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

certain average-case lattice problem, known as short integer solutions (SIS), is at least as hard to solve as a worst-case lattice problem. She then showed...

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

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

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...

of the random lattice argument of C.A. Rogers. Many problems in the chemical and physical sciences can be related to packing problems where more than...

Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, E24. It is one of the best models for the kissing number problem. It...

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

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...

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...

Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge...

In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and...

mathematics, the E8 lattice is a special lattice in R8. It can be characterized as the unique positive-definite, even, unimodular lattice of rank 8. The name...

nine possible definable packings. The 8-dimensional E8 lattice and 24-dimensional Leech lattice have also been proven to be optimal in their respective...

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...

scenario the protein folding problem is NP-complete. Different versions of lattice proteins may adopt different types of lattice (typically square and triangular...

asymmetric cryptosystem uses a variant of the learning with errors lattice problem as its basic trapdoor function. It won the NIST competition for the...

In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important...

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...

complete lattice is a partially ordered set in which all subsets have both a supremum (join) and an infimum (meet). A conditionally complete lattice satisfies...

assumption that the shortest vector problem (SVP) is hard in these ideal lattices. In general terms, ideal lattices are lattices corresponding to ideals in rings...

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...

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

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

quantum algorithms for two major problems: the graph isomorphism problem and certain shortest vector problems (SVPs) in lattices. More precisely, an efficient...

Computational geometry – see Closest pair of points problem Cryptanalysis – for lattice problem Databases – e.g. content-based image retrieval Coding...

errors problem is the fact that the solution to the RLWE problem can be used to solve a version of the shortest vector problem (SVP) in a lattice (a polynomial-time...

one-dimensional (1D) lattice problem. In 1944 Onsager was able to get an exact solution to a two-dimensional (2D) lattice problem at the critical density...

COIN-OR Linear Program Solver Communication Linking Protocol Congruence lattice problem Constraint Logic Programming Constraint logic programming (Real) Control...

perform for this task, as it can be applied to break lattice-based cryptography. The hidden shift problem states: Given an oracle O {\displaystyle O} that...