
Still Wrong Use of Pairings in Cryptography
Several pairing-based cryptographic protocols are recently proposed with a
wide variety of new novel applications including the ones in emerging
technologies like cloud computing, internet of things (IoT), e-health systems
and wearable technologies. There have been however a wide range of incorrect
use of these primitives. The paper of Galbraith, Paterson, and Smart (2006)
pointed out most of the issues related to the incorrect use of pairing-based
cryptography. However, we noticed that some recently proposed applications
still do not use these primitives correctly. This leads to unrealizable,
insecure or too inefficient designs of pairing-based protocols. We observed
that one reason is not being aware of the recent advancements on solving the
discrete logarithm problems in some groups. The main purpose of this article is
to give an understandable, informative, and the most up-to-date criteria for
the correct use of pairing-based cryptography. We thereby deliberately avoid
most of the technical details and rather give special emphasis on the
importance of the correct use of bilinear maps by realizing secure
cryptographic protocols. We list a collection of some recent papers having
wrong security assumptions or realizability/efficiency issues. Finally, we give
a compact and an up-to-date recipe of the correct use of pairings.Comment: 25 page
Faster computation of the Tate pairing
This paper proposes new explicit formulas for the doubling and addition step
in Miller's algorithm to compute the Tate pairing. For Edwards curves the
formulas come from a new way of seeing the arithmetic. We state the first
geometric interpretation of the group law on Edwards curves by presenting the
functions which arise in the addition and doubling. Computing the coefficients
of the functions and the sum or double of the points is faster than with all
previously proposed formulas for pairings on Edwards curves. They are even
competitive with all published formulas for pairing computation on Weierstrass
curves. We also speed up pairing computation on Weierstrass curves in Jacobian
coordinates. Finally, we present several examples of pairing-friendly Edwards
curves.Comment: 15 pages, 2 figures. Final version accepted for publication in
Journal of Number Theor
Tame Class Field Theory for Global Function Fields
We give a function field specific, algebraic proof of the main results of
class field theory for abelian extensions of degree coprime to the
characteristic. By adapting some methods known for number fields and combining
them in a new way, we obtain a different and much simplified proof, which
builds directly on a standard basic knowledge of the theory of function fields.
Our methods are explicit and constructive and thus relevant for algorithmic
applications. We use generalized forms of the Tate-Lichtenbaum and Ate
pairings, which are well-known in cryptography, as an important tool.Comment: 25 pages, to appear in Journal of Number Theor
Semiclassical Theory of Bardeen-Cooper-Schrieffer Pairing-Gap Fluctuations
Superfluidity and superconductivity are genuine many-body manifestations of
quantum coherence. For finite-size systems the associated pairing gap
fluctuates as a function of size or shape. We provide a parameter free
theoretical description of pairing fluctuations in mesoscopic systems
characterized by order/chaos dynamics. The theory accurately describes
experimental observations of nuclear superfluidity (regular system), predicts
universal fluctuations of superconductivity in small chaotic metallic grains,
and provides a global analysis in ultracold Fermi gases.Comment: 4 pages, 2 figure
Coexistence of Pairing Tendencies and Ferromagnetism in a Doped Two-Orbital Hubbard Model on Two-Leg Ladders
Using the Density Matrix Renormalization Group and two-leg ladders, we
investigate an electronic two-orbital Hubbard model including plaquette
diagonal hopping amplitudes. Our goal is to search for regimes where charges
added to the undoped state form pairs, presumably a precursor of a
superconducting state.For the electronic density , i.e. the undoped
limit, our investigations show a robust antiferromagnetic ground
state, as in previous investigations. Doping away from and for large
values of the Hund coupling , a ferromagnetic region is found to be stable.
Moreover, when the interorbital on-site Hubbard repulsion is smaller than the
Hund coupling, i.e. for in the standard notation of multiorbital Hubbard
models, our results indicate the coexistence of pairing tendencies and
ferromagnetism close to . These results are compatible with previous
investigations using one dimensional systems. Although further research is
needed to clarify if the range of couplings used here is of relevance for real
materials, such as superconducting heavy fermions or pnictides, our theoretical
results address a possible mechanism for pairing that may be active in the
presence of short-range ferromagnetic fluctuations.Comment: 8 pages, 4 Fig
Is N-doped SrO magnetic? A first-principles view
N-doped SrO seems to be one of the model systems for d^0 magnetism, in which
magnetism (or ideally, ferromagnetism) was ascribed to the localized N 2p spins
mediated by delocalized O 2p holes. Here we offer a different view, using
density functional calculations. We find that N-doped SrO with solely
substitutional N impurities as widely assumed in the literature is unstable,
and instead that a pairing state of substitutional and interstitial N
impurities is significantly more stable and has a much lower formation energy
than the former by 6.7 eV. The stable (N_{sub}-N_{int})^{2-} dimers behave like
a charged (N_2)^{2-} molecule and have each a molecular spin=1. However, their
spin-polarized molecular levels lie well inside the wide band gap of SrO and
thus the exchange interaction is negligibly weak. As a consequence, N-doped SrO
could not be ferromagnetic but paramagnetic.Comment: 7 pages, 2 figures, Appl. Phys. Lett., in pres
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