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Lattice problem

In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices. The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a…

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Overview

Shortest vector problem (SVP)

Hardness results

  • PCP Probabilistically checkable proof (complexity)
  • Arora Sanjeev Arora (computer scientist)
  • OpenAI
  • Lean Lean (proof assistant)

GapSVP

Closest vector problem (CVP)

GapCVP

Shortest independent vectors problem (SIVP)

Use in cryptography

Advanced semantic analysis

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Map overview Semantic statistics

Lattice problem

Nodes54
Edges53
Triples13
Avg. degree1.96
Density0.037037
Components1

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Lattice problem

Top relations

related to Use in cryptography · 13
Lattice problem → Ajtai, Average-case, However, Lattice, Lenstra, LLL, Lovász, Many, Moreover, NP-hard, The, The Lenstra, This

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Important terminology

displaystyle lattice basis vector problem algorithm problems given norm dimension svp beta shortest np-hard must lambda algorithms hardness gamma cvp

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lattice problemrelated to Use in cryptographyAverage-case0.60section
Lattice problemrelated to Use in cryptographyHowever0.60section
Lattice problemrelated to Use in cryptographyNP-hard0.60section
Lattice problemrelated to Use in cryptographyMany0.60section
Lattice problemrelated to Use in cryptographyMoreover0.60section
Lattice problemrelated to Use in cryptographyThe0.60section
Lattice problemrelated to Use in cryptographyLattice0.60section
Lattice problemrelated to Use in cryptographyThe Lenstra0.60section
Lattice problemrelated to Use in cryptographyLenstra0.60section
Lattice problemrelated to Use in cryptographyLovász0.60section
Lattice problemrelated to Use in cryptographyLLL0.60section
Lattice problemrelated to Use in cryptographyThis0.60section

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