Computation in Optimal Extension Fields

This thesis focuses on a class of Galois field used to achieve fast finite field arithmetic which we call Optimal Extension Fields (OEFs), first introduced in cite{baileypaar98}. We extend this work by presenting an adaptation of Itoh and Tsujii\u27s algorithm for finite field inversion applied to OEFs. In particular, we use the facts that the action of the Frobenius map in $GF(p^m)$ can be computed with only $m-1$ subfield multiplications and that inverses in $GF(p)$ may be computed cheaply using known techniques. As a result, we show that one extension field inversion can be computed with a logarithmic number of extension field multiplications. In addition, we provide new variants of the Karatsuba-Ofman algorithm for extension field multiplication which give a performance increase. Further, we provide an OEF construction algorithm together with tables of Type I and Type II OEFs along with statistics on the number of pseudo-Mersenne primes and OEFs. We apply this new work to provide implementation results for elliptic curve cryptosystems on both DEC Alpha workstations and Pentium-class PCs. These results show that OEFs when used with our new inversion and multiplication algorithms provide a substantial performance increase over other reported methods

Vulnerabilities in first-generation RFID-enabled credit cards

Credit cards ; Radio frequency identification systems

The polarization of the planet-hosting WASP-18 system

We report observations of the linear polarization of the WASP-18 system, which harbors a very massive ( approx 10 M_J) planet orbiting very close to its star with an orbital period of 0.94 days. We find the WASP-18 system is polarized at about 200 parts-per-million (ppm), likely from the interstellar medium predominantly, with no strong evidence for phase dependent modulation from reflected light from the planet. We set an upper limit of 40 ppm (99% confidence level) on the amplitude of a reflected polarized light planetary signal. We compare the results with models for a number of processes that may produce polarized light in a planetary system to determine if we can rule out any phenomena with this limit. Models of reflected light from thick clouds can approach or exceed this limit, but such clouds are unlikely at the high temperature of the WASP-18b atmosphere. Additionally, we model the expected polarization resulting from the transit of the planet across the star and find this has an amplitude of about 1.6 ppm, which is well below our detection limits. We also model the polarization due to the tidal distortion of the star by the massive planet and find this is also too small to be measured currently.Comment: 23 pages, 10 Figures, 6 Tables, Accepted to A

Phase-locked polarization by photospheric reflection in the semidetached eclipsing binary μ1\mu^1 Sco

We report the detection of phase-locked polarization in the bright ($m_V$=2.98-3.24) semidetached eclipsing binary $\mu^1$ Sco (HD 151890). The phenomenon was observed in multiple photometric bands using two different HIPPI-class (HIgh Precision Polarimetric Instrument)polarimeters with telescopes ranging in size from 35-cm to 3.9-m. The peak-to-trough amplitude of the polarization is wavelength dependent and large, $\sim$700 parts-per-million in green light, and is easily seen with even the smallest telescope. We fit the polarization phase curve with a SYNSPEC/VLIDORT polarized radiative transfer model and a Wilson-Devinney geometric formalism, which we describe in detail. Light from each star reflected by the photosphere of the other, together with a much smaller contribution from tidal distortion and eclipse effects, wholly accounts for the polarization amplitude. In the past polarization in semidetached binaries has been attributed mostly to scattering from extra-stellar gas. Our new interpretation facilitates determining masses of such stars in non-eclipsing systems.Comment: 16 pages, 8 figures, 8 tables. Accepted to MNRA

The rotation of alpha Oph investigated using polarimetry

Recently we have demonstrated that high-precision polarization observations can detect the polarization resulting from the rotational distortion of a rapidly rotating B-type star. Here we investigate the extension of this approach to an A-type star. Linear-polarization observations of $\alpha$ Oph (A5IV) have been obtained over wavelengths from 400 to 750 nm. They show the wavelength dependence expected for a rapidly-rotating star combined with a contribution from interstellar polarization. We model the observations by fitting rotating-star polarization models and adding additional constraints including a measured $v_e \sin{i}$. However, we cannot fully separate the effects of rotation rate and inclination, leaving a range of possible solutions. We determine a rotation rate $\omega = \Omega/\Omega_ c$ between 0.83 and 0.98 and an axial inclination i > 60 deg. The rotation-axis position angle is found to be 142 $\pm$ 4 deg, differing by 16 deg from a value obtained by interferometry. This might be due to precession of the rotation axis due to interaction with the binary companion. Other parameters resulting from the analysis include a polar temperature Tp = 8725 $\pm$ 175 K, polar gravity $\log{g_p} = 3.93 \pm 0.08$ (dex cgs), and polar radius $R_{\rm p} = 2.52 \pm 0.06$ Rsun. Comparison with rotating-star evolutionary models indicates that $\alpha$ Oph is in the later half of its main-sequence evolution and must have had an initial $\omega$ of 0.8 or greater. The interstellar polarization has a maximum value at a wavelength ($\lambda_{\rm max}$) of $440 \pm 110$ nm, consistent with values found for other nearby stars.Comment: 14 pages, 11 figures, 5 tables, Accepted in MNRA

A high-sensitivity polarimeter using a ferro-electric liquid crystal modulator

We describe the HIgh Precision Polarimetric Instrument (HIPPI), a polarimeter built at UNSW (The University of New South Wales) Australia and used on the Anglo-Australian Telescope (AAT). HIPPI is an aperture polarimeter using a ferro-electric liquid crystal modulator. HIPPI measures the linear polarization of starlight with a sensitivity in fractional polarization of ∼4 × 10−6 on low-polarization objects and a precision of better than 0.01 per cent on highly polarized stars. The detectors have a high dynamic range allowing observations of the brightest stars in the sky as well as much fainter objects. The telescope polarization of the AAT is found to be 48 ± 5 × 10−6 in the g′ bandPeer reviewedFinal Accepted Versio