Many problems become easier if the input basis consists of short vectors. An algorithm that solves the Shortest Basis Problem (SBP) must, given a lattice basis ⁠ ⁠, output an equivalent basis ′ …

This page presents sample lattices for testing algorithms that solve the shortest vector problem (SVP) in euclidean lattices. The SVP challenge helps assessing the strength of SVP …

Aug 25, 2003 · The Shortest Vector Problem (SVP) is the most famous and widely stud-ied computational problem on lattices. Given a lattice L (typically repre-sented by a basis), SVP …

Definition 1.1 (Shortest Vector Problem, exact form). The exact form of SVP has three common variants, which we restrict to integer lattices (and so integral bases) without loss of generality: …

We will focus on three computational problems regarding lattices: The Shortest Vector Problem (SVP): nd the shortest non-zero vector in the lattice. The closest Vector Problem (CVP): nd the …

In this lecture, we begin studying the relationships between lattice problems. The two we will focus on are the Shortest Vector Problem, and the related inhomogeneous Closest Vector Problem, …

The shortest vector problem (SVP) asks to find a nonzero vector in a lattice. The problem can be defined with respect to any norm, but the Euclidean norm is the most common.

The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice \(\mathcal{L}\) (typically represented by a basis), SVP asks to find …

The Shortest Lattice Vector Problem (SVP) consists in finding x∈Zn \0 minimizing kB·xk, where B ∈Qm×n is given as input. The Closest Lattice Vector Problem (CVP) consists in finding x∈Zn …

Lattice Problems. The most well-known computational problems on lattices is the shortest vector problem: De nition 3.2 (Shortest Vector Problem (SVP)). Given an arbitrary basis b 1;:::;b nof …