Short Bases of Lattices over Number Fields

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Short Bases of Lattices over Number Fields
Lattices over number elds arise from a variety of sources in algorithmic algebra and more recently cryptography. Similar to the classical case of Z-lattices, the choice of a nice, short (pseudo)-basis is important in many applications. In this article, we provide the rst algorithm that computes such a short (pseudo)-basis. We utilize the LLL algorithm for Z-lattices together with the Bosma-Pohst-Cohen Hermite Normal Form and some size reduction technique to nd a pseudo-basis where each basis vector belongs to the lattice and the product of the norms of the basis vectors is bounded by the lattice determinant, up to a multiplicative factor that is a eld invariant. As it runs in polynomial time, this provides an eective variant of Minkowski's second theorem for lattices over number elds.
Claus Fieker, Damien Stehlé
Added 15 Aug 2010
Updated 15 Aug 2010
Type Conference
Year 2010
Where ANTS
Authors Claus Fieker, Damien Stehlé
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