259,542 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
Non-perturbative renormalization of HQET and QCD
We discuss the necessity of non-perturbative renormalization in QCD and HQET
and explain the general strategy for solving this problem. A few selected
topics are discussed in some detail, namely the importance of off-shell
improvement in the MOM-scheme on the lattice, recent progress in the
implementation of finite volume schemes and then particular emphasis is put on
the recent idea to carry out a non-perturbative renormalization of the Heavy
Quark Effective Theory.Comment: 13 pages, Lattice2002(plenary
On the Computation of Power in Volume Integral Equation Formulations
We present simple and stable formulas for computing power (including
absorbed/radiated, scattered and extinction power) in current-based volume
integral equation formulations. The proposed formulas are given in terms of
vector-matrix-vector products of quantities found solely in the associated
linear system. In addition to their efficiency, the derived expressions can
guarantee the positivity of the computed power. We also discuss the application
of Poynting's theorem for the case of sources immersed in dissipative
materials. The formulas are validated against results obtained both with
analytical and numerical methods for scattering and radiation benchmark cases
Counting and effective rigidity in algebra and geometry
The purpose of this article is to produce effective versions of some rigidity
results in algebra and geometry. On the geometric side, we focus on the
spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic
hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum
determines the commensurability class of the 2-manifold (resp., 3-manifold). We
establish effective versions of these rigidity results by ensuring that, for
two incommensurable arithmetic manifolds of bounded volume, the length sets
(resp., the complex length sets) must disagree for a length that can be
explicitly bounded as a function of volume. We also prove an effective version
of a similar rigidity result established by the second author with Reid on a
surface analog of the length spectrum for hyperbolic 3-manifolds. These
effective results have corresponding algebraic analogs involving maximal
subfields and quaternion subalgebras of quaternion algebras. To prove these
effective rigidity results, we establish results on the asymptotic behavior of
certain algebraic and geometric counting functions which are of independent
interest.Comment: v.2, 39 pages. To appear in Invent. Mat
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