Lattice Basis Reduction
Lattice Basis Reduction is a mathematical technique used to simplify the representation of a lattice, which is a grid-like structure in multidimensional space. By transforming a set of basis vectors into a shorter and more orthogonal set, it makes computations involving the lattice more efficient. This process is particularly useful in areas like cryptography and integer programming.
One of the most well-known algorithms for Lattice Basis Reduction is the Lenstra–Lenstra–Lovász (LLL) algorithm. It reduces the basis vectors while preserving the lattice structure, allowing for easier problem-solving. This technique has applications in computer science, number theory, and optimization.