In this paper, we report that we have solved the shortest vector problem (SVP) over a 128-dimensional lattice, which is currently the highest dimension of the SVP that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the SVP in lattices. In 2010 Micciancio et al. proposed a Gauss Sieve algorithm for heuristically solving the SVP using list L o...

The constraint imposed by Gauss' law is used to show that the matrix elements of n-point Wightman Functions of gluon field and quark current operators at different space time points vanish when taken between physical states. – 2 – 1. Introduction. Christ and Lee[1,2] have warned against the common practice of starting from a formal path integral approach prior to choosing a gauge. In fact, for ...

We address the PageRank problem of associating a relative importance value to all web pages in the Internet so that a search engine can use them to sort which pages to show to the user. This precludes finding the eigenvector associated with a particular eigenvalue of the link matrix constructed from the topology graph of the web. In this paper, we investigate the potential benefits of addressin...

In the previous article (Found Phys. Lett. 16 325-341), we showed that a reciprocity of the Gauss sums is connected with the wave and particle complementary. In this article, we revise the previous investigation by considering a relation between the Gauss optics and the Gauss sum based upon the recent studies of the Weil representation for a finite group.

The paper presents an improved sectional discretization method for evaluating the response of reinforced concrete sections. The section is subdivided into parametric subdomains that allow the modelization of any complex geometry while taking advantage of the Gauss quadrature techniques. In particular, curved boundaries are dealt with two nested parametric transformations, reducing the modeling ...

Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditio...

An optical vortex (phase singularity) with a high topological strength resides on the axis of a high-order light beam. The breakup of this vortex under elliptic perturbation into a straight row of unit-strength vortices is described. This behavior is studied in helical Ince-Gauss beams and astigmatic, generalized Hermite-Laguerre-Gauss beams, which are perturbations of Laguerre-Gauss beams. App...

Experimental results on the multiplicative orders of Gauss periods in finite fields are presented. These results indicate that Gauss periods have high order and are often primitive (self-dual) normal elements in finite fields. It is shown that Gauss periods can be exponentiated in quadratic time. An application is an efficient pseudorandom bit generator.