Realizing arbitrary-precision modular multiplication with a fixed-precision multiplier datapath

Within the context of cryptographic hardware, the term scalability refers to the ability to process operands of any size, regardless of the precision of the underlying data path or registers. In this paper we present a simple yet effective technique for increasing the scalability of a fixed-precision Montgomery multiplier. Our idea is to extend the datapath of a Montgomery multiplier in such a way that it can also perform an ordinary multiplication of two n-bit operands (without modular reduction), yielding a 2n-bit result. This conventional (nxn->2n)-bit multiplication is then used as a “sub-routine” to realize arbitrary-precision Montgomery multiplication according to standard software algorithms such as Coarsely Integrated Operand Scanning (CIOS). We show that performing a 2n-bit modular multiplication on an n-bit multiplier can be done in 5n clock cycles, whereby we assume that the n-bit modular multiplication takes n cycles. Extending a Montgomery multiplier for this extra functionality requires just some minor modifications of the datapath and entails a slight increase in silicon area

Estimating spinning binary parameters and testing alternative theories of gravity with LISA

We investigate the effect of spin-orbit and spin-spin couplings on the estimation of parameters for inspiralling compact binaries of massive black holes, and for neutron stars inspiralling into intermediate-mass black holes, using hypothetical data from the proposed Laser Interferometer Space Antenna (LISA). We work both in Einstein's theory and in alternative theories of gravity of the scalar-tensor and massive-graviton types. We restrict the analysis to non-precessing spinning binaries, i.e. to cases where the spins are aligned normal to the orbital plane. We find that the accuracy with which intrinsic binary parameters such as chirp mass and reduced mass can be estimated within general relativity is degraded by between one and two orders of magnitude. We find that the bound on the coupling parameter omega_BD of scalar-tensor gravity is significantly reduced by the presence of spin couplings, while the reduction in the graviton-mass bound is milder. Using fast Monte-Carlo simulations of 10^4 binaries, we show that inclusion of spin terms in massive black-hole binaries has little effect on the angular resolution or on distance determination accuracy. For stellar mass inspirals into intermediate-mass black holes, the angular resolution and the distance are determined only poorly, in all cases considered. We also show that, if LISA's low-frequency noise sensitivity can be extrapolated from 10^-4 Hz to as low as 10^-5 Hz, the accuracy of determining both extrinsic parameters (distance, sky location) and intrinsic parameters (chirp mass, reduced mass) of massive binaries may be greatly improved.Comment: 29 pages, 9 figures. Matches version accepted in Physical Review D. More stringent checks in the inversion of the Fisher matri

The basic parameters of gamma-ray-loud blazars

We determined the basic parameters, such as the central black hole mass ($M$), the boosting factor (or Doppler factor) ($\delta$), the propagation angle ($\Phi$) and the distance along the axis to the site of $\gamma$-ray production ($d$) for 23 $\gamma$-ray-loud blazars using their available variability timescales. In this method, the absorption effect depends on the $\gamma$-ray energy, emission size and property of the accretion disk. Using the intrinsic $\gamma$-ray luminosity as a fraction $\lambda$ of the Eddington luminosity, $L^{in}_{\gamma}=\lambda L_{Ledd.}$ and the optical depth equal to unity, we can determine the upper limit of the central black hole masses. We found that the black hole masses range between $10^{7}M_{\odot}$ and $10^{9}M_{\odot}$ when $\lambda$ = 0.1 and 1.0 are adopted. Since this method is based on gamma-ray emissions and the short time-scale of the sources, it can also be used for central black hole mass determination of high redshift gamma-ray sources. In the case of the upper limit of black hole mass there is no clear difference between BLs and FSRQs, which suggests that the central black hole masses do not play an important role in the evolutionary sequence of blazars.Comment: 8 pages, 3 figures, 1 table, Accepted by A&

A three-dimensional lattice gas model for amphiphilic fluid dynamics

We describe a three-dimensional hydrodynamic lattice-gas model of amphiphilic fluids. This model of the non-equilibrium properties of oil-water-surfactant systems, which is a non-trivial extension of an earlier two-dimensional realisation due to Boghosian, Coveney and Emerton [Boghosian, Coveney, and Emerton 1996, Proc. Roy. Soc. A 452, 1221-1250], can be studied effectively only when it is implemented using high-performance computing and visualisation techniques. We describe essential aspects of the model's theoretical basis and computer implementation, and report on the phenomenological properties of the model which confirm that it correctly captures binary oil-water and surfactant-water behaviour, as well as the complex phase behaviour of ternary amphiphilic fluids.Comment: 34 pages, 13 figures, high resolution figures available on reques

Long Range Correlation in Granular Shear Flow II: Theoretical Implications

Numerical simulations are used to test the kinetic theory constitutive relations of inertial granular shear flow. These predictions are shown to be accurate in the dilute regime, where only binary collisions are relevant, but underestimate the measured value in the dense regime, where force networks of size $\xi$ are present. The discrepancy in the dense regime is due to non-collisional forces that we measure directly in our simulations and arise from elastic deformations of the force networks. We model the non-collisional stress by summing over all paths that elastic waves travel through force networks. This results in an analytical theory that successfully predicts the stress tensor over the entire inertial regime without any adjustable parameters