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Encyclopedia of Cryptography and Security pp 346–347Cite as

Lattice Reduction

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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. 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 tradeoff between the quality of the basis and the running time.

Interesting lattice bases are called reduced, but there are many different notions of reduction, such as those of Minkowski, Hermite–Korkine–Zolotarev, Lenstra–Lenstra–Lovász, etc. Typically, a reduced basis is made of vectors which are in some sense short, and which are somehow orthogonal. To explain what we mean by short, we need to introduce the so-called successive minima of a lattice.

The intersection of a d-dimensional...

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References

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Authors
  1. Phong Q. Nguyen
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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Henk C. A. van Tilborg

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© 2005 International Federation for Information Processing

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Nguyen, P.Q. (2005). Lattice Reduction. In: van Tilborg, H.C.A. (eds) Encyclopedia of Cryptography and Security. Springer, Boston, MA . https://doi.org/10.1007/0-387-23483-7_226

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