About: Lenstra–Lenstra–Lovász lattice basis reduction algorithm

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The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis with n-dimensional integer coordinates, for a lattice L (a discrete subgroup of Rn) with , the LLL algorithm calculates an LLL-reduced (short, nearly orthogonal) lattice basis in time where is the largest length of under the Euclidean norm, that is, .

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rdfs:label	Lenstra–Lenstra–Lovász lattice basis reduction algorithm (en)
rdfs:comment	The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis with n-dimensional integer coordinates, for a lattice L (a discrete subgroup of Rn) with , the LLL algorithm calculates an LLL-reduced (short, nearly orthogonal) lattice basis in time where is the largest length of under the Euclidean norm, that is, . (en)
sameAs	Lenstra–Lenstra–Lovász lattice basis reduction algorithm
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Harv dbt:Reflist dbt:Short_description dbt:Use_dmy_dates dbt:Number-theoretic_algorithms
Subject	Computational number theory Lattice points Theory of cryptography
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm?oldid=1068943873&ns=0
Wikipage page ID	1735228 (xsd:integer)
page length (characters) of wiki page	15175 (xsd:nonNegativeInteger)
Wikipage revision ID	1068943873 (xsd:integer)
Link from a Wikipage to another Wikipage	Magma (computer algebra system) NTRUEncrypt Naccache–Stern knapsack cryptosystem Algorithm Andrew Odlyzko Arjen Lenstra Basis (linear algebra) SageMath Computational number theory Dirichlet's approximation theorem Mertens conjecture PARI/GP Quadratic equation Wolfram Mathematica Zero of a function Linear combination Linear programming Public-key cryptography Time complexity Coppersmith method Hendrik Lenstra Herman te Riele Orthogonality Lattice points GAP (computer algebra system) Golden ratio Gram–Schmidt process Factorization of polynomials Integer relation algorithm Maple (software) Isabelle (proof assistant) Lattice (group) Lattice problem Lattice reduction László Lovász MIMO Macaulay2 Polynomial RSA (cryptosystem) Theory of cryptography
has abstract	The Lenstra–Lenstra–Lovász (LLL) lattice basis reduction algorithm is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. Given a basis with n-dimensional integer coordinates, for a lattice L (a discrete subgroup of Rn) with , the LLL algorithm calculates an LLL-reduced (short, nearly orthogonal) lattice basis in time where is the largest length of under the Euclidean norm, that is, . The original applications were to give polynomial-time algorithms for factorizing polynomials with rational coefficients, for finding simultaneous rational approximations to real numbers, and for solving the integer linear programming problem in fixed dimensions. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Lenstra–Lenstra–Lovász_lattice_basis_reduction_algorithm
is Wikipage redirect of	Lenstra-Lenstra-Lovász lattice basis reduction algorithm Lenstra–Lenstra–Lovasz lattice basis reduction algorithm Lenstra-Lenstra-Lovasz algorithm Lenstra-Lenstra-Lovasz lattice basis reduction algorithm Lenstra-Lenstra-Lovasz lattice reduction algorithm Lenstra-Lenstra-Lovász lattice reduction algorithm LLL-reduced LLL algorithm LLL basis reduction method
is Link from a Wikipage to another Wikipage of	Machin-like formula Magma (computer algebra system) NTRUEncrypt András Frank Arjen Lenstra Berlekamp–Zassenhaus algorithm Brigitte Vallée Lenstra-Lenstra-Lovász lattice basis reduction algorithm Lenstra–Lenstra–Lovasz lattice basis reduction algorithm Mertens conjecture List of polynomial topics Coppersmith's attack Coppersmith method Hendrik Lenstra Hermite normal form List of algorithms Minkowski's theorem Finite field Factorization of polynomials Integer relation algorithm Korkine–Zolotarev lattice basis reduction algorithm LLL Euclidean algorithm Lovász Lattice (group) Lattice problem Lattice reduction László Lovász Lenstra-Lenstra-Lovasz algorithm Lenstra-Lenstra-Lovasz lattice basis reduction algorithm Lenstra-Lenstra-Lovasz lattice reduction algorithm Lenstra-Lenstra-Lovász lattice reduction algorithm

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