We give deterministic~ O (22n+ o (n))-time algorithms to solve all the most important
computational problems on point lattices in NP, including the Shortest Vector Problem …

We present the state of the art solvers of the Shortest and Closest Lattice Vector Problems in
the Euclidean norm. We recall the three main families of algorithms for these problems …

A central problem of geometry is the tiling of space with simple structures. The classical
solutions, such as triangles, squares, and hexagons in the plane and cubes and other …

Variations on Encoding Circuits for Stabilizer Quantum Codes Page 1 Variations on Encoding
Circuits for Stabilizer Quantum Codes Markus Grassl Centre for Quantum Technologies …

The purpose of this paper is to study convex bodies CC for which there exists no convex
body C′⊊ CC^′\subsetneqC of the same lattice width. Such bodies will be called 'lattice …

The shortest vector problem (SVP) and closest vector problem (CVP) are the most widely
known problems on point lattices. SVP and CVP have been extensively studied both as …

In a recent article we introduced a new class of shapes, called\emph {soft cells} which fill
space as\emph {soft tilings} without gaps and overlaps while minimizing the number of sharp …

In this paper, we recall the basic results of the reduction theory of positive definite quadratic
forms. Since finding the shortest vectors in a lattice is an NP-hard problem, the low …

In this paper we shall investigate the boundary of an extremal body K. Using the
characterization of the extremal bodies proved by Venkov and McMullen (Theorem 1) we …

Analysis of Symmetric-Key Cryptosystems and Subset-Sum Problem Page 1 Analysis of
Symmetric-Key Cryptosystems and Subset-Sum Problem A thesis submitted in Partial Fulfillment …