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In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability...

coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance...

on the hardness of well-studied lattice problems, and Cynthia Dwork showed that a certain average-case lattice problem, known as short integer solutions...

finite lattice representation problem, or finite congruence lattice problem, asks whether every finite lattice is isomorphic to the congruence lattice of...

solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began...

congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed...

assumptions used in cryptography (including RSA, discrete log, and some lattice problems) can be based on worst-case assumptions via worst-case-to-average-case...

random packing of equal spheres generally has a density around 63.5%. A lattice arrangement (commonly called a regular arrangement) is one in which the...

theory of lattices, the dual lattice is a construction analogous to that of a dual vector space. In certain respects, the geometry of the dual lattice of a...

learning problem. Regev showed that the LWE problem is as hard to solve as several worst-case lattice problems. Subsequently, the LWE problem has been...

discrete mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts...

Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was...

mechanics, the particle in a one-dimensional lattice is a problem that occurs in the model of a periodic crystal lattice. The potential is caused by ions in the...

consists in mapping a many-body lattice problem to a many-body local problem, called an impurity model. While the lattice problem is in general intractable...

Packing problems are a class of optimization problems in mathematics that involve attempting to pack objects together into containers. The goal is to...

The Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. The Clay Institute...

may still be preferred for solving multiple closest vector problems (CVPs) in the same lattice, where it can be more efficient. The definition of a KZ-reduced...

Ajtai and Dwork devised in 1997 a lattice-based public-key cryptosystem; Ajtai has done extensive work on lattice problems. For his numerous contributions...

generalization of the previously mentioned problems, as well as graph isomorphism and certain lattice problems. Efficient quantum algorithms are known for...

In geometry and crystallography, a Bravais lattice, named after Auguste Bravais (1850), is an infinite array of discrete points generated by a set of...