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Among all the bases of a lattice, some are more useful than others. The goal of lattice reduction (also known as lattice basis reduction) is to find interesting bases, such as bases consisting of vectors which are relatively short and almost orthogonal. From a mathematical point of view, one is interested in proving the existence of at least one basis (in an arbitrary lattice) satisfying strong properties. From a computational point of view, one is rather interested in computing such bases in a reasonable time, given an arbitrary basis. In practice, one often has to settle for a trade-off between the quality of the basis and the running time.
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Nguyen, P. (2011). Lattice Reduction. In: van Tilborg, H.C.A., Jajodia, S. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA. https://doi.org/10.1007/978-1-4419-5906-5_457
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