About: Lattice reduction

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In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice.

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rdfs:label	Lattice reduction (en) 格规约 (zh)
rdfs:comment	In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice. (en) 格基归约（英語：Lattice basis reduction）在数学中的目标是给出一个整数格基作为输入，找出一个向量较短且近似正交的基。有许多不同算法可以实现格规约，运行时间至少是格的维数的指数次。 (zh)
foaf:depiction
dcterms:subject	Cryptography Lattice points Linear algebra Computational number theory Theory of cryptography Lattice-based cryptography Post-quantum cryptography
Wikipage page ID	4786593 (xsd:integer)
Wikipage revision ID	1116429667 (xsd:integer)
Link from a Wikipage to another Wikipage	Basis (linear algebra) Determinant Integer programming Cryptography Matrix (mathematics) Orthogonal Greatest common divisor Lattice points NP-hard Cryptanalysis P (complexity) Public-key cryptography Spigot algorithm Lattice (group) Linear algebra Euclidean algorithm Number Theory Library Parallelepiped Korkine–Zolotarev lattice basis reduction algorithm Lenstra–Lenstra–Lovász lattice basis reduction algorithm Computational number theory Theory of cryptography Lattice-based cryptography Post-quantum cryptography Polynomial time LLL algorithm
Link from a Wikipage to an external page	https://github.com/christianpeel/LLLplus.jl/blob/master/src/seysen.jl https://github.com/dstehle/fplll
sameAs	Lattice reduction Lattice reduction Lattice reduction Lattice reduction
dbp:wikiPageUsesTemplate	dbt:Citation_needed dbt:Reflist
thumbnail	wiki-commons:Special:FilePath/Lattice-reduction.svg?width=300
has abstract	In mathematics, the goal of lattice basis reduction is to find a basis with short, nearly orthogonal vectors when given an integer lattice basis as input. This is realized using different algorithms, whose running time is usually at least exponential in the dimension of the lattice. (en) 格基归约（英語：Lattice basis reduction）在数学中的目标是给出一个整数格基作为输入，找出一个向量较短且近似正交的基。有许多不同算法可以实现格规约，运行时间至少是格的维数的指数次。 (zh)
prov:wasDerivedFrom	wikipedia-en:Lattice_reduction?oldid=1116429667&ns=0
page length (characters) of wiki page	7672 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Lattice_reduction
is Link from a Wikipage to another Wikipage of	László Lovász GGH encryption scheme Jessica Sklar Lattice problem Lattice sieving Fibonacci number Korkine–Zolotarev lattice basis reduction algorithm Lenstra–Lenstra–Lovász lattice basis reduction algorithm Reduction Susanne Wetzel Integer set library Unimodular matrix Wigner–Seitz cell Sums of three cubes NTRUEncrypt Lattice basis reduction
is Wikipage redirect of	Lattice basis reduction
is Wikipage disambiguates of	Reduction
is foaf:primaryTopic of	wikipedia-en:Lattice_reduction

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