9,206 research outputs found
A Comparison of Double Point Multiplication Algorithms and their Implementation over Binary Elliptic Curves
Efficient implementation of double point multiplication is crucial for elliptic curve cryptographic systems. We revisit three recently proposed simultaneous double point multiplication algorithms. We propose hardware architectures for these algorithms, and provide a comparative analysis of their performance. We implement the proposed architectures on Xilinx Virtex-4 FPGA, and report on the area and time results . Our results indicate that differential addition chain based algorithms are better suited to compute double point multiplication over binary elliptic curves for both high performance and resource constrained applications
Fast, uniform, and compact scalar multiplication for elliptic curves and genus 2 Jacobians with applications to signature schemes
We give a general framework for uniform, constant-time one-and
two-dimensional scalar multiplication algorithms for elliptic curves and
Jacobians of genus 2 curves that operate by projecting to the x-line or Kummer
surface, where we can exploit faster and more uniform pseudomultiplication,
before recovering the proper "signed" output back on the curve or Jacobian.
This extends the work of L{\'o}pez and Dahab, Okeya and Sakurai, and Brier and
Joye to genus 2, and also to two-dimensional scalar multiplication. Our results
show that many existing fast pseudomultiplication implementations (hitherto
limited to applications in Diffie--Hellman key exchange) can be wrapped with
simple and efficient pre-and post-computations to yield competitive full scalar
multiplication algorithms, ready for use in more general discrete
logarithm-based cryptosystems, including signature schemes. This is especially
interesting for genus 2, where Kummer surfaces can outperform comparable
elliptic curve systems. As an example, we construct an instance of the Schnorr
signature scheme driven by Kummer surface arithmetic
Nuclear profile dependence of elliptic flow from a parton cascade
The transverse profile dependence of elliptic flow is studied in a parton
cascade model. We compare results from the binary scaling profile to results
from the wounded nucleon scaling profile. The impact parameter dependence of
elliptic flow is shown to depend sensitively on the transverse profile of
initial particles, however, if elliptic flow is plotted as a function of the
relative multiplicity, the nuclear profile dependence disappears. The
insensitivity was found previously in a hydrodynamical calculation. Our
calculations indicate that the insensitivity is also valid with additional
viscous corrections. In addition, the minimum bias differential elliptic flow
is demonstrated to be insensitive to the nuclear profile of the system
Open heavy flavor in Pb+Pb collisions at sqrt(s)=2.76 TeV within a transport model
The space-time evolution of open heavy flavor is studied in Pb+Pb collisions
at sqrt(s)=2.76 TeV using the partonic transport model Boltzmann Approach to
MultiParton Scatterings (BAMPS). An updated version of BAMPS is presented which
allows interactions among all partons: gluons, light quarks, and heavy quarks.
Heavy quarks, in particular, interact with the rest of the medium via binary
scatterings with a running coupling and a Debye screening which is matched by
comparing to hard thermal loop calculations. The lack of radiative processes in
the heavy flavor sector is accounted for by scaling the binary cross section
with a phenomenological factor K=3.5, which describes well the elliptic flow
v_2 and nuclear modification factor R_AA at RHIC. Within this framework we
calculate in a comprehensive study the v_2 and R_AA of all interesting open
heavy flavor particles at the LHC: electrons, muons, D mesons, and non-prompt
J/psi from B mesons. We compare to experimental data, where it is already
available, or make predictions. To do this accurately next-to-leading order
initial heavy quark distributions are employed which agree well with
proton-proton data of heavy flavor at sqrt(s)=7 TeV.Comment: 7 pages, 10 figures, muon calculations updated, references added,
published versio
Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics
The centrality dependence of the charged multiplicity, transverse energy, and
elliptic flow coefficient is studied in a hydrodynamic model, using a variety
of different initializations which model the initial energy or entropy
production process as a hard or soft process, respectively. While the charged
multiplicity depends strongly on the chosen initialization, the p_t-integrated
elliptic flow for charged particles as a function of charged particle
multiplicity and the p_t-differential elliptic flow for charged particles in
minimum bias events turn out to be almost independent of the initial energy
density profile.Comment: 11 pages RevTex, including 10 postscript figures. Slightly modified
discussion of Figs. 5 and 6, updated references. This version to appear in
Nuclear Physics
Abel's Theorem in the Noncommutative Case
We define noncommutative binary forms. Using the typical representation of
Hermite we prove the fundamental theorem of algebra and we derive a
noncommutative Cardano formula for cubic forms. We define quantized elliptic
and hyperelliptic differentials of the first kind. Following Abel we prove
Abel's Theorem.Comment: 30 page
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