Search results
Results from the WOW.Com Content Network
In computer science, lattice problems are a class of optimization problems related to mathematical objects called lattices.The conjectured intractability of such problems is central to the construction of secure lattice-based cryptosystems: lattice problems are an example of NP-hard problems which have been shown to be average-case hard, providing a test case for the security of cryptographic ...
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
A lattice in the sense of a 3-dimensional array of regularly spaced points coinciding with e.g. the atom or molecule positions in a crystal, or more generally, the orbit of a group action under translational symmetry, is a translation of the translation lattice: a coset, which need not contain the origin, and therefore need not be a lattice in ...
Many lattice-based cryptographic schemes are known to be secure assuming the worst-case hardness of certain lattice problems. [ 3 ] [ 6 ] [ 7 ] I.e., if there exists an algorithm that can efficiently break the cryptographic scheme with non-negligible probability, then there exists an efficient algorithm that solves a certain lattice problem on ...
In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice.
The word problem for free bounded lattices is the problem of determining which of these elements of W(X) denote the same element in the free bounded lattice FX, and hence in every bounded lattice. The word problem may be resolved as follows. A relation ≤ ~ on W(X) may be defined inductively by setting w ≤ ~ v if and only if one of the ...
Lattice path of length 5 in ℤ 2 with S = { (2,0), (1,1), (0,-1) }.. In combinatorics, a lattice path L in the d-dimensional integer lattice of length k with steps in the set S, is a sequence of vectors ,, …, such that each consecutive difference lies in S. [1]
In the mathematical study of order, a metric lattice L is a lattice that admits a positive valuation: a function v ∈ L → ℝ satisfying, for any a, b ∈ L, [1] + = + and > > (). Relation to other notions