Refinements of Miller's Algorithm over Weierstrass Curves Revisited

In 1986 Victor Miller described an algorithm for computing the Weil pairing in his unpublished manuscript. This algorithm has then become the core of all pairing-based cryptosystems. Many improvements of the algorithm have been presented. Most of them involve a choice of elliptic curves of a \emph{special} forms to exploit a possible twist during Tate pairing computation. Other improvements involve a reduction of the number of iterations in the Miller's algorithm. For the generic case, Blake, Murty and Xu proposed three refinements to Miller's algorithm over Weierstrass curves. Though their refinements which only reduce the total number of vertical lines in Miller's algorithm, did not give an efficient computation as other optimizations, but they can be applied for computing \emph{both} of Weil and Tate pairings on \emph{all} pairing-friendly elliptic curves. In this paper we extend the Blake-Murty-Xu's method and show how to perform an elimination of all vertical lines in Miller's algorithm during Weil/Tate pairings computation on \emph{general} elliptic curves. Experimental results show that our algorithm is faster about 25% in comparison with the original Miller's algorithm.Comment: 17 page

Residential relocation in response to light rail transit investment: case study of the Hudson-Bergen Light Rail system

© 2016, The Author(s).It is widely acknowledged that the improved accessibility enabled by investment in public transport services can, under favorable market conditions, impact the local real estate market within the zone of influence of the service’s stations. The motivation for this study is to establish the nature of two such impacts, specifically the spatial and socio-economic patterns of residential relocations that are driven by the new light rail transit (LRT) service. Using empirical data (n = 1,023) from the Hudson–Bergen Light Rail system in New Jersey (US), we report findings regarding the impacts of the introduction of the new LRT service. We investigate two linked dimensions; the first is the distinctive socio-economic profile of LRT passengers who self-report having relocated to the new transit corridor due, at least in part, to the new transit service. The second is their proximity (following their residential relocation) to the new LRT line’s stations. We present a novel analysis that accounts for endogeneity between these two dimensions of residential relocation. Of light rail passengers who engaged in a residential relocation in the 5 years prior to the survey, two-thirds (69 %) indicate that proximity to the light rail service was a ‘somewhat’ or ‘very’ important consideration. Via the multivariate analysis, we demonstrate that small household size, low income, youth (as opposed to older age), and low car ownership are each positively linked, ceteris paribus, with having engaged in a residential relocation motivated by the new transit service. Finally, higher household income is found to be associated with distance (after relocation) to the nearest transit station, which is consistent with bid-rent theory

Realizing Topological Mott Insulators from the RKKY Interaction

We engineer topological insulating phases in a fermion-fermion mixture on the honeycomb lattice, without resorting to artificial gauge fields or spin-orbit couplings and considering only local interactions. Essentially, upon integrating out the fast component (characterized by a larger hopping amplitude) in a finite region of dopings, we obtain an effective interaction between the slow fermions at half-filling, which acquires a Haldane mass with opposite parity in the two valleys of the Dirac cones, thus triggering a quantum anomalous Hall effect. We carefully analyze the competition between the induced Semenoff-type mass (producing charge density wave orders in real space) versus the Haldane mass (quantum anomalous Hall phase), as a function of the chemical potential of the fast fermions. If the second species involves spin-1/2 particles, this interaction may induce a quantum spin Hall phase. Such fermion-fermion mixtures can be realized in optical lattices or in graphene heterostructures

Three-Body Recombination near a Narrow Feshbach Resonance in 6 Li

We experimentally measure and theoretically analyze the three-atom recombination rate, L3, around a narrow s-wave magnetic Feshbach resonance of 6Li−6Li at 543.3 G. By examining both the magnetic field dependence and, especially, the temperature dependence of L3 over a wide range of temperatures from a few μK to above 200 μK, we show that three-atom recombination through a narrow resonance follows a universal behavior determined by the long-range van der Waals potential and can be described by a set of rate equations in which three-body recombination proceeds via successive pairwise interactions. We expect the underlying physical picture to be applicable not only to narrow s wave resonances, but also to resonances in nonzero partial waves, and not only at ultracold temperatures, but also at much higher temperatures