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lattice with basis

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  • Lattice problem — In computer science, lattice problems are a class of optimization problems on lattices. The conjectured intractability of such problems is central to construction of secure lattice based cryptosystems. For applications in such cryptosystems,… …   Wikipedia

  • Lattice based cryptography — is the generic term for asymmetric cryptographic primitives based on lattice. HistoryLattice have first been discovered by mathematicans Lagrange and Gauss. Lattice have been used laterly in computer algorithms and in cryptanalysis. In 1996 Atjai …   Wikipedia

  • Lattice sieving — is a technique for finding smooth values of a bivariate polynomial f(a,b) over a large region. It is almost exclusively used in connection with the number field sieve.The algorithm implicitly involves the ideal structure of the number field of… …   Wikipedia

  • Lattice (group) — A lattice in the Euclidean plane. In mathematics, especially in geometry and group theory, a lattice in Rn is a discrete subgroup of Rn which spans the real vector space Rn. Every lattice in Rn …   Wikipedia

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

  • Lattice (discrete subgroup) — In Lie theory and related areas of mathematics, a lattice in a locally compact topological group is a discrete subgroup with the property that the quotient space has finite invariant measure. In the special case of subgroups of R n , this amounts …   Wikipedia

  • Lattice phase equaliser — A lattice phase equaliser or lattice filter is an example of an all pass filter. That is, the attenuation of the filter is constant at all frequencies but the relative phase between input and output varies with frequency. The lattice filter… …   Wikipedia

  • Lattice problems — In the following computational problems on lattices are described. These problems are essential for lattice based cryptosystems.The Shortest Vector Problem (SVP)In SVP, a basis B of a lattice L is given and one must find the shortest non zero… …   Wikipedia

  • Reciprocal lattice — In physics, the reciprocal lattice of a lattice (usually a Bravais lattice) is the lattice in which the Fourier transform of the spatial function of the original lattice (or direct lattice) is represented. This space is also known as momentum… …   Wikipedia

  • Unimodular lattice — In mathematics, a unimodular lattice is a lattice of discriminant 1 or −1.The E 8 lattice and the Leech lattice are two famous examples. Definitions *A lattice is a free abelian group of finite rank with an integral symmetric bilinear form (·,·) …   Wikipedia

  • Lenstra–Lenstra–Lovász lattice basis reduction algorithm — The Lenstra–Lenstra–Lovász lattice basis reduction (LLL) is a polynomial time lattice reduction algorithm invented by Arjen Lenstra, Hendrik Lenstra and László Lovász. Given as input d lattice basis vectors with n dimensional integer coordinates… …   Wikipedia

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