Lattice reduction in two dimensions: the black vectors are the given basis for the lattice (represented by blue dots), the red vectors are the reduced basis
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.
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...
(n)}} ) in the lattice dimension. The former class of algorithms most notably includes lattice enumeration and random sampling reduction, while the latter...
Dimension reduction, the process of reducing the number of random variables under consideration Latticereduction, given an integer lattice basis as input...
relies on the difficulty of latticereduction. The idea included in this trapdoor function is that, given any basis for a lattice, it is easy to generate...
related, though not equivalent, to the algorithmic problem of latticereduction in certain lattices. Careful choice of parameters is necessary to thwart some...
2}+2{F_{n+1}}^{2}\right)} These can be found experimentally using latticereduction, and are useful in setting up the special number field sieve to factorize...
Izabachène, P.Q. Nguyen, and X. Xie Structural LatticeReduction: Generalized Worst-Case to Average-Case Reductions and Homomorphic Cryptosystems. In EUROCRYPT...
Elsenhans & Jahnel (2009) used a method of Noam Elkies (2000) involving latticereduction to search for all solutions to the Diophantine equation x 3 + y 3...
(determinant −1). The unimodular matrix used (possibly implicitly) in latticereduction and in the Hermite normal form of matrices. The Kronecker product...
Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. It is a lattice gauge...
The lattice Boltzmann methods (LBM), originated from the lattice gas automata (LGA) method (Hardy-Pomeau-Pazzis and Frisch-Hasslacher-Pomeau models), is...
theory of lattices, the dual lattice is a construction analogous to that of a dual vector space. In certain respects, the geometry of the dual lattice of a...
product on the weight lattice. The connected Dynkin diagrams (corresponding to simple groups) are pictured below. For a split reductive group G over a field...
rational coefficients in the seminal paper that introduced the LLL latticereduction algorithm with Hendrik Willem Lenstra and László Lovász. Lenstra is...
discrete mathematics, ideal lattices are a special class of lattices and a generalization of cyclic lattices. Ideal lattices naturally occur in many parts...
In physics, lattice gauge theory is the study of gauge theories on a spacetime that has been discretized into a lattice. Gauge theories are important...
chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction (half-cell or full cell reaction) from the standard...
dipoles forming superposed resonance rings in helical pathways throughout lattices of microtubules. The oscillations are either electric, due to charge separation...
In computability theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine...
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