Recently, the authors proposed a method for computing the Tate pairing using a distortion map for y2 = x5 − αx (α = ±2) over finite fields of characteristic five. In this paper, we show the Ate pairing, an invariant of the Tate pairing, can be applied to this curve. This leads to about 50% computational cost-saving over the Tate pairing.

Since Tate pairing was suggested to construct a cryptosystem, fast computation of Tate pairing has been researched recently. Barreto et. al[3] and Galbraith[8] provided efficient algorithms for Tate pairing on y = x − x + b in characteristic 3 and Duursma and Lee[6] gave a closed formula for Tate pairing on y = x − x + d in characteristic p. In this paper, we present completely general and expl...

For the Tate pairing implementation over hyperelliptic curves, there is a development by DuursmaLee and Barreto et al., and those computations are focused on degenerate divisors. As divisors are not degenerate form in general, it is necessary to find algorithms on general divisors for the Tate pairing computation. In this paper, we present two efficient methods for computing the Tate pairing ov...

The dynamics by which homologous chromosomes pair is currently unknown. Here, we use fluorescence in situ hybridization in combination with three-dimensional optical microscopy to show that homologous pairing of the somatic chromosome arm 2L in Drosophila occurs by independent initiation of pairing at discrete loci rather than by a processive zippering of sites along the length of chromosome. B...

A pair ( a , b ) of positive integers is pythagorean if 2 + = □ i.e. square). called double-pythapotent there another k l such that pair, and it quadratic pythapotent which not multiple pair. To each we assign an elliptic curve Γ with torsion group Z / × 4 has rank over Q only Similarly, to 8 Moreover, in the later case obtain every isomorphic form where As side-result get then are infinitely m...