FPGA and ASIC Implementations of the ηT\eta_T Pairing in Characteristic Three

Since their introduction in constructive cryptographic applications, pairings over (hyper)elliptic curves are at the heart of an ever increasing number of protocols. As they rely critically on efficient algorithms and implementations of pairing primitives, the study of hardware accelerators became an active research area. In this paper, we propose two coprocessors for the reduced $\eta_T$ pairing introduced by Barreto {\it et al.} as an alternative means of computing the Tate pairing on supersingular elliptic curves. We prototyped our architectures on FPGAs. According to our place-and-route results, our coprocessors compare favorably with other solutions described in the open literature. We also present the first ASIC implementation of the reduced $\eta_T$ pairing

Propagation characteristics in the earth-ionosphere waveguide for VLF waves emitted from trapping cones at high latitudes

It is important to clarify the relationship between VLF-ELF wave characteristics on the ground and in the ionosphere for a comprehensive understanding of the ground-based observation data. In this paper, the amplitude and polarization of VLF waves at various places on the ground are calculated with an ionospheric model at high latitudes, through a full wave technique when various size of trapping cones are existing. Some results of the numerical calculation are presented. Major results are as follows : (1) Waves with an amplitude within 12 dB of the maximum intensity are found in an area of 300km (east-west direction)×400km (north-south direction) when some part of the trapping cone overlaps with the transmission cone. (2) The left-handed polarization wave can exist even within a distance of 100km from the point of maximum intensity, where the intensity is as strong as ∿ -10dB of the maximum intensity

Intensity and polarization characteristics along the earth\u27s surface for the ELF-VLF waves emitted from a transmission cone in the high latitude

A computer code has been developed, which incorporates a full-wave treatment of down-going ELF-VLF wave injected at any altitude in the ionosphere. Ground conductivity is included as a variable in the code. The code expands a spatially confined electromagnetic wave into a finite set of plane waves. For each elemental plane wave, the field components are calculated by a full-wave method, and the field distribution is obtained by FFT analysis of the full-wave solutions. In this paper, numerical calculations are carried out for both daytime and nighttime ionosphere models in high latitude. The distributions of intensity as well as polarization on the ground are presented in the case that ELF-VLF waves having a spatial amplitude distribution are injected onto the ionosphere

Full wave calculation for a Gaussian VLF wave injection into the ionospherer

Both spatial distributions of the field intensity and the polarization at the ground of a spatially confined whistler mode wave, which has a Gaussian amplitude incident onto the ionosphere from above are computed by a full wave method. The propagation paths in the earth-ionosphere wave guide are estimated by tracing the peaks of these wave distributions at different altitudes. From these calculations, the following interesting results are obtained : (1) The spatial attenuation rate of the wave intensity in the earth-ionosphere wave guide mode is about -10dB/100km for a distance less than a few hundred kilometers from the source. (2) The polarization is right-handed circular just underneath the source point, but it becomes left handed at some distance away