lattice

A finite set together with a partial ordering on its elements such that for every pair of elements there is a least upper bound and a greatest lower bound.

Example: A lattice is formed by a finite set S of security levels -- i.e., a set S of all ordered pairs (x,c), where x is one of a finite set X of hierarchically ordered classification levels X(1), non-hierarchical categories C(1), ..., C(M) -- together with the "dominate" relation. Security level (x,c) is said to "dominate" (x',c') if and only if (a) x is greater (higher) than or equal to x' and (b) c includes at least all of the elements of c'. (See: dominate, lattice model.)

Tutorial: Lattices are used in some branches of cryptography, both as a basis for hard computational problems upon which cryptographic algorithms can be defined, and also as a basis for attacks on cryptographic algorithms.