After Miller’s original algorithm for the Tate pairing computation, many improved algorithms have been suggested, to name just a few, by Galbraith et al. and Barreto et al., especially for the fields with characteristic three. Also Duursma and Lee found a closed formula of the Tate pairing computation for the fields with characteristic three. In this paper, we show that a similar argument is al...

In this paper the benefits of implementation of the Tate pairing computation in dedicated hardware are discussed. The main observation lies in the fact that arithmetic architectures in the extension field GF (3) are good candidates for parallelization, leading to a similar calculation time in hardware as for operations over the base field GF (3). Using this approach an architecture for the hard...

We present the diametric theorem for additive anticodes with respect to the Lee distance in Zn2k , where Z2k is an additive cyclic group of order 2. We also investigate optimal anticodes in Znpk for the homogeneous distance and in Zm for the Krotov-type distance.

We present a general technique for the efficient computation of pairings on supersingular Abelian varieties. This formulation, which we call the eta pairing, generalises results of Duursma and Lee for computing the Tate pairing on supersingular elliptic curves in characteristic three. We then show how our general technique leads to a new algorithm which is about twice as fast as the Duursma-Lee...

This paper gives the minimum generating sets of three types of one generator (1 + u)-quasi twisted (QT) codes over F 2 + uF 2 , u 2 = 0. Moreover, it discusses the generating sets and the lower bounds on the minimum Lee distance of a special class of A 2 type one generator (1 + u)-QT codes. Some good (optimal or suboptimal) linear codes over F 2 are obtained by these types of one generator (1 +...

Inhaltsverzeichnis 1 Einleitung 2 2 CASE-Tool Marktanalysen in der Literatur 2 3 Untersuchungsmethodik 3 3.1 Ziel der Untersuchung 3 3.2 Bestimmung der Untersuchungsform 3 3.3 Auswahl der Untersuchungseinheiten 4 3.4 Datenerhebung und -erfassung 5 3.4.1 Kriterienkatalog 5 3.4.2 Evaluierungskonzept 5 4 Darstellung, Interpretation und Diskussion der Ergebnisse 5 4.1 Überblick 5 4.2 Tendenzaussage...

Recently Tate pairing and its variations are attracted in cryptography. Their operations consist of a main iteration loop and a final exponentiation. The final exponentiation is necessary for generating a unique value of the bilinear pairing in the extension fields. The speed of the main loop has become fast by the recent improvements, e.g., the Duursma-Lee algorithm and ηT pairing. In this pap...

background and objectives: enteropathogenic escherichia coli (epec) divided into two groups typical and atypical (aspect). the main virulence genes are located in a pathogenicity island called lee ( locus of enterocyte effacement ). lee frequently inserted in trna genes of selc , pheu and phev in the bacterial chromosome. tepec and aepec strains have some differences in their pathogenicity. the...

Lee distance Gray codes for k-ary n-cubes and torus networks are presented. Using these Lee distance Gray codes, it is further shown how to directly generate edge disjoint Hamiltonian cycles for a class of k-ary n-cubes, 2-D tori, and hypercubes.