Lll8499.cc:8499 - Lenstra–Lenstra–Lovász lattice basis …

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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 $${\displaystyle \mathbf {B} =\{\mathbf {b} _{1},\mathbf {b} _{2},\dots ,\mathbf {b} _{d}\}}$$ with n … See more

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What does LLL stand for?

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...

What is an LLL-reduced lattice basis?

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, . [2] [3]

What is the LLL algorithm?

[7] In particular, the LLL algorithm forms a core of one of the integer relation algorithms. For example, if it is believed that r =1.618034 is a (slightly rounded) root to an unknown quadratic equation with integer coefficients, one may apply LLL reduction to the lattice in spanned by and .

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Lenstra–Lenstra–Lovász lattice basis …
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https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm

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 $${\displaystyle \mathbf {B} =\{\mathbf {b} _{1},\mathbf {b} _{2},\dots ,\mathbf {b} _{d}\}}$$ with n … See more

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What does LLL stand for?
wikipedia.org

https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm

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...

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What is an LLL-reduced lattice basis?
wikipedia.org

https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm

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, . [2] [3]

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What is the LLL algorithm?
wikipedia.org

https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm

[7] In particular, the LLL algorithm forms a core of one of the integer relation algorithms. For example, if it is believed that r =1.618034 is a (slightly rounded) root to an unknown quadratic equation with integer coefficients, one may apply LLL reduction to the lattice in spanned by and .

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