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

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

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