Simultaneous reduction of a lattice basis and its reciprocal basis |
| |
Authors: | M Seysen |
| |
Institution: | (1) Scheißheimer Str. 339, D-80809 München, Germany |
| |
Abstract: | Given a latticeL we are looking for a basisB=b
1, ...b
n
] ofL with the property that bothB and the associated basisB
*=b
1
*
, ...,b
n
*
] of the reciprocal latticeL
* consist of short vectors. For any such basisB with reciprocal basisB
* let
. Håstad and Lagarias 7] show that each latticeL of full rank has a basisB withS(B) exp(c
1·n
1/3) for a constantc
1 independent ofn. We improve this upper bound toS(B) exp(c
2·(lnn)2) withc
2 independent ofn.We will also introduce some new kinds of lattice basis reduction and an algorithm to compute one of them. The new algorithm proceeds by reducing the quantity
. In combination with an exhaustive search procedure, one obtains an algorithm to compute the shortest vector and a Korkine-Zolotarev reduced basis of a lattice that is efficient in practice for dimension up to 30. |
| |
Keywords: | 11 H 55 |
本文献已被 SpringerLink 等数据库收录! |
|