Lattice reduction is a hard problem of interest to both publickey cryptography and cryptanalysis. Despite its importance, extremely few algorithms are known. The best algorithm known in high dimension is due to Schnorr, proposed in 1987 as a block generalization of the famous LLL algorithm. This paper deals with Schnorr’s algorithm and potential improvements. We prove that Schnorr’s algorithm o...

We firstly review the constant term method (CTM), illustrating its combinatorial connections and show how it can be used to solve a certain class of lattice path problems. We show the connection between the CTM, the transfer matrix method (eigenvectors and eigenvalues), partial difference equations, the Bethe Ansatz and orthogonal polynomials. Secondly, we solve a lattice path problem first pos...

in this article, we suggested a novel design of polarization splitter based on coupler waveguide on inp substrate at 1.55mm wavelength. photonic crystal structure is consisted of two dimensional (2d) air holes embedded in inp/ingaasp material with an effective refractive index of 3.2634 which is arranged in a hexagonal lattice. the photonic band gap (pbg) of this structure is determined using t...

We reformulate the Hamiltonian approach to lattice gauge theories such that, at the classical level, the gauge group does not act canonically, but instead as a Poisson-Lie group. At the quantum level, it then gets promoted to a quantum group gauge symmetry. The theory depends on two parameters-the deformation parameter and the lattice spacing a. We show that the system of Kogut and Susskind is ...

There is accumulating evidence in lattice QCD that attempts to locate confining fields in vacuum configurations bring results explicitly depending on the lattice spacing (that is, ultraviolet cut off). Generically, one deals with lowdimensional vacuum defects which occupy a vanishing fraction of the total four-dimensional space. We review briefly existing data on the vacuum defects and their si...

We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the difference between the full and the effective theory in the continuum limit. In the full theory we find a term non-analytic in 1/m, revealing the asymptotic ...

The properties of the momentum space quark propagator in Landau gauge are examined for the overlap quark action in quenched lattice QCD. Numerical calculations were done on two lattices with different lattice spacing a and similar physical volumes to explore the quark propagator in the continuum limit. We have calculated the nonperturbative wavefunction renormalization function Z(p) and the non...

Using tadpole-improved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios x054,6,10 and inverse lattice spacing in the range as 5660–840 MeV. The tadpole corrections to the action, which are established selfconsistently, are defined for two cases, mean link tadpoles in the Landau gau...

We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Λ QCD while the localization volume of the modes tends to zero in physical units with the lattice spacing tending to zero. The situation changes drastically when we study "vortex removed" configurations.